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--- Day 19: Tractor Beam ---
Unsure of the state of Santa's ship, you borrowed the tractor beam technology from Triton. Time to test it out.
When you're safely away from anything else, you activate the tractor beam, but nothing happens. It's hard to tell whether it's working if there's nothing to use it on. Fortunately, your ship's drone system can be configured to deploy a drone to specific coordinates and then check whether it's being pulled. There's even an Intcode program (your puzzle input) that gives you access to the drone system.
The program uses two input instructions to request the X and Y position to which the drone should be deployed. Negative numbers are invalid and will confuse the drone; all numbers should be zero or positive.
Then, the program will output whether the drone is stationary (0) or being pulled by something (1). For example, the coordinate X=0, Y=0 is directly in front of the tractor beam emitter, so the drone control program will always report 1 at that location.
To better understand the tractor beam, it is important to get a good picture of the beam itself. For example, suppose you scan the 10x10 grid of points closest to the emitter:
X
0-> 9
0#.........
|.#........
v..##......
...###....
....###...
Y .....####.
......####
......####
.......###
9........##
In this example, the number of points affected by the tractor beam in the 10x10 area closest to the emitter is 27.
However, you'll need to scan a larger area to understand the shape of the beam. How many points are affected by the tractor beam in the 50x50 area closest to the emitter? (For each of X and Y, this will be 0 through 49.)
| 300
|
--- Day 23: Experimental Emergency Teleportation ---
Using your torch to search the darkness of the rocky cavern, you finally locate the man's friend: a small reindeer.
You're not sure how it got so far in this cave. It looks sick - too sick to walk - and too heavy for you to carry all the way back. Sleighs won't be invented for another 1500 years, of course.
The only option is experimental emergency teleportation.
You hit the "experimental emergency teleportation" button on the device and push I accept the risk on no fewer than 18 different warning messages. Immediately, the device deploys hundreds of tiny nanobots which fly around the cavern, apparently assembling themselves into a very specific formation. The device lists the X,Y,Z position (pos) for each nanobot as well as its signal radius (r) on its tiny screen (your puzzle input).
Each nanobot can transmit signals to any integer coordinate which is a distance away from it less than or equal to its signal radius (as measured by Manhattan distance). Coordinates a distance away of less than or equal to a nanobot's signal radius are said to be in range of that nanobot.
Before you start the teleportation process, you should determine which nanobot is the strongest (that is, which has the largest signal radius) and then, for that nanobot, the total number of nanobots that are in range of it, including itself.
For example, given the following nanobots:
pos=<0,0,0>, r=4
pos=<1,0,0>, r=1
pos=<4,0,0>, r=3
pos=<0,2,0>, r=1
pos=<0,5,0>, r=3
pos=<0,0,3>, r=1
pos=<1,1,1>, r=1
pos=<1,1,2>, r=1
pos=<1,3,1>, r=1
The strongest nanobot is the first one (position 0,0,0) because its signal radius, 4 is the largest. Using that nanobot's location and signal radius, the following nanobots are in or out of range:
The nanobot at 0,0,0 is distance 0 away, and so it is in range.
The nanobot at 1,0,0 is distance 1 away, and so it is in range.
The nanobot at 4,0,0 is distance 4 away, and so it is in range.
The nanobot at 0,2,0 is distance 2 away, and so it is in range.
The nanobot at 0,5,0 is distance 5 away, and so it is not in range.
The nanobot at 0,0,3 is distance 3 away, and so it is in range.
The nanobot at 1,1,1 is distance 3 away, and so it is in range.
The nanobot at 1,1,2 is distance 4 away, and so it is in range.
The nanobot at 1,3,1 is distance 5 away, and so it is not in range.
In this example, in total, 7 nanobots are in range of the nanobot with the largest signal radius.
Find the nanobot with the largest signal radius. How many nanobots are in range of its signals?
| 301
|
--- Day 12: Digital Plumber ---
Walking along the memory banks of the stream, you find a small village that is experiencing a little confusion: some programs can't communicate with each other.
Programs in this village communicate using a fixed system of pipes. Messages are passed between programs using these pipes, but most programs aren't connected to each other directly. Instead, programs pass messages between each other until the message reaches the intended recipient.
For some reason, though, some of these messages aren't ever reaching their intended recipient, and the programs suspect that some pipes are missing. They would like you to investigate.
You walk through the village and record the ID of each program and the IDs with which it can communicate directly (your puzzle input). Each program has one or more programs with which it can communicate, and these pipes are bidirectional; if 8 says it can communicate with 11, then 11 will say it can communicate with 8.
You need to figure out how many programs are in the group that contains program ID 0.
For example, suppose you go door-to-door like a travelling salesman and record the following list:
0 <-> 2
1 <-> 1
2 <-> 0, 3, 4
3 <-> 2, 4
4 <-> 2, 3, 6
5 <-> 6
6 <-> 4, 5
In this example, the following programs are in the group that contains program ID 0:
Program 0 by definition.
Program 2, directly connected to program 0.
Program 3 via program 2.
Program 4 via program 2.
Program 5 via programs 6, then 4, then 2.
Program 6 via programs 4, then 2.
Therefore, a total of 6 programs are in this group; all but program 1, which has a pipe that connects it to itself.
How many programs are in the group that contains program ID 0?
| 302
|
--- Day 10: Balance Bots ---
You come upon a factory in which many robots are zooming around handing small microchips to each other.
Upon closer examination, you notice that each bot only proceeds when it has two microchips, and once it does, it gives each one to a different bot or puts it in a marked "output" bin. Sometimes, bots take microchips from "input" bins, too.
Inspecting one of the microchips, it seems like they each contain a single number; the bots must use some logic to decide what to do with each chip. You access the local control computer and download the bots' instructions (your puzzle input).
Some of the instructions specify that a specific-valued microchip should be given to a specific bot; the rest of the instructions indicate what a given bot should do with its lower-value or higher-value chip.
For example, consider the following instructions:
value 5 goes to bot 2
bot 2 gives low to bot 1 and high to bot 0
value 3 goes to bot 1
bot 1 gives low to output 1 and high to bot 0
bot 0 gives low to output 2 and high to output 0
value 2 goes to bot 2
Initially, bot 1 starts with a value-3 chip, and bot 2 starts with a value-2 chip and a value-5 chip.
Because bot 2 has two microchips, it gives its lower one (2) to bot 1 and its higher one (5) to bot 0.
Then, bot 1 has two microchips; it puts the value-2 chip in output 1 and gives the value-3 chip to bot 0.
Finally, bot 0 has two microchips; it puts the 3 in output 2 and the 5 in output 0.
In the end, output bin 0 contains a value-5 microchip, output bin 1 contains a value-2 microchip, and output bin 2 contains a value-3 microchip. In this configuration, bot number 2 is responsible for comparing value-5 microchips with value-2 microchips.
Based on your instructions, what is the number of the bot that is responsible for comparing value-61 microchips with value-17 microchips?
Your puzzle answer was 56.
--- Part Two ---
What do you get if you multiply together the values of one chip in each of outputs 0, 1, and 2?
| 303
|
--- Day 1: No Time for a Taxicab ---
Santa's sleigh uses a very high-precision clock to guide its movements, and the clock's oscillator is regulated by stars. Unfortunately, the stars have been stolen... by the Easter Bunny. To save Christmas, Santa needs you to retrieve all fifty stars by December 25th.
Collect stars by solving puzzles. Two puzzles will be made available on each day in the Advent calendar; the second puzzle is unlocked when you complete the first. Each puzzle grants one star. Good luck!
You're airdropped near Easter Bunny Headquarters in a city somewhere. "Near", unfortunately, is as close as you can get - the instructions on the Easter Bunny Recruiting Document the Elves intercepted start here, and nobody had time to work them out further.
The Document indicates that you should start at the given coordinates (where you just landed) and face North. Then, follow the provided sequence: either turn left (L) or right (R) 90 degrees, then walk forward the given number of blocks, ending at a new intersection.
There's no time to follow such ridiculous instructions on foot, though, so you take a moment and work out the destination. Given that you can only walk on the street grid of the city, how far is the shortest path to the destination?
For example:
Following R2, L3 leaves you 2 blocks East and 3 blocks North, or 5 blocks away.
R2, R2, R2 leaves you 2 blocks due South of your starting position, which is 2 blocks away.
R5, L5, R5, R3 leaves you 12 blocks away.
How many blocks away is Easter Bunny HQ?
Your puzzle answer was 246.
--- Part Two ---
Then, you notice the instructions continue on the back of the Recruiting Document. Easter Bunny HQ is actually at the first location you visit twice.
For example, if your instructions are R8, R4, R4, R8, the first location you visit twice is 4 blocks away, due East.
How many blocks away is the first location you visit twice?
| 304
|
--- Day 24: Planet of Discord ---
You land on Eris, your last stop before reaching Santa. As soon as you do, your sensors start picking up strange life forms moving around: Eris is infested with bugs! With an over 24-hour roundtrip for messages between you and Earth, you'll have to deal with this problem on your own.
Eris isn't a very large place; a scan of the entire area fits into a 5x5 grid (your puzzle input). The scan shows bugs (#) and empty spaces (.).
Each minute, The bugs live and die based on the number of bugs in the four adjacent tiles:
A bug dies (becoming an empty space) unless there is exactly one bug adjacent to it.
An empty space becomes infested with a bug if exactly one or two bugs are adjacent to it.
Otherwise, a bug or empty space remains the same. (Tiles on the edges of the grid have fewer than four adjacent tiles; the missing tiles count as empty space.) This process happens in every location simultaneously; that is, within the same minute, the number of adjacent bugs is counted for every tile first, and then the tiles are updated.
Here are the first few minutes of an example scenario:
Initial state:
....#
#..#.
#..##
..#..
#....
After 1 minute:
#..#.
####.
###.#
##.##
.##..
After 2 minutes:
#####
....#
....#
...#.
#.###
After 3 minutes:
#....
####.
...##
#.##.
.##.#
After 4 minutes:
####.
....#
##..#
.....
##...
To understand the nature of the bugs, watch for the first time a layout of bugs and empty spaces matches any previous layout. In the example above, the first layout to appear twice is:
.....
.....
.....
#....
.#...
To calculate the biodiversity rating for this layout, consider each tile left-to-right in the top row, then left-to-right in the second row, and so on. Each of these tiles is worth biodiversity points equal to increasing powers of two: 1, 2, 4, 8, 16, 32, and so on. Add up the biodiversity points for tiles with bugs; in this example, the 16th tile (32768 points) and 22nd tile (2097152 points) have bugs, a total biodiversity rating of 2129920.
What is the biodiversity rating for the first layout that appears twice?
| 305
|
--- Day 1: Trebuchet?! ---
Something is wrong with global snow production, and you've been selected to take a look. The Elves have even given you a map; on it, they've used stars to mark the top fifty locations that are likely to be having problems.
You've been doing this long enough to know that to restore snow operations, you need to check all fifty stars by December 25th.
Collect stars by solving puzzles. Two puzzles will be made available on each day in the Advent calendar; the second puzzle is unlocked when you complete the first. Each puzzle grants one star. Good luck!
You try to ask why they can't just use a weather machine ("not powerful enough") and where they're even sending you ("the sky") and why your map looks mostly blank ("you sure ask a lot of questions") and hang on did you just say the sky ("of course, where do you think snow comes from") when you realize that the Elves are already loading you into a trebuchet ("please hold still, we need to strap you in").
As they're making the final adjustments, they discover that their calibration document (your puzzle input) has been amended by a very young Elf who was apparently just excited to show off her art skills. Consequently, the Elves are having trouble reading the values on the document.
The newly-improved calibration document consists of lines of text; each line originally contained a specific calibration value that the Elves now need to recover. On each line, the calibration value can be found by combining the first digit and the last digit (in that order) to form a single two-digit number.
For example:
1abc2
pqr3stu8vwx
a1b2c3d4e5f
treb7uchet
In this example, the calibration values of these four lines are 12, 38, 15, and 77. Adding these together produces 142.
Consider your entire calibration document. What is the sum of all of the calibration values?
Your puzzle answer was 54331.
--- Part Two ---
Your calculation isn't quite right. It looks like some of the digits are actually spelled out with letters: one, two, three, four, five, six, seven, eight, and nine also count as valid "digits".
Equipped with this new information, you now need to find the real first and last digit on each line. For example:
two1nine
eightwothree
abcone2threexyz
xtwone3four
4nineeightseven2
zoneight234
7pqrstsixteen
In this example, the calibration values are 29, 83, 13, 24, 42, 14, and 76. Adding these together produces 281.
What is the sum of all of the calibration values?
| 306
|
--- Day 20: Jurassic Jigsaw ---
The high-speed train leaves the forest and quickly carries you south. You can even see a desert in the distance! Since you have some spare time, you might as well see if there was anything interesting in the image the Mythical Information Bureau satellite captured.
After decoding the satellite messages, you discover that the data actually contains many small images created by the satellite's camera array. The camera array consists of many cameras; rather than produce a single square image, they produce many smaller square image tiles that need to be reassembled back into a single image.
Each camera in the camera array returns a single monochrome image tile with a random unique ID number. The tiles (your puzzle input) arrived in a random order.
Worse yet, the camera array appears to be malfunctioning: each image tile has been rotated and flipped to a random orientation. Your first task is to reassemble the original image by orienting the tiles so they fit together.
To show how the tiles should be reassembled, each tile's image data includes a border that should line up exactly with its adjacent tiles. All tiles have this border, and the border lines up exactly when the tiles are both oriented correctly. Tiles at the edge of the image also have this border, but the outermost edges won't line up with any other tiles.
For example, suppose you have the following nine tiles:
Tile 2311:
..##.#..#.
##..#.....
#...##..#.
####.#...#
##.##.###.
##...#.###
.#.#.#..##
..#....#..
###...#.#.
..###..###
Tile 1951:
#.##...##.
#.####...#
.....#..##
#...######
.##.#....#
.###.#####
###.##.##.
.###....#.
..#.#..#.#
#...##.#..
Tile 1171:
####...##.
#..##.#..#
##.#..#.#.
.###.####.
..###.####
.##....##.
.#...####.
#.##.####.
####..#...
.....##...
Tile 1427:
###.##.#..
.#..#.##..
.#.##.#..#
#.#.#.##.#
....#...##
...##..##.
...#.#####
.#.####.#.
..#..###.#
..##.#..#.
Tile 1489:
##.#.#....
..##...#..
.##..##...
..#...#...
#####...#.
#..#.#.#.#
...#.#.#..
##.#...##.
..##.##.##
###.##.#..
Tile 2473:
#....####.
#..#.##...
#.##..#...
######.#.#
.#...#.#.#
.#########
.###.#..#.
########.#
##...##.#.
..###.#.#.
Tile 2971:
..#.#....#
#...###...
#.#.###...
##.##..#..
.#####..##
.#..####.#
#..#.#..#.
..####.###
..#.#.###.
...#.#.#.#
Tile 2729:
...#.#.#.#
####.#....
..#.#.....
....#..#.#
.##..##.#.
.#.####...
####.#.#..
##.####...
##..#.##..
#.##...##.
Tile 3079:
#.#.#####.
.#..######
..#.......
######....
####.#..#.
.#...#.##.
#.#####.##
..#.###...
..#.......
..#.###...
By rotating, flipping, and rearranging them, you can find a square arrangement that causes all adjacent borders to line up:
#...##.#.. ..###..### #.#.#####.
..#.#..#.# ###...#.#. .#..######
.###....#. ..#....#.. ..#.......
###.##.##. .#.#.#..## ######....
.###.##### ##...#.### ####.#..#.
.##.#....# ##.##.###. .#...#.##.
#...###### ####.#...# #.#####.##
.....#..## #...##..#. ..#.###...
#.####...# ##..#..... ..#.......
#.##...##. ..##.#..#. ..#.###...
#.##...##. ..##.#..#. ..#.###...
##..#.##.. ..#..###.# ##.##....#
##.####... .#.####.#. ..#.###..#
####.#.#.. ...#.##### ###.#..###
.#.####... ...##..##. .######.##
.##..##.#. ....#...## #.#.#.#...
....#..#.# #.#.#.##.# #.###.###.
..#.#..... .#.##.#..# #.###.##..
####.#.... .#..#.##.. .######...
...#.#.#.# ###.##.#.. .##...####
...#.#.#.# ###.##.#.. .##...####
..#.#.###. ..##.##.## #..#.##..#
..####.### ##.#...##. .#.#..#.##
#..#.#..#. ...#.#.#.. .####.###.
.#..####.# #..#.#.#.# ####.###..
.#####..## #####...#. .##....##.
##.##..#.. ..#...#... .####...#.
#.#.###... .##..##... .####.##.#
#...###... ..##...#.. ...#..####
..#.#....# ##.#.#.... ...##.....
For reference, the IDs of the above tiles are:
1951 2311 3079
2729 1427 2473
2971 1489 1171
To check that you've assembled the image correctly, multiply the IDs of the four corner tiles together. If you do this with the assembled tiles from the example above, you get 1951 * 3079 * 2971 * 1171 = 20899048083289.
Assemble the tiles into an image. What do you get if you multiply together the IDs of the four corner tiles?
| 307
|
--- Day 18: Duet ---
You discover a tablet containing some strange assembly code labeled simply "Duet". Rather than bother the sound card with it, you decide to run the code yourself. Unfortunately, you don't see any documentation, so you're left to figure out what the instructions mean on your own.
It seems like the assembly is meant to operate on a set of registers that are each named with a single letter and that can each hold a single integer. You suppose each register should start with a value of 0.
There aren't that many instructions, so it shouldn't be hard to figure out what they do. Here's what you determine:
snd X plays a sound with a frequency equal to the value of X.
set X Y sets register X to the value of Y.
add X Y increases register X by the value of Y.
mul X Y sets register X to the result of multiplying the value contained in register X by the value of Y.
mod X Y sets register X to the remainder of dividing the value contained in register X by the value of Y (that is, it sets X to the result of X modulo Y).
rcv X recovers the frequency of the last sound played, but only when the value of X is not zero. (If it is zero, the command does nothing.)
jgz X Y jumps with an offset of the value of Y, but only if the value of X is greater than zero. (An offset of 2 skips the next instruction, an offset of -1 jumps to the previous instruction, and so on.)
Many of the instructions can take either a register (a single letter) or a number. The value of a register is the integer it contains; the value of a number is that number.
After each jump instruction, the program continues with the instruction to which the jump jumped. After any other instruction, the program continues with the next instruction. Continuing (or jumping) off either end of the program terminates it.
For example:
set a 1
add a 2
mul a a
mod a 5
snd a
set a 0
rcv a
jgz a -1
set a 1
jgz a -2
The first four instructions set a to 1, add 2 to it, square it, and then set it to itself modulo 5, resulting in a value of 4.
Then, a sound with frequency 4 (the value of a) is played.
After that, a is set to 0, causing the subsequent rcv and jgz instructions to both be skipped (rcv because a is 0, and jgz because a is not greater than 0).
Finally, a is set to 1, causing the next jgz instruction to activate, jumping back two instructions to another jump, which jumps again to the rcv, which ultimately triggers the recover operation.
At the time the recover operation is executed, the frequency of the last sound played is 4.
What is the value of the recovered frequency (the value of the most recently played sound) the first time a rcv instruction is executed with a non-zero value?
| 308
|
--- Day 5: Alchemical Reduction ---
You've managed to sneak in to the prototype suit manufacturing lab. The Elves are making decent progress, but are still struggling with the suit's size reduction capabilities.
While the very latest in 1518 alchemical technology might have solved their problem eventually, you can do better. You scan the chemical composition of the suit's material and discover that it is formed by extremely long polymers (one of which is available as your puzzle input).
The polymer is formed by smaller units which, when triggered, react with each other such that two adjacent units of the same type and opposite polarity are destroyed. Units' types are represented by letters; units' polarity is represented by capitalization. For instance, r and R are units with the same type but opposite polarity, whereas r and s are entirely different types and do not react.
For example:
In aA, a and A react, leaving nothing behind.
In abBA, bB destroys itself, leaving aA. As above, this then destroys itself, leaving nothing.
In abAB, no two adjacent units are of the same type, and so nothing happens.
In aabAAB, even though aa and AA are of the same type, their polarities match, and so nothing happens.
Now, consider a larger example, dabAcCaCBAcCcaDA:
dabAcCaCBAcCcaDA The first 'cC' is removed.
dabAaCBAcCcaDA This creates 'Aa', which is removed.
dabCBAcCcaDA Either 'cC' or 'Cc' are removed (the result is the same).
dabCBAcaDA No further actions can be taken.
After all possible reactions, the resulting polymer contains 10 units.
How many units remain after fully reacting the polymer you scanned? (Note: in this puzzle and others, the input is large; if you copy/paste your input, make sure you get the whole thing.)
| 309
|
--- Day 3: Squares With Three Sides ---
Now that you can think clearly, you move deeper into the labyrinth of hallways and office furniture that makes up this part of Easter Bunny HQ. This must be a graphic design department; the walls are covered in specifications for triangles.
Or are they?
The design document gives the side lengths of each triangle it describes, but... 5 10 25? Some of these aren't triangles. You can't help but mark the impossible ones.
In a valid triangle, the sum of any two sides must be larger than the remaining side. For example, the "triangle" given above is impossible, because 5 + 10 is not larger than 25.
In your puzzle input, how many of the listed triangles are possible?
| 310
|
--- Day 2: Inventory Management System ---
You stop falling through time, catch your breath, and check the screen on the device. "Destination reached. Current Year: 1518. Current Location: North Pole Utility Closet 83N10." You made it! Now, to find those anomalies.
Outside the utility closet, you hear footsteps and a voice. "...I'm not sure either. But now that so many people have chimneys, maybe he could sneak in that way?" Another voice responds, "Actually, we've been working on a new kind of suit that would let him fit through tight spaces like that. But, I heard that a few days ago, they lost the prototype fabric, the design plans, everything! Nobody on the team can even seem to remember important details of the project!"
"Wouldn't they have had enough fabric to fill several boxes in the warehouse? They'd be stored together, so the box IDs should be similar. Too bad it would take forever to search the warehouse for two similar box IDs..." They walk too far away to hear any more.
Late at night, you sneak to the warehouse - who knows what kinds of paradoxes you could cause if you were discovered - and use your fancy wrist device to quickly scan every box and produce a list of the likely candidates (your puzzle input).
To make sure you didn't miss any, you scan the likely candidate boxes again, counting the number that have an ID containing exactly two of any letter and then separately counting those with exactly three of any letter. You can multiply those two counts together to get a rudimentary checksum and compare it to what your device predicts.
For example, if you see the following box IDs:
abcdef contains no letters that appear exactly two or three times.
bababc contains two a and three b, so it counts for both.
abbcde contains two b, but no letter appears exactly three times.
abcccd contains three c, but no letter appears exactly two times.
aabcdd contains two a and two d, but it only counts once.
abcdee contains two e.
ababab contains three a and three b, but it only counts once.
Of these box IDs, four of them contain a letter which appears exactly twice, and three of them contain a letter which appears exactly three times. Multiplying these together produces a checksum of 4 * 3 = 12.
What is the checksum for your list of box IDs?
Your puzzle answer was 3952.
--- Part Two ---
Confident that your list of box IDs is complete, you're ready to find the boxes full of prototype fabric.
The boxes will have IDs which differ by exactly one character at the same position in both strings. For example, given the following box IDs:
abcde
fghij
klmno
pqrst
fguij
axcye
wvxyz
The IDs abcde and axcye are close, but they differ by two characters (the second and fourth). However, the IDs fghij and fguij differ by exactly one character, the third (h and u). Those must be the correct boxes.
What letters are common between the two correct box IDs? (In the example above, this is found by removing the differing character from either ID, producing fgij.)
| 311
|
--- Day 9: Smoke Basin ---
These caves seem to be lava tubes. Parts are even still volcanically active; small hydrothermal vents release smoke into the caves that slowly settles like rain.
If you can model how the smoke flows through the caves, you might be able to avoid it and be that much safer. The submarine generates a heightmap of the floor of the nearby caves for you (your puzzle input).
Smoke flows to the lowest point of the area it's in. For example, consider the following heightmap:
2199943210
3987894921
9856789892
8767896789
9899965678
Each number corresponds to the height of a particular location, where 9 is the highest and 0 is the lowest a location can be.
Your first goal is to find the low points - the locations that are lower than any of its adjacent locations. Most locations have four adjacent locations (up, down, left, and right); locations on the edge or corner of the map have three or two adjacent locations, respectively. (Diagonal locations do not count as adjacent.)
In the above example, there are four low points, all highlighted: two are in the first row (a 1 and a 0), one is in the third row (a 5), and one is in the bottom row (also a 5). All other locations on the heightmap have some lower adjacent location, and so are not low points.
The risk level of a low point is 1 plus its height. In the above example, the risk levels of the low points are 2, 1, 6, and 6. The sum of the risk levels of all low points in the heightmap is therefore 15.
Find all of the low points on your heightmap. What is the sum of the risk levels of all low points on your heightmap?
| 312
|
--- Day 7: Amplification Circuit ---
Based on the navigational maps, you're going to need to send more power to your ship's thrusters to reach Santa in time. To do this, you'll need to configure a series of amplifiers already installed on the ship.
There are five amplifiers connected in series; each one receives an input signal and produces an output signal. They are connected such that the first amplifier's output leads to the second amplifier's input, the second amplifier's output leads to the third amplifier's input, and so on. The first amplifier's input value is 0, and the last amplifier's output leads to your ship's thrusters.
O-------O O-------O O-------O O-------O O-------O
0 ->| Amp A |->| Amp B |->| Amp C |->| Amp D |->| Amp E |-> (to thrusters)
O-------O O-------O O-------O O-------O O-------O
The Elves have sent you some Amplifier Controller Software (your puzzle input), a program that should run on your existing Intcode computer. Each amplifier will need to run a copy of the program.
When a copy of the program starts running on an amplifier, it will first use an input instruction to ask the amplifier for its current phase setting (an integer from 0 to 4). Each phase setting is used exactly once, but the Elves can't remember which amplifier needs which phase setting.
The program will then call another input instruction to get the amplifier's input signal, compute the correct output signal, and supply it back to the amplifier with an output instruction. (If the amplifier has not yet received an input signal, it waits until one arrives.)
Your job is to find the largest output signal that can be sent to the thrusters by trying every possible combination of phase settings on the amplifiers. Make sure that memory is not shared or reused between copies of the program.
For example, suppose you want to try the phase setting sequence 3,1,2,4,0, which would mean setting amplifier A to phase setting 3, amplifier B to setting 1, C to 2, D to 4, and E to 0. Then, you could determine the output signal that gets sent from amplifier E to the thrusters with the following steps:
Start the copy of the amplifier controller software that will run on amplifier A. At its first input instruction, provide it the amplifier's phase setting, 3. At its second input instruction, provide it the input signal, 0. After some calculations, it will use an output instruction to indicate the amplifier's output signal.
Start the software for amplifier B. Provide it the phase setting (1) and then whatever output signal was produced from amplifier A. It will then produce a new output signal destined for amplifier C.
Start the software for amplifier C, provide the phase setting (2) and the value from amplifier B, then collect its output signal.
Run amplifier D's software, provide the phase setting (4) and input value, and collect its output signal.
Run amplifier E's software, provide the phase setting (0) and input value, and collect its output signal.
The final output signal from amplifier E would be sent to the thrusters. However, this phase setting sequence may not have been the best one; another sequence might have sent a higher signal to the thrusters.
Here are some example programs:
Max thruster signal 43210 (from phase setting sequence 4,3,2,1,0):
3,15,3,16,1002,16,10,16,1,16,15,15,4,15,99,0,0
Max thruster signal 54321 (from phase setting sequence 0,1,2,3,4):
3,23,3,24,1002,24,10,24,1002,23,-1,23,
101,5,23,23,1,24,23,23,4,23,99,0,0
Max thruster signal 65210 (from phase setting sequence 1,0,4,3,2):
3,31,3,32,1002,32,10,32,1001,31,-2,31,1007,31,0,33,
1002,33,7,33,1,33,31,31,1,32,31,31,4,31,99,0,0,0
Try every combination of phase settings on the amplifiers. What is the highest signal that can be sent to the thrusters?
Your puzzle answer was 255590.
--- Part Two ---
It's no good - in this configuration, the amplifiers can't generate a large enough output signal to produce the thrust you'll need. The Elves quickly talk you through rewiring the amplifiers into a feedback loop:
O-------O O-------O O-------O O-------O O-------O
0 -+->| Amp A |->| Amp B |->| Amp C |->| Amp D |->| Amp E |-.
| O-------O O-------O O-------O O-------O O-------O |
| |
'--------------------------------------------------------+
|
v
(to thrusters)
Most of the amplifiers are connected as they were before; amplifier A's output is connected to amplifier B's input, and so on. However, the output from amplifier E is now connected into amplifier A's input. This creates the feedback loop: the signal will be sent through the amplifiers many times.
In feedback loop mode, the amplifiers need totally different phase settings: integers from 5 to 9, again each used exactly once. These settings will cause the Amplifier Controller Software to repeatedly take input and produce output many times before halting. Provide each amplifier its phase setting at its first input instruction; all further input/output instructions are for signals.
Don't restart the Amplifier Controller Software on any amplifier during this process. Each one should continue receiving and sending signals until it halts.
All signals sent or received in this process will be between pairs of amplifiers except the very first signal and the very last signal. To start the process, a 0 signal is sent to amplifier A's input exactly once.
Eventually, the software on the amplifiers will halt after they have processed the final loop. When this happens, the last output signal from amplifier E is sent to the thrusters. Your job is to find the largest output signal that can be sent to the thrusters using the new phase settings and feedback loop arrangement.
Here are some example programs:
Max thruster signal 139629729 (from phase setting sequence 9,8,7,6,5):
3,26,1001,26,-4,26,3,27,1002,27,2,27,1,27,26,
27,4,27,1001,28,-1,28,1005,28,6,99,0,0,5
Max thruster signal 18216 (from phase setting sequence 9,7,8,5,6):
3,52,1001,52,-5,52,3,53,1,52,56,54,1007,54,5,55,1005,55,26,1001,54,
-5,54,1105,1,12,1,53,54,53,1008,54,0,55,1001,55,1,55,2,53,55,53,4,
53,1001,56,-1,56,1005,56,6,99,0,0,0,0,10
Try every combination of the new phase settings on the amplifier feedback loop. What is the highest signal that can be sent to the thrusters?
| 313
|
--- Day 4: Giant Squid ---
You're already almost 1.5km (almost a mile) below the surface of the ocean, already so deep that you can't see any sunlight. What you can see, however, is a giant squid that has attached itself to the outside of your submarine.
Maybe it wants to play bingo?
Bingo is played on a set of boards each consisting of a 5x5 grid of numbers. Numbers are chosen at random, and the chosen number is marked on all boards on which it appears. (Numbers may not appear on all boards.) If all numbers in any row or any column of a board are marked, that board wins. (Diagonals don't count.)
The submarine has a bingo subsystem to help passengers (currently, you and the giant squid) pass the time. It automatically generates a random order in which to draw numbers and a random set of boards (your puzzle input). For example:
7,4,9,5,11,17,23,2,0,14,21,24,10,16,13,6,15,25,12,22,18,20,8,19,3,26,1
22 13 17 11 0
8 2 23 4 24
21 9 14 16 7
6 10 3 18 5
1 12 20 15 19
3 15 0 2 22
9 18 13 17 5
19 8 7 25 23
20 11 10 24 4
14 21 16 12 6
14 21 17 24 4
10 16 15 9 19
18 8 23 26 20
22 11 13 6 5
2 0 12 3 7
After the first five numbers are drawn (7, 4, 9, 5, and 11), there are no winners, but the boards are marked as follows (shown here adjacent to each other to save space):
22 13 17 11 0 3 15 0 2 22 14 21 17 24 4
8 2 23 4 24 9 18 13 17 5 10 16 15 9 19
21 9 14 16 7 19 8 7 25 23 18 8 23 26 20
6 10 3 18 5 20 11 10 24 4 22 11 13 6 5
1 12 20 15 19 14 21 16 12 6 2 0 12 3 7
After the next six numbers are drawn (17, 23, 2, 0, 14, and 21), there are still no winners:
22 13 17 11 0 3 15 0 2 22 14 21 17 24 4
8 2 23 4 24 9 18 13 17 5 10 16 15 9 19
21 9 14 16 7 19 8 7 25 23 18 8 23 26 20
6 10 3 18 5 20 11 10 24 4 22 11 13 6 5
1 12 20 15 19 14 21 16 12 6 2 0 12 3 7
Finally, 24 is drawn:
22 13 17 11 0 3 15 0 2 22 14 21 17 24 4
8 2 23 4 24 9 18 13 17 5 10 16 15 9 19
21 9 14 16 7 19 8 7 25 23 18 8 23 26 20
6 10 3 18 5 20 11 10 24 4 22 11 13 6 5
1 12 20 15 19 14 21 16 12 6 2 0 12 3 7
At this point, the third board wins because it has at least one complete row or column of marked numbers (in this case, the entire top row is marked: 14 21 17 24 4).
The score of the winning board can now be calculated. Start by finding the sum of all unmarked numbers on that board; in this case, the sum is 188. Then, multiply that sum by the number that was just called when the board won, 24, to get the final score, 188 * 24 = 4512.
To guarantee victory against the giant squid, figure out which board will win first. What will your final score be if you choose that board?
| 314
|
--- Day 20: Race Condition ---
The Historians are quite pixelated again. This time, a massive, black building looms over you - you're right outside the CPU!
While The Historians get to work, a nearby program sees that you're idle and challenges you to a race. Apparently, you've arrived just in time for the frequently-held race condition festival!
The race takes place on a particularly long and twisting code path; programs compete to see who can finish in the fewest picoseconds. The winner even gets their very own mutex!
They hand you a map of the racetrack (your puzzle input). For example:
###############
#...#...#.....#
#.#.#.#.#.###.#
#S#...#.#.#...#
#######.#.#.###
#######.#.#...#
#######.#.###.#
###..E#...#...#
###.#######.###
#...###...#...#
#.#####.#.###.#
#.#...#.#.#...#
#.#.#.#.#.#.###
#...#...#...###
###############
The map consists of track (.) - including the start (S) and end (E) positions (both of which also count as track) - and walls (#).
When a program runs through the racetrack, it starts at the start position. Then, it is allowed to move up, down, left, or right; each such move takes 1 picosecond. The goal is to reach the end position as quickly as possible. In this example racetrack, the fastest time is 84 picoseconds.
Because there is only a single path from the start to the end and the programs all go the same speed, the races used to be pretty boring. To make things more interesting, they introduced a new rule to the races: programs are allowed to cheat.
The rules for cheating are very strict. Exactly once during a race, a program may disable collision for up to 2 picoseconds. This allows the program to pass through walls as if they were regular track. At the end of the cheat, the program must be back on normal track again; otherwise, it will receive a segmentation fault and get disqualified.
So, a program could complete the course in 72 picoseconds (saving 12 picoseconds) by cheating for the two moves marked 1 and 2:
###############
#...#...12....#
#.#.#.#.#.###.#
#S#...#.#.#...#
#######.#.#.###
#######.#.#...#
#######.#.###.#
###..E#...#...#
###.#######.###
#...###...#...#
#.#####.#.###.#
#.#...#.#.#...#
#.#.#.#.#.#.###
#...#...#...###
###############
Or, a program could complete the course in 64 picoseconds (saving 20 picoseconds) by cheating for the two moves marked 1 and 2:
###############
#...#...#.....#
#.#.#.#.#.###.#
#S#...#.#.#...#
#######.#.#.###
#######.#.#...#
#######.#.###.#
###..E#...12..#
###.#######.###
#...###...#...#
#.#####.#.###.#
#.#...#.#.#...#
#.#.#.#.#.#.###
#...#...#...###
###############
This cheat saves 38 picoseconds:
###############
#...#...#.....#
#.#.#.#.#.###.#
#S#...#.#.#...#
#######.#.#.###
#######.#.#...#
#######.#.###.#
###..E#...#...#
###.####1##.###
#...###.2.#...#
#.#####.#.###.#
#.#...#.#.#...#
#.#.#.#.#.#.###
#...#...#...###
###############
This cheat saves 64 picoseconds and takes the program directly to the end:
###############
#...#...#.....#
#.#.#.#.#.###.#
#S#...#.#.#...#
#######.#.#.###
#######.#.#...#
#######.#.###.#
###..21...#...#
###.#######.###
#...###...#...#
#.#####.#.###.#
#.#...#.#.#...#
#.#.#.#.#.#.###
#...#...#...###
###############
Each cheat has a distinct start position (the position where the cheat is activated, just before the first move that is allowed to go through walls) and end position; cheats are uniquely identified by their start position and end position.
In this example, the total number of cheats (grouped by the amount of time they save) are as follows:
There are 14 cheats that save 2 picoseconds.
There are 14 cheats that save 4 picoseconds.
There are 2 cheats that save 6 picoseconds.
There are 4 cheats that save 8 picoseconds.
There are 2 cheats that save 10 picoseconds.
There are 3 cheats that save 12 picoseconds.
There is one cheat that saves 20 picoseconds.
There is one cheat that saves 36 picoseconds.
There is one cheat that saves 38 picoseconds.
There is one cheat that saves 40 picoseconds.
There is one cheat that saves 64 picoseconds.
You aren't sure what the conditions of the racetrack will be like, so to give yourself as many options as possible, you'll need a list of the best cheats. How many cheats would save you at least 100 picoseconds?
| 315
|
--- Day 8: Matchsticks ---
Space on the sleigh is limited this year, and so Santa will be bringing his list as a digital copy. He needs to know how much space it will take up when stored.
It is common in many programming languages to provide a way to escape special characters in strings. For example, C, JavaScript, Perl, Python, and even PHP handle special characters in very similar ways.
However, it is important to realize the difference between the number of characters in the code representation of the string literal and the number of characters in the in-memory string itself.
For example:
"" is 2 characters of code (the two double quotes), but the string contains zero characters.
"abc" is 5 characters of code, but 3 characters in the string data.
"aaa\"aaa" is 10 characters of code, but the string itself contains six "a" characters and a single, escaped quote character, for a total of 7 characters in the string data.
"\x27" is 6 characters of code, but the string itself contains just one - an apostrophe ('), escaped using hexadecimal notation.
Santa's list is a file that contains many double-quoted string literals, one on each line. The only escape sequences used are \\ (which represents a single backslash), \" (which represents a lone double-quote character), and \x plus two hexadecimal characters (which represents a single character with that ASCII code).
Disregarding the whitespace in the file, what is the number of characters of code for string literals minus the number of characters in memory for the values of the strings in total for the entire file?
For example, given the four strings above, the total number of characters of string code (2 + 5 + 10 + 6 = 23) minus the total number of characters in memory for string values (0 + 3 + 7 + 1 = 11) is 23 - 11 = 12.
Your puzzle answer was 1342.
--- Part Two ---
Now, let's go the other way. In addition to finding the number of characters of code, you should now encode each code representation as a new string and find the number of characters of the new encoded representation, including the surrounding double quotes.
For example:
"" encodes to "\"\"", an increase from 2 characters to 6.
"abc" encodes to "\"abc\"", an increase from 5 characters to 9.
"aaa\"aaa" encodes to "\"aaa\\\"aaa\"", an increase from 10 characters to 16.
"\x27" encodes to "\"\\x27\"", an increase from 6 characters to 11.
Your task is to find the total number of characters to represent the newly encoded strings minus the number of characters of code in each original string literal. For example, for the strings above, the total encoded length (6 + 9 + 16 + 11 = 42) minus the characters in the original code representation (23, just like in the first part of this puzzle) is 42 - 23 = 19.
| 316
|
--- Day 5: Binary Boarding ---
You board your plane only to discover a new problem: you dropped your boarding pass! You aren't sure which seat is yours, and all of the flight attendants are busy with the flood of people that suddenly made it through passport control.
You write a quick program to use your phone's camera to scan all of the nearby boarding passes (your puzzle input); perhaps you can find your seat through process of elimination.
Instead of zones or groups, this airline uses binary space partitioning to seat people. A seat might be specified like FBFBBFFRLR, where F means "front", B means "back", L means "left", and R means "right".
The first 7 characters will either be F or B; these specify exactly one of the 128 rows on the plane (numbered 0 through 127). Each letter tells you which half of a region the given seat is in. Start with the whole list of rows; the first letter indicates whether the seat is in the front (0 through 63) or the back (64 through 127). The next letter indicates which half of that region the seat is in, and so on until you're left with exactly one row.
For example, consider just the first seven characters of FBFBBFFRLR:
Start by considering the whole range, rows 0 through 127.
F means to take the lower half, keeping rows 0 through 63.
B means to take the upper half, keeping rows 32 through 63.
F means to take the lower half, keeping rows 32 through 47.
B means to take the upper half, keeping rows 40 through 47.
B keeps rows 44 through 47.
F keeps rows 44 through 45.
The final F keeps the lower of the two, row 44.
The last three characters will be either L or R; these specify exactly one of the 8 columns of seats on the plane (numbered 0 through 7). The same process as above proceeds again, this time with only three steps. L means to keep the lower half, while R means to keep the upper half.
For example, consider just the last 3 characters of FBFBBFFRLR:
Start by considering the whole range, columns 0 through 7.
R means to take the upper half, keeping columns 4 through 7.
L means to take the lower half, keeping columns 4 through 5.
The final R keeps the upper of the two, column 5.
So, decoding FBFBBFFRLR reveals that it is the seat at row 44, column 5.
Every seat also has a unique seat ID: multiply the row by 8, then add the column. In this example, the seat has ID 44 * 8 + 5 = 357.
Here are some other boarding passes:
BFFFBBFRRR: row 70, column 7, seat ID 567.
FFFBBBFRRR: row 14, column 7, seat ID 119.
BBFFBBFRLL: row 102, column 4, seat ID 820.
As a sanity check, look through your list of boarding passes. What is the highest seat ID on a boarding pass?
| 317
|
--- Day 25: Full of Hot Air ---
As the expedition finally reaches the extraction point, several large hot air balloons drift down to meet you. Crews quickly start unloading the equipment the balloons brought: many hot air balloon kits, some fuel tanks, and a fuel heating machine.
The fuel heating machine is a new addition to the process. When this mountain was a volcano, the ambient temperature was more reasonable; now, it's so cold that the fuel won't work at all without being warmed up first.
The Elves, seemingly in an attempt to make the new machine feel welcome, have already attached a pair of googly eyes and started calling it "Bob".
To heat the fuel, Bob needs to know the total amount of fuel that will be processed ahead of time so it can correctly calibrate heat output and flow rate. This amount is simply the sum of the fuel requirements of all of the hot air balloons, and those fuel requirements are even listed clearly on the side of each hot air balloon's burner.
You assume the Elves will have no trouble adding up some numbers and are about to go back to figuring out which balloon is yours when you get a tap on the shoulder. Apparently, the fuel requirements use numbers written in a format the Elves don't recognize; predictably, they'd like your help deciphering them.
You make a list of all of the fuel requirements (your puzzle input), but you don't recognize the number format either. For example:
1=-0-2
12111
2=0=
21
2=01
111
20012
112
1=-1=
1-12
12
1=
122
Fortunately, Bob is labeled with a support phone number. Not to be deterred, you call and ask for help.
"That's right, just supply the fuel amount to the-- oh, for more than one burner? No problem, you just need to add together our Special Numeral-Analogue Fuel Units. Patent pending! They're way better than normal numbers for--"
You mention that it's quite cold up here and ask if they can skip ahead.
"Okay, our Special Numeral-Analogue Fuel Units - SNAFU for short - are sort of like normal numbers. You know how starting on the right, normal numbers have a ones place, a tens place, a hundreds place, and so on, where the digit in each place tells you how many of that value you have?"
"SNAFU works the same way, except it uses powers of five instead of ten. Starting from the right, you have a ones place, a fives place, a twenty-fives place, a one-hundred-and-twenty-fives place, and so on. It's that easy!"
You ask why some of the digits look like - or = instead of "digits".
"You know, I never did ask the engineers why they did that. Instead of using digits four through zero, the digits are 2, 1, 0, minus (written -), and double-minus (written =). Minus is worth -1, and double-minus is worth -2."
"So, because ten (in normal numbers) is two fives and no ones, in SNAFU it is written 20. Since eight (in normal numbers) is two fives minus two ones, it is written 2=."
"You can do it the other direction, too. Say you have the SNAFU number 2=-01. That's 2 in the 625s place, = (double-minus) in the 125s place, - (minus) in the 25s place, 0 in the 5s place, and 1 in the 1s place. (2 times 625) plus (-2 times 125) plus (-1 times 25) plus (0 times 5) plus (1 times 1). That's 1250 plus -250 plus -25 plus 0 plus 1. 976!"
"I see here that you're connected via our premium uplink service, so I'll transmit our handy SNAFU brochure to you now. Did you need anything else?"
You ask if the fuel will even work in these temperatures.
"Wait, it's how cold? There's no way the fuel - or any fuel - would work in those conditions! There are only a few places in the-- where did you say you are again?"
Just then, you notice one of the Elves pour a few drops from a snowflake-shaped container into one of the fuel tanks, thank the support representative for their time, and disconnect the call.
The SNAFU brochure contains a few more examples of decimal ("normal") numbers and their SNAFU counterparts:
Decimal SNAFU
1 1
2 2
3 1=
4 1-
5 10
6 11
7 12
8 2=
9 2-
10 20
15 1=0
20 1-0
2022 1=11-2
12345 1-0---0
314159265 1121-1110-1=0
Based on this process, the SNAFU numbers in the example above can be converted to decimal numbers as follows:
SNAFU Decimal
1=-0-2 1747
12111 906
2=0= 198
21 11
2=01 201
111 31
20012 1257
112 32
1=-1= 353
1-12 107
12 7
1= 3
122 37
In decimal, the sum of these numbers is 4890.
As you go to input this number on Bob's console, you discover that some buttons you expected are missing. Instead, you are met with buttons labeled =, -, 0, 1, and 2. Bob needs the input value expressed as a SNAFU number, not in decimal.
Reversing the process, you can determine that for the decimal number 4890, the SNAFU number you need to supply to Bob's console is 2=-1=0.
The Elves are starting to get cold. What SNAFU number do you supply to Bob's console?
| 318
|
--- Day 20: Grove Positioning System ---
It's finally time to meet back up with the Elves. When you try to contact them, however, you get no reply. Perhaps you're out of range?
You know they're headed to the grove where the star fruit grows, so if you can figure out where that is, you should be able to meet back up with them.
Fortunately, your handheld device has a file (your puzzle input) that contains the grove's coordinates! Unfortunately, the file is encrypted - just in case the device were to fall into the wrong hands.
Maybe you can decrypt it?
When you were still back at the camp, you overheard some Elves talking about coordinate file encryption. The main operation involved in decrypting the file is called mixing.
The encrypted file is a list of numbers. To mix the file, move each number forward or backward in the file a number of positions equal to the value of the number being moved. The list is circular, so moving a number off one end of the list wraps back around to the other end as if the ends were connected.
For example, to move the 1 in a sequence like 4, 5, 6, 1, 7, 8, 9, the 1 moves one position forward: 4, 5, 6, 7, 1, 8, 9. To move the -2 in a sequence like 4, -2, 5, 6, 7, 8, 9, the -2 moves two positions backward, wrapping around: 4, 5, 6, 7, 8, -2, 9.
The numbers should be moved in the order they originally appear in the encrypted file. Numbers moving around during the mixing process do not change the order in which the numbers are moved.
Consider this encrypted file:
1
2
-3
3
-2
0
4
Mixing this file proceeds as follows:
Initial arrangement:
1, 2, -3, 3, -2, 0, 4
1 moves between 2 and -3:
2, 1, -3, 3, -2, 0, 4
2 moves between -3 and 3:
1, -3, 2, 3, -2, 0, 4
-3 moves between -2 and 0:
1, 2, 3, -2, -3, 0, 4
3 moves between 0 and 4:
1, 2, -2, -3, 0, 3, 4
-2 moves between 4 and 1:
1, 2, -3, 0, 3, 4, -2
0 does not move:
1, 2, -3, 0, 3, 4, -2
4 moves between -3 and 0:
1, 2, -3, 4, 0, 3, -2
Then, the grove coordinates can be found by looking at the 1000th, 2000th, and 3000th numbers after the value 0, wrapping around the list as necessary. In the above example, the 1000th number after 0 is 4, the 2000th is -3, and the 3000th is 2; adding these together produces 3.
Mix your encrypted file exactly once. What is the sum of the three numbers that form the grove coordinates?
| 319
|
--- Day 11: Corporate Policy ---
Santa's previous password expired, and he needs help choosing a new one.
To help him remember his new password after the old one expires, Santa has devised a method of coming up with a password based on the previous one. Corporate policy dictates that passwords must be exactly eight lowercase letters (for security reasons), so he finds his new password by incrementing his old password string repeatedly until it is valid.
Incrementing is just like counting with numbers: xx, xy, xz, ya, yb, and so on. Increase the rightmost letter one step; if it was z, it wraps around to a, and repeat with the next letter to the left until one doesn't wrap around.
Unfortunately for Santa, a new Security-Elf recently started, and he has imposed some additional password requirements:
Passwords must include one increasing straight of at least three letters, like abc, bcd, cde, and so on, up to xyz. They cannot skip letters; abd doesn't count.
Passwords may not contain the letters i, o, or l, as these letters can be mistaken for other characters and are therefore confusing.
Passwords must contain at least two different, non-overlapping pairs of letters, like aa, bb, or zz.
For example:
hijklmmn meets the first requirement (because it contains the straight hij) but fails the second requirement requirement (because it contains i and l).
abbceffg meets the third requirement (because it repeats bb and ff) but fails the first requirement.
abbcegjk fails the third requirement, because it only has one double letter (bb).
The next password after abcdefgh is abcdffaa.
The next password after ghijklmn is ghjaabcc, because you eventually skip all the passwords that start with ghi..., since i is not allowed.
Given Santa's current password (your puzzle input), what should his next password be?
Your puzzle answer was hxbxxyzz.
--- Part Two ---
Santa's password expired again. What's the next one?
| 320
|
--- Day 11: Cosmic Expansion ---
You continue following signs for "Hot Springs" and eventually come across an observatory. The Elf within turns out to be a researcher studying cosmic expansion using the giant telescope here.
He doesn't know anything about the missing machine parts; he's only visiting for this research project. However, he confirms that the hot springs are the next-closest area likely to have people; he'll even take you straight there once he's done with today's observation analysis.
Maybe you can help him with the analysis to speed things up?
The researcher has collected a bunch of data and compiled the data into a single giant image (your puzzle input). The image includes empty space (.) and galaxies (#). For example:
...#......
.......#..
#.........
..........
......#...
.#........
.........#
..........
.......#..
#...#.....
The researcher is trying to figure out the sum of the lengths of the shortest path between every pair of galaxies. However, there's a catch: the universe expanded in the time it took the light from those galaxies to reach the observatory.
Due to something involving gravitational effects, only some space expands. In fact, the result is that any rows or columns that contain no galaxies should all actually be twice as big.
In the above example, three columns and two rows contain no galaxies:
v v v
...#......
.......#..
#.........
>..........<
......#...
.#........
.........#
>..........<
.......#..
#...#.....
^ ^ ^
These rows and columns need to be twice as big; the result of cosmic expansion therefore looks like this:
....#........
.........#...
#............
.............
.............
........#....
.#...........
............#
.............
.............
.........#...
#....#.......
Equipped with this expanded universe, the shortest path between every pair of galaxies can be found. It can help to assign every galaxy a unique number:
....1........
.........2...
3............
.............
.............
........4....
.5...........
............6
.............
.............
.........7...
8....9.......
In these 9 galaxies, there are 36 pairs. Only count each pair once; order within the pair doesn't matter. For each pair, find any shortest path between the two galaxies using only steps that move up, down, left, or right exactly one . or # at a time. (The shortest path between two galaxies is allowed to pass through another galaxy.)
For example, here is one of the shortest paths between galaxies 5 and 9:
....1........
.........2...
3............
.............
.............
........4....
.5...........
.##.........6
..##.........
...##........
....##...7...
8....9.......
This path has length 9 because it takes a minimum of nine steps to get from galaxy 5 to galaxy 9 (the eight locations marked # plus the step onto galaxy 9 itself). Here are some other example shortest path lengths:
Between galaxy 1 and galaxy 7: 15
Between galaxy 3 and galaxy 6: 17
Between galaxy 8 and galaxy 9: 5
In this example, after expanding the universe, the sum of the shortest path between all 36 pairs of galaxies is 374.
Expand the universe, then find the length of the shortest path between every pair of galaxies. What is the sum of these lengths?
Your puzzle answer was 9550717.
--- Part Two ---
The galaxies are much older (and thus much farther apart) than the researcher initially estimated.
Now, instead of the expansion you did before, make each empty row or column one million times larger. That is, each empty row should be replaced with 1000000 empty rows, and each empty column should be replaced with 1000000 empty columns.
(In the example above, if each empty row or column were merely 10 times larger, the sum of the shortest paths between every pair of galaxies would be 1030. If each empty row or column were merely 100 times larger, the sum of the shortest paths between every pair of galaxies would be 8410. However, your universe will need to expand far beyond these values.)
Starting with the same initial image, expand the universe according to these new rules, then find the length of the shortest path between every pair of galaxies. What is the sum of these lengths?
| 321
|
--- Day 17: Conway Cubes ---
As your flight slowly drifts through the sky, the Elves at the Mythical Information Bureau at the North Pole contact you. They'd like some help debugging a malfunctioning experimental energy source aboard one of their super-secret imaging satellites.
The experimental energy source is based on cutting-edge technology: a set of Conway Cubes contained in a pocket dimension! When you hear it's having problems, you can't help but agree to take a look.
The pocket dimension contains an infinite 3-dimensional grid. At every integer 3-dimensional coordinate (x,y,z), there exists a single cube which is either active or inactive.
In the initial state of the pocket dimension, almost all cubes start inactive. The only exception to this is a small flat region of cubes (your puzzle input); the cubes in this region start in the specified active (#) or inactive (.) state.
The energy source then proceeds to boot up by executing six cycles.
Each cube only ever considers its neighbors: any of the 26 other cubes where any of their coordinates differ by at most 1. For example, given the cube at x=1,y=2,z=3, its neighbors include the cube at x=2,y=2,z=2, the cube at x=0,y=2,z=3, and so on.
During a cycle, all cubes simultaneously change their state according to the following rules:
If a cube is active and exactly 2 or 3 of its neighbors are also active, the cube remains active. Otherwise, the cube becomes inactive.
If a cube is inactive but exactly 3 of its neighbors are active, the cube becomes active. Otherwise, the cube remains inactive.
The engineers responsible for this experimental energy source would like you to simulate the pocket dimension and determine what the configuration of cubes should be at the end of the six-cycle boot process.
For example, consider the following initial state:
.#.
..#
###
Even though the pocket dimension is 3-dimensional, this initial state represents a small 2-dimensional slice of it. (In particular, this initial state defines a 3x3x1 region of the 3-dimensional space.)
Simulating a few cycles from this initial state produces the following configurations, where the result of each cycle is shown layer-by-layer at each given z coordinate (and the frame of view follows the active cells in each cycle):
Before any cycles:
z=0
.#.
..#
###
After 1 cycle:
z=-1
#..
..#
.#.
z=0
#.#
.##
.#.
z=1
#..
..#
.#.
After 2 cycles:
z=-2
.....
.....
..#..
.....
.....
z=-1
..#..
.#..#
....#
.#...
.....
z=0
##...
##...
#....
....#
.###.
z=1
..#..
.#..#
....#
.#...
.....
z=2
.....
.....
..#..
.....
.....
After 3 cycles:
z=-2
.......
.......
..##...
..###..
.......
.......
.......
z=-1
..#....
...#...
#......
.....##
.#...#.
..#.#..
...#...
z=0
...#...
.......
#......
.......
.....##
.##.#..
...#...
z=1
..#....
...#...
#......
.....##
.#...#.
..#.#..
...#...
z=2
.......
.......
..##...
..###..
.......
.......
.......
After the full six-cycle boot process completes, 112 cubes are left in the active state.
Starting with your given initial configuration, simulate six cycles. How many cubes are left in the active state after the sixth cycle?
| 322
|
--- Day 13: Knights of the Dinner Table ---
In years past, the holiday feast with your family hasn't gone so well. Not everyone gets along! This year, you resolve, will be different. You're going to find the optimal seating arrangement and avoid all those awkward conversations.
You start by writing up a list of everyone invited and the amount their happiness would increase or decrease if they were to find themselves sitting next to each other person. You have a circular table that will be just big enough to fit everyone comfortably, and so each person will have exactly two neighbors.
For example, suppose you have only four attendees planned, and you calculate their potential happiness as follows:
Alice would gain 54 happiness units by sitting next to Bob.
Alice would lose 79 happiness units by sitting next to Carol.
Alice would lose 2 happiness units by sitting next to David.
Bob would gain 83 happiness units by sitting next to Alice.
Bob would lose 7 happiness units by sitting next to Carol.
Bob would lose 63 happiness units by sitting next to David.
Carol would lose 62 happiness units by sitting next to Alice.
Carol would gain 60 happiness units by sitting next to Bob.
Carol would gain 55 happiness units by sitting next to David.
David would gain 46 happiness units by sitting next to Alice.
David would lose 7 happiness units by sitting next to Bob.
David would gain 41 happiness units by sitting next to Carol.
Then, if you seat Alice next to David, Alice would lose 2 happiness units (because David talks so much), but David would gain 46 happiness units (because Alice is such a good listener), for a total change of 44.
If you continue around the table, you could then seat Bob next to Alice (Bob gains 83, Alice gains 54). Finally, seat Carol, who sits next to Bob (Carol gains 60, Bob loses 7) and David (Carol gains 55, David gains 41). The arrangement looks like this:
+41 +46
+55 David -2
Carol Alice
+60 Bob +54
-7 +83
After trying every other seating arrangement in this hypothetical scenario, you find that this one is the most optimal, with a total change in happiness of 330.
What is the total change in happiness for the optimal seating arrangement of the actual guest list?
| 323
|
--- Day 22: Grid Computing ---
You gain access to a massive storage cluster arranged in a grid; each storage node is only connected to the four nodes directly adjacent to it (three if the node is on an edge, two if it's in a corner).
You can directly access data only on node /dev/grid/node-x0-y0, but you can perform some limited actions on the other nodes:
You can get the disk usage of all nodes (via df). The result of doing this is in your puzzle input.
You can instruct a node to move (not copy) all of its data to an adjacent node (if the destination node has enough space to receive the data). The sending node is left empty after this operation.
Nodes are named by their position: the node named node-x10-y10 is adjacent to nodes node-x9-y10, node-x11-y10, node-x10-y9, and node-x10-y11.
Before you begin, you need to understand the arrangement of data on these nodes. Even though you can only move data between directly connected nodes, you're going to need to rearrange a lot of the data to get access to the data you need. Therefore, you need to work out how you might be able to shift data around.
To do this, you'd like to count the number of viable pairs of nodes. A viable pair is any two nodes (A,B), regardless of whether they are directly connected, such that:
Node A is not empty (its Used is not zero).
Nodes A and B are not the same node.
The data on node A (its Used) would fit on node B (its Avail).
How many viable pairs of nodes are there?
Your puzzle answer was 937.
--- Part Two ---
Now that you have a better understanding of the grid, it's time to get to work.
Your goal is to gain access to the data which begins in the node with y=0 and the highest x (that is, the node in the top-right corner).
For example, suppose you have the following grid:
Filesystem Size Used Avail Use%
/dev/grid/node-x0-y0 10T 8T 2T 80%
/dev/grid/node-x0-y1 11T 6T 5T 54%
/dev/grid/node-x0-y2 32T 28T 4T 87%
/dev/grid/node-x1-y0 9T 7T 2T 77%
/dev/grid/node-x1-y1 8T 0T 8T 0%
/dev/grid/node-x1-y2 11T 7T 4T 63%
/dev/grid/node-x2-y0 10T 6T 4T 60%
/dev/grid/node-x2-y1 9T 8T 1T 88%
/dev/grid/node-x2-y2 9T 6T 3T 66%
In this example, you have a storage grid 3 nodes wide and 3 nodes tall. The node you can access directly, node-x0-y0, is almost full. The node containing the data you want to access, node-x2-y0 (because it has y=0 and the highest x value), contains 6 terabytes of data - enough to fit on your node, if only you could make enough space to move it there.
Fortunately, node-x1-y1 looks like it has enough free space to enable you to move some of this data around. In fact, it seems like all of the nodes have enough space to hold any node's data (except node-x0-y2, which is much larger, very full, and not moving any time soon). So, initially, the grid's capacities and connections look like this:
( 8T/10T) -- 7T/ 9T -- [ 6T/10T]
| | |
6T/11T -- 0T/ 8T -- 8T/ 9T
| | |
28T/32T -- 7T/11T -- 6T/ 9T
The node you can access directly is in parentheses; the data you want starts in the node marked by square brackets.
In this example, most of the nodes are interchangable: they're full enough that no other node's data would fit, but small enough that their data could be moved around. Let's draw these nodes as .. The exceptions are the empty node, which we'll draw as _, and the very large, very full node, which we'll draw as #. Let's also draw the goal data as G. Then, it looks like this:
(.) . G
. _ .
# . .
The goal is to move the data in the top right, G, to the node in parentheses. To do this, we can issue some commands to the grid and rearrange the data:
Move data from node-y0-x1 to node-y1-x1, leaving node node-y0-x1 empty:
(.) _ G
. . .
# . .
Move the goal data from node-y0-x2 to node-y0-x1:
(.) G _
. . .
# . .
At this point, we're quite close. However, we have no deletion command, so we have to move some more data around. So, next, we move the data from node-y1-x2 to node-y0-x2:
(.) G .
. . _
# . .
Move the data from node-y1-x1 to node-y1-x2:
(.) G .
. _ .
# . .
Move the data from node-y1-x0 to node-y1-x1:
(.) G .
_ . .
# . .
Next, we can free up space on our node by moving the data from node-y0-x0 to node-y1-x0:
(_) G .
. . .
# . .
Finally, we can access the goal data by moving the it from node-y0-x1 to node-y0-x0:
(G) _ .
. . .
# . .
So, after 7 steps, we've accessed the data we want. Unfortunately, each of these moves takes time, and we need to be efficient:
What is the fewest number of steps required to move your goal data to node-x0-y0?
| 324
|
--- Day 9: All in a Single Night ---
Every year, Santa manages to deliver all of his presents in a single night.
This year, however, he has some new locations to visit; his elves have provided him the distances between every pair of locations. He can start and end at any two (different) locations he wants, but he must visit each location exactly once. What is the shortest distance he can travel to achieve this?
For example, given the following distances:
London to Dublin = 464
London to Belfast = 518
Dublin to Belfast = 141
The possible routes are therefore:
Dublin -> London -> Belfast = 982
London -> Dublin -> Belfast = 605
London -> Belfast -> Dublin = 659
Dublin -> Belfast -> London = 659
Belfast -> Dublin -> London = 605
Belfast -> London -> Dublin = 982
The shortest of these is London -> Dublin -> Belfast = 605, and so the answer is 605 in this example.
What is the distance of the shortest route?
Your puzzle answer was 141.
--- Part Two ---
The next year, just to show off, Santa decides to take the route with the longest distance instead.
He can still start and end at any two (different) locations he wants, and he still must visit each location exactly once.
For example, given the distances above, the longest route would be 982 via (for example) Dublin -> London -> Belfast.
What is the distance of the longest route?
| 325
|
--- Day 7: Some Assembly Required ---
This year, Santa brought little Bobby Tables a set of wires and bitwise logic gates! Unfortunately, little Bobby is a little under the recommended age range, and he needs help assembling the circuit.
Each wire has an identifier (some lowercase letters) and can carry a 16-bit signal (a number from 0 to 65535). A signal is provided to each wire by a gate, another wire, or some specific value. Each wire can only get a signal from one source, but can provide its signal to multiple destinations. A gate provides no signal until all of its inputs have a signal.
The included instructions booklet describes how to connect the parts together: x AND y -> z means to connect wires x and y to an AND gate, and then connect its output to wire z.
For example:
123 -> x means that the signal 123 is provided to wire x.
x AND y -> z means that the bitwise AND of wire x and wire y is provided to wire z.
p LSHIFT 2 -> q means that the value from wire p is left-shifted by 2 and then provided to wire q.
NOT e -> f means that the bitwise complement of the value from wire e is provided to wire f.
Other possible gates include OR (bitwise OR) and RSHIFT (right-shift). If, for some reason, you'd like to emulate the circuit instead, almost all programming languages (for example, C, JavaScript, or Python) provide operators for these gates.
For example, here is a simple circuit:
123 -> x
456 -> y
x AND y -> d
x OR y -> e
x LSHIFT 2 -> f
y RSHIFT 2 -> g
NOT x -> h
NOT y -> i
After it is run, these are the signals on the wires:
d: 72
e: 507
f: 492
g: 114
h: 65412
i: 65079
x: 123
y: 456
In little Bobby's kit's instructions booklet (provided as your puzzle input), what signal is ultimately provided to wire a?
| 326
|
--- Day 10: Elves Look, Elves Say ---
Today, the Elves are playing a game called look-and-say. They take turns making sequences by reading aloud the previous sequence and using that reading as the next sequence. For example, 211 is read as "one two, two ones", which becomes 1221 (1 2, 2 1s).
Look-and-say sequences are generated iteratively, using the previous value as input for the next step. For each step, take the previous value, and replace each run of digits (like 111) with the number of digits (3) followed by the digit itself (1).
For example:
1 becomes 11 (1 copy of digit 1).
11 becomes 21 (2 copies of digit 1).
21 becomes 1211 (one 2 followed by one 1).
1211 becomes 111221 (one 1, one 2, and two 1s).
111221 becomes 312211 (three 1s, two 2s, and one 1).
Starting with the digits in your puzzle input, apply this process 40 times. What is the length of the result?
| 327
|
--- Day 15: Science for Hungry People ---
Today, you set out on the task of perfecting your milk-dunking cookie recipe. All you have to do is find the right balance of ingredients.
Your recipe leaves room for exactly 100 teaspoons of ingredients. You make a list of the remaining ingredients you could use to finish the recipe (your puzzle input) and their properties per teaspoon:
capacity (how well it helps the cookie absorb milk)
durability (how well it keeps the cookie intact when full of milk)
flavor (how tasty it makes the cookie)
texture (how it improves the feel of the cookie)
calories (how many calories it adds to the cookie)
You can only measure ingredients in whole-teaspoon amounts accurately, and you have to be accurate so you can reproduce your results in the future. The total score of a cookie can be found by adding up each of the properties (negative totals become 0) and then multiplying together everything except calories.
For instance, suppose you have these two ingredients:
Butterscotch: capacity -1, durability -2, flavor 6, texture 3, calories 8
Cinnamon: capacity 2, durability 3, flavor -2, texture -1, calories 3
Then, choosing to use 44 teaspoons of butterscotch and 56 teaspoons of cinnamon (because the amounts of each ingredient must add up to 100) would result in a cookie with the following properties:
A capacity of 44*-1 + 56*2 = 68
A durability of 44*-2 + 56*3 = 80
A flavor of 44*6 + 56*-2 = 152
A texture of 44*3 + 56*-1 = 76
Multiplying these together (68 * 80 * 152 * 76, ignoring calories for now) results in a total score of 62842880, which happens to be the best score possible given these ingredients. If any properties had produced a negative total, it would have instead become zero, causing the whole score to multiply to zero.
Given the ingredients in your kitchen and their properties, what is the total score of the highest-scoring cookie you can make?
Your puzzle answer was 13882464.
--- Part Two ---
Your cookie recipe becomes wildly popular! Someone asks if you can make another recipe that has exactly 500 calories per cookie (so they can use it as a meal replacement). Keep the rest of your award-winning process the same (100 teaspoons, same ingredients, same scoring system).
For example, given the ingredients above, if you had instead selected 40 teaspoons of butterscotch and 60 teaspoons of cinnamon (which still adds to 100), the total calorie count would be 40*8 + 60*3 = 500. The total score would go down, though: only 57600000, the best you can do in such trying circumstances.
Given the ingredients in your kitchen and their properties, what is the total score of the highest-scoring cookie you can make with a calorie total of 500?
| 328
|
--- Day 16: Proboscidea Volcanium ---
The sensors have led you to the origin of the distress signal: yet another handheld device, just like the one the Elves gave you. However, you don't see any Elves around; instead, the device is surrounded by elephants! They must have gotten lost in these tunnels, and one of the elephants apparently figured out how to turn on the distress signal.
The ground rumbles again, much stronger this time. What kind of cave is this, exactly? You scan the cave with your handheld device; it reports mostly igneous rock, some ash, pockets of pressurized gas, magma... this isn't just a cave, it's a volcano!
You need to get the elephants out of here, quickly. Your device estimates that you have 30 minutes before the volcano erupts, so you don't have time to go back out the way you came in.
You scan the cave for other options and discover a network of pipes and pressure-release valves. You aren't sure how such a system got into a volcano, but you don't have time to complain; your device produces a report (your puzzle input) of each valve's flow rate if it were opened (in pressure per minute) and the tunnels you could use to move between the valves.
There's even a valve in the room you and the elephants are currently standing in labeled AA. You estimate it will take you one minute to open a single valve and one minute to follow any tunnel from one valve to another. What is the most pressure you could release?
For example, suppose you had the following scan output:
Valve AA has flow rate=0; tunnels lead to valves DD, II, BB
Valve BB has flow rate=13; tunnels lead to valves CC, AA
Valve CC has flow rate=2; tunnels lead to valves DD, BB
Valve DD has flow rate=20; tunnels lead to valves CC, AA, EE
Valve EE has flow rate=3; tunnels lead to valves FF, DD
Valve FF has flow rate=0; tunnels lead to valves EE, GG
Valve GG has flow rate=0; tunnels lead to valves FF, HH
Valve HH has flow rate=22; tunnel leads to valve GG
Valve II has flow rate=0; tunnels lead to valves AA, JJ
Valve JJ has flow rate=21; tunnel leads to valve II
All of the valves begin closed. You start at valve AA, but it must be damaged or jammed or something: its flow rate is 0, so there's no point in opening it. However, you could spend one minute moving to valve BB and another minute opening it; doing so would release pressure during the remaining 28 minutes at a flow rate of 13, a total eventual pressure release of 28 * 13 = 364. Then, you could spend your third minute moving to valve CC and your fourth minute opening it, providing an additional 26 minutes of eventual pressure release at a flow rate of 2, or 52 total pressure released by valve CC.
Making your way through the tunnels like this, you could probably open many or all of the valves by the time 30 minutes have elapsed. However, you need to release as much pressure as possible, so you'll need to be methodical. Instead, consider this approach:
== Minute 1 ==
No valves are open.
You move to valve DD.
== Minute 2 ==
No valves are open.
You open valve DD.
== Minute 3 ==
Valve DD is open, releasing 20 pressure.
You move to valve CC.
== Minute 4 ==
Valve DD is open, releasing 20 pressure.
You move to valve BB.
== Minute 5 ==
Valve DD is open, releasing 20 pressure.
You open valve BB.
== Minute 6 ==
Valves BB and DD are open, releasing 33 pressure.
You move to valve AA.
== Minute 7 ==
Valves BB and DD are open, releasing 33 pressure.
You move to valve II.
== Minute 8 ==
Valves BB and DD are open, releasing 33 pressure.
You move to valve JJ.
== Minute 9 ==
Valves BB and DD are open, releasing 33 pressure.
You open valve JJ.
== Minute 10 ==
Valves BB, DD, and JJ are open, releasing 54 pressure.
You move to valve II.
== Minute 11 ==
Valves BB, DD, and JJ are open, releasing 54 pressure.
You move to valve AA.
== Minute 12 ==
Valves BB, DD, and JJ are open, releasing 54 pressure.
You move to valve DD.
== Minute 13 ==
Valves BB, DD, and JJ are open, releasing 54 pressure.
You move to valve EE.
== Minute 14 ==
Valves BB, DD, and JJ are open, releasing 54 pressure.
You move to valve FF.
== Minute 15 ==
Valves BB, DD, and JJ are open, releasing 54 pressure.
You move to valve GG.
== Minute 16 ==
Valves BB, DD, and JJ are open, releasing 54 pressure.
You move to valve HH.
== Minute 17 ==
Valves BB, DD, and JJ are open, releasing 54 pressure.
You open valve HH.
== Minute 18 ==
Valves BB, DD, HH, and JJ are open, releasing 76 pressure.
You move to valve GG.
== Minute 19 ==
Valves BB, DD, HH, and JJ are open, releasing 76 pressure.
You move to valve FF.
== Minute 20 ==
Valves BB, DD, HH, and JJ are open, releasing 76 pressure.
You move to valve EE.
== Minute 21 ==
Valves BB, DD, HH, and JJ are open, releasing 76 pressure.
You open valve EE.
== Minute 22 ==
Valves BB, DD, EE, HH, and JJ are open, releasing 79 pressure.
You move to valve DD.
== Minute 23 ==
Valves BB, DD, EE, HH, and JJ are open, releasing 79 pressure.
You move to valve CC.
== Minute 24 ==
Valves BB, DD, EE, HH, and JJ are open, releasing 79 pressure.
You open valve CC.
== Minute 25 ==
Valves BB, CC, DD, EE, HH, and JJ are open, releasing 81 pressure.
== Minute 26 ==
Valves BB, CC, DD, EE, HH, and JJ are open, releasing 81 pressure.
== Minute 27 ==
Valves BB, CC, DD, EE, HH, and JJ are open, releasing 81 pressure.
== Minute 28 ==
Valves BB, CC, DD, EE, HH, and JJ are open, releasing 81 pressure.
== Minute 29 ==
Valves BB, CC, DD, EE, HH, and JJ are open, releasing 81 pressure.
== Minute 30 ==
Valves BB, CC, DD, EE, HH, and JJ are open, releasing 81 pressure.
This approach lets you release the most pressure possible in 30 minutes with this valve layout, 1651.
Work out the steps to release the most pressure in 30 minutes. What is the most pressure you can release?
| 329
|
--- Day 13: Packet Scanners ---
You need to cross a vast firewall. The firewall consists of several layers, each with a security scanner that moves back and forth across the layer. To succeed, you must not be detected by a scanner.
By studying the firewall briefly, you are able to record (in your puzzle input) the depth of each layer and the range of the scanning area for the scanner within it, written as depth: range. Each layer has a thickness of exactly 1. A layer at depth 0 begins immediately inside the firewall; a layer at depth 1 would start immediately after that.
For example, suppose you've recorded the following:
0: 3
1: 2
4: 4
6: 4
This means that there is a layer immediately inside the firewall (with range 3), a second layer immediately after that (with range 2), a third layer which begins at depth 4 (with range 4), and a fourth layer which begins at depth 6 (also with range 4). Visually, it might look like this:
0 1 2 3 4 5 6
[ ] [ ] ... ... [ ] ... [ ]
[ ] [ ] [ ] [ ]
[ ] [ ] [ ]
[ ] [ ]
Within each layer, a security scanner moves back and forth within its range. Each security scanner starts at the top and moves down until it reaches the bottom, then moves up until it reaches the top, and repeats. A security scanner takes one picosecond to move one step. Drawing scanners as S, the first few picoseconds look like this:
Picosecond 0:
0 1 2 3 4 5 6
[S] [S] ... ... [S] ... [S]
[ ] [ ] [ ] [ ]
[ ] [ ] [ ]
[ ] [ ]
Picosecond 1:
0 1 2 3 4 5 6
[ ] [ ] ... ... [ ] ... [ ]
[S] [S] [S] [S]
[ ] [ ] [ ]
[ ] [ ]
Picosecond 2:
0 1 2 3 4 5 6
[ ] [S] ... ... [ ] ... [ ]
[ ] [ ] [ ] [ ]
[S] [S] [S]
[ ] [ ]
Picosecond 3:
0 1 2 3 4 5 6
[ ] [ ] ... ... [ ] ... [ ]
[S] [S] [ ] [ ]
[ ] [ ] [ ]
[S] [S]
Your plan is to hitch a ride on a packet about to move through the firewall. The packet will travel along the top of each layer, and it moves at one layer per picosecond. Each picosecond, the packet moves one layer forward (its first move takes it into layer 0), and then the scanners move one step. If there is a scanner at the top of the layer as your packet enters it, you are caught. (If a scanner moves into the top of its layer while you are there, you are not caught: it doesn't have time to notice you before you leave.) If you were to do this in the configuration above, marking your current position with parentheses, your passage through the firewall would look like this:
Initial state:
0 1 2 3 4 5 6
[S] [S] ... ... [S] ... [S]
[ ] [ ] [ ] [ ]
[ ] [ ] [ ]
[ ] [ ]
Picosecond 0:
0 1 2 3 4 5 6
(S) [S] ... ... [S] ... [S]
[ ] [ ] [ ] [ ]
[ ] [ ] [ ]
[ ] [ ]
0 1 2 3 4 5 6
( ) [ ] ... ... [ ] ... [ ]
[S] [S] [S] [S]
[ ] [ ] [ ]
[ ] [ ]
Picosecond 1:
0 1 2 3 4 5 6
[ ] ( ) ... ... [ ] ... [ ]
[S] [S] [S] [S]
[ ] [ ] [ ]
[ ] [ ]
0 1 2 3 4 5 6
[ ] (S) ... ... [ ] ... [ ]
[ ] [ ] [ ] [ ]
[S] [S] [S]
[ ] [ ]
Picosecond 2:
0 1 2 3 4 5 6
[ ] [S] (.) ... [ ] ... [ ]
[ ] [ ] [ ] [ ]
[S] [S] [S]
[ ] [ ]
0 1 2 3 4 5 6
[ ] [ ] (.) ... [ ] ... [ ]
[S] [S] [ ] [ ]
[ ] [ ] [ ]
[S] [S]
Picosecond 3:
0 1 2 3 4 5 6
[ ] [ ] ... (.) [ ] ... [ ]
[S] [S] [ ] [ ]
[ ] [ ] [ ]
[S] [S]
0 1 2 3 4 5 6
[S] [S] ... (.) [ ] ... [ ]
[ ] [ ] [ ] [ ]
[ ] [S] [S]
[ ] [ ]
Picosecond 4:
0 1 2 3 4 5 6
[S] [S] ... ... ( ) ... [ ]
[ ] [ ] [ ] [ ]
[ ] [S] [S]
[ ] [ ]
0 1 2 3 4 5 6
[ ] [ ] ... ... ( ) ... [ ]
[S] [S] [S] [S]
[ ] [ ] [ ]
[ ] [ ]
Picosecond 5:
0 1 2 3 4 5 6
[ ] [ ] ... ... [ ] (.) [ ]
[S] [S] [S] [S]
[ ] [ ] [ ]
[ ] [ ]
0 1 2 3 4 5 6
[ ] [S] ... ... [S] (.) [S]
[ ] [ ] [ ] [ ]
[S] [ ] [ ]
[ ] [ ]
Picosecond 6:
0 1 2 3 4 5 6
[ ] [S] ... ... [S] ... (S)
[ ] [ ] [ ] [ ]
[S] [ ] [ ]
[ ] [ ]
0 1 2 3 4 5 6
[ ] [ ] ... ... [ ] ... ( )
[S] [S] [S] [S]
[ ] [ ] [ ]
[ ] [ ]
In this situation, you are caught in layers 0 and 6, because your packet entered the layer when its scanner was at the top when you entered it. You are not caught in layer 1, since the scanner moved into the top of the layer once you were already there.
The severity of getting caught on a layer is equal to its depth multiplied by its range. (Ignore layers in which you do not get caught.) The severity of the whole trip is the sum of these values. In the example above, the trip severity is 0*3 + 6*4 = 24.
Given the details of the firewall you've recorded, if you leave immediately, what is the severity of your whole trip?
| 330
|
--- Day 13: Transparent Origami ---
You reach another volcanically active part of the cave. It would be nice if you could do some kind of thermal imaging so you could tell ahead of time which caves are too hot to safely enter.
Fortunately, the submarine seems to be equipped with a thermal camera! When you activate it, you are greeted with:
Congratulations on your purchase! To activate this infrared thermal imaging
camera system, please enter the code found on page 1 of the manual.
Apparently, the Elves have never used this feature. To your surprise, you manage to find the manual; as you go to open it, page 1 falls out. It's a large sheet of transparent paper! The transparent paper is marked with random dots and includes instructions on how to fold it up (your puzzle input). For example:
6,10
0,14
9,10
0,3
10,4
4,11
6,0
6,12
4,1
0,13
10,12
3,4
3,0
8,4
1,10
2,14
8,10
9,0
fold along y=7
fold along x=5
The first section is a list of dots on the transparent paper. 0,0 represents the top-left coordinate. The first value, x, increases to the right. The second value, y, increases downward. So, the coordinate 3,0 is to the right of 0,0, and the coordinate 0,7 is below 0,0. The coordinates in this example form the following pattern, where # is a dot on the paper and . is an empty, unmarked position:
...#..#..#.
....#......
...........
#..........
...#....#.#
...........
...........
...........
...........
...........
.#....#.##.
....#......
......#...#
#..........
#.#........
Then, there is a list of fold instructions. Each instruction indicates a line on the transparent paper and wants you to fold the paper up (for horizontal y=... lines) or left (for vertical x=... lines). In this example, the first fold instruction is fold along y=7, which designates the line formed by all of the positions where y is 7 (marked here with -):
...#..#..#.
....#......
...........
#..........
...#....#.#
...........
...........
-----------
...........
...........
.#....#.##.
....#......
......#...#
#..........
#.#........
Because this is a horizontal line, fold the bottom half up. Some of the dots might end up overlapping after the fold is complete, but dots will never appear exactly on a fold line. The result of doing this fold looks like this:
#.##..#..#.
#...#......
......#...#
#...#......
.#.#..#.###
...........
...........
Now, only 17 dots are visible.
Notice, for example, the two dots in the bottom left corner before the transparent paper is folded; after the fold is complete, those dots appear in the top left corner (at 0,0 and 0,1). Because the paper is transparent, the dot just below them in the result (at 0,3) remains visible, as it can be seen through the transparent paper.
Also notice that some dots can end up overlapping; in this case, the dots merge together and become a single dot.
The second fold instruction is fold along x=5, which indicates this line:
#.##.|#..#.
#...#|.....
.....|#...#
#...#|.....
.#.#.|#.###
.....|.....
.....|.....
Because this is a vertical line, fold left:
#####
#...#
#...#
#...#
#####
.....
.....
The instructions made a square!
The transparent paper is pretty big, so for now, focus on just completing the first fold. After the first fold in the example above, 17 dots are visible - dots that end up overlapping after the fold is completed count as a single dot.
How many dots are visible after completing just the first fold instruction on your transparent paper?
| 331
|
--- Day 12: Rain Risk ---
Your ferry made decent progress toward the island, but the storm came in faster than anyone expected. The ferry needs to take evasive actions!
Unfortunately, the ship's navigation computer seems to be malfunctioning; rather than giving a route directly to safety, it produced extremely circuitous instructions. When the captain uses the PA system to ask if anyone can help, you quickly volunteer.
The navigation instructions (your puzzle input) consists of a sequence of single-character actions paired with integer input values. After staring at them for a few minutes, you work out what they probably mean:
Action N means to move north by the given value.
Action S means to move south by the given value.
Action E means to move east by the given value.
Action W means to move west by the given value.
Action L means to turn left the given number of degrees.
Action R means to turn right the given number of degrees.
Action F means to move forward by the given value in the direction the ship is currently facing.
The ship starts by facing east. Only the L and R actions change the direction the ship is facing. (That is, if the ship is facing east and the next instruction is N10, the ship would move north 10 units, but would still move east if the following action were F.)
For example:
F10
N3
F7
R90
F11
These instructions would be handled as follows:
F10 would move the ship 10 units east (because the ship starts by facing east) to east 10, north 0.
N3 would move the ship 3 units north to east 10, north 3.
F7 would move the ship another 7 units east (because the ship is still facing east) to east 17, north 3.
R90 would cause the ship to turn right by 90 degrees and face south; it remains at east 17, north 3.
F11 would move the ship 11 units south to east 17, south 8.
At the end of these instructions, the ship's Manhattan distance (sum of the absolute values of its east/west position and its north/south position) from its starting position is 17 + 8 = 25.
Figure out where the navigation instructions lead. What is the Manhattan distance between that location and the ship's starting position?
Your puzzle answer was 381.
--- Part Two ---
Before you can give the destination to the captain, you realize that the actual action meanings were printed on the back of the instructions the whole time.
Almost all of the actions indicate how to move a waypoint which is relative to the ship's position:
Action N means to move the waypoint north by the given value.
Action S means to move the waypoint south by the given value.
Action E means to move the waypoint east by the given value.
Action W means to move the waypoint west by the given value.
Action L means to rotate the waypoint around the ship left (counter-clockwise) the given number of degrees.
Action R means to rotate the waypoint around the ship right (clockwise) the given number of degrees.
Action F means to move forward to the waypoint a number of times equal to the given value.
The waypoint starts 10 units east and 1 unit north relative to the ship. The waypoint is relative to the ship; that is, if the ship moves, the waypoint moves with it.
For example, using the same instructions as above:
F10 moves the ship to the waypoint 10 times (a total of 100 units east and 10 units north), leaving the ship at east 100, north 10. The waypoint stays 10 units east and 1 unit north of the ship.
N3 moves the waypoint 3 units north to 10 units east and 4 units north of the ship. The ship remains at east 100, north 10.
F7 moves the ship to the waypoint 7 times (a total of 70 units east and 28 units north), leaving the ship at east 170, north 38. The waypoint stays 10 units east and 4 units north of the ship.
R90 rotates the waypoint around the ship clockwise 90 degrees, moving it to 4 units east and 10 units south of the ship. The ship remains at east 170, north 38.
F11 moves the ship to the waypoint 11 times (a total of 44 units east and 110 units south), leaving the ship at east 214, south 72. The waypoint stays 4 units east and 10 units south of the ship.
After these operations, the ship's Manhattan distance from its starting position is 214 + 72 = 286.
Figure out where the navigation instructions actually lead. What is the Manhattan distance between that location and the ship's starting position?
| 332
|
--- Day 13: Point of Incidence ---
With your help, the hot springs team locates an appropriate spring which launches you neatly and precisely up to the edge of Lava Island.
There's just one problem: you don't see any lava.
You do see a lot of ash and igneous rock; there are even what look like gray mountains scattered around. After a while, you make your way to a nearby cluster of mountains only to discover that the valley between them is completely full of large mirrors. Most of the mirrors seem to be aligned in a consistent way; perhaps you should head in that direction?
As you move through the valley of mirrors, you find that several of them have fallen from the large metal frames keeping them in place. The mirrors are extremely flat and shiny, and many of the fallen mirrors have lodged into the ash at strange angles. Because the terrain is all one color, it's hard to tell where it's safe to walk or where you're about to run into a mirror.
You note down the patterns of ash (.) and rocks (#) that you see as you walk (your puzzle input); perhaps by carefully analyzing these patterns, you can figure out where the mirrors are!
For example:
#.##..##.
..#.##.#.
##......#
##......#
..#.##.#.
..##..##.
#.#.##.#.
#...##..#
#....#..#
..##..###
#####.##.
#####.##.
..##..###
#....#..#
To find the reflection in each pattern, you need to find a perfect reflection across either a horizontal line between two rows or across a vertical line between two columns.
In the first pattern, the reflection is across a vertical line between two columns; arrows on each of the two columns point at the line between the columns:
123456789
><
#.##..##.
..#.##.#.
##......#
##......#
..#.##.#.
..##..##.
#.#.##.#.
><
123456789
In this pattern, the line of reflection is the vertical line between columns 5 and 6. Because the vertical line is not perfectly in the middle of the pattern, part of the pattern (column 1) has nowhere to reflect onto and can be ignored; every other column has a reflected column within the pattern and must match exactly: column 2 matches column 9, column 3 matches 8, 4 matches 7, and 5 matches 6.
The second pattern reflects across a horizontal line instead:
1 #...##..# 1
2 #....#..# 2
3 ..##..### 3
4v#####.##.v4
5^#####.##.^5
6 ..##..### 6
7 #....#..# 7
This pattern reflects across the horizontal line between rows 4 and 5. Row 1 would reflect with a hypothetical row 8, but since that's not in the pattern, row 1 doesn't need to match anything. The remaining rows match: row 2 matches row 7, row 3 matches row 6, and row 4 matches row 5.
To summarize your pattern notes, add up the number of columns to the left of each vertical line of reflection; to that, also add 100 multiplied by the number of rows above each horizontal line of reflection. In the above example, the first pattern's vertical line has 5 columns to its left and the second pattern's horizontal line has 4 rows above it, a total of 405.
Find the line of reflection in each of the patterns in your notes. What number do you get after summarizing all of your notes?
Your puzzle answer was 34889.
--- Part Two ---
You resume walking through the valley of mirrors and - SMACK! - run directly into one. Hopefully nobody was watching, because that must have been pretty embarrassing.
Upon closer inspection, you discover that every mirror has exactly one smudge: exactly one . or # should be the opposite type.
In each pattern, you'll need to locate and fix the smudge that causes a different reflection line to be valid. (The old reflection line won't necessarily continue being valid after the smudge is fixed.)
Here's the above example again:
#.##..##.
..#.##.#.
##......#
##......#
..#.##.#.
..##..##.
#.#.##.#.
#...##..#
#....#..#
..##..###
#####.##.
#####.##.
..##..###
#....#..#
The first pattern's smudge is in the top-left corner. If the top-left # were instead ., it would have a different, horizontal line of reflection:
1 ..##..##. 1
2 ..#.##.#. 2
3v##......#v3
4^##......#^4
5 ..#.##.#. 5
6 ..##..##. 6
7 #.#.##.#. 7
With the smudge in the top-left corner repaired, a new horizontal line of reflection between rows 3 and 4 now exists. Row 7 has no corresponding reflected row and can be ignored, but every other row matches exactly: row 1 matches row 6, row 2 matches row 5, and row 3 matches row 4.
In the second pattern, the smudge can be fixed by changing the fifth symbol on row 2 from . to #:
1v#...##..#v1
2^#...##..#^2
3 ..##..### 3
4 #####.##. 4
5 #####.##. 5
6 ..##..### 6
7 #....#..# 7
Now, the pattern has a different horizontal line of reflection between rows 1 and 2.
Summarize your notes as before, but instead use the new different reflection lines. In this example, the first pattern's new horizontal line has 3 rows above it and the second pattern's new horizontal line has 1 row above it, summarizing to the value 400.
In each pattern, fix the smudge and find the different line of reflection. What number do you get after summarizing the new reflection line in each pattern in your notes?
| 333
|
--- Day 2: Rock Paper Scissors ---
The Elves begin to set up camp on the beach. To decide whose tent gets to be closest to the snack storage, a giant Rock Paper Scissors tournament is already in progress.
Rock Paper Scissors is a game between two players. Each game contains many rounds; in each round, the players each simultaneously choose one of Rock, Paper, or Scissors using a hand shape. Then, a winner for that round is selected: Rock defeats Scissors, Scissors defeats Paper, and Paper defeats Rock. If both players choose the same shape, the round instead ends in a draw.
Appreciative of your help yesterday, one Elf gives you an encrypted strategy guide (your puzzle input) that they say will be sure to help you win. "The first column is what your opponent is going to play: A for Rock, B for Paper, and C for Scissors. The second column--" Suddenly, the Elf is called away to help with someone's tent.
The second column, you reason, must be what you should play in response: X for Rock, Y for Paper, and Z for Scissors. Winning every time would be suspicious, so the responses must have been carefully chosen.
The winner of the whole tournament is the player with the highest score. Your total score is the sum of your scores for each round. The score for a single round is the score for the shape you selected (1 for Rock, 2 for Paper, and 3 for Scissors) plus the score for the outcome of the round (0 if you lost, 3 if the round was a draw, and 6 if you won).
Since you can't be sure if the Elf is trying to help you or trick you, you should calculate the score you would get if you were to follow the strategy guide.
For example, suppose you were given the following strategy guide:
A Y
B X
C Z
This strategy guide predicts and recommends the following:
In the first round, your opponent will choose Rock (A), and you should choose Paper (Y). This ends in a win for you with a score of 8 (2 because you chose Paper + 6 because you won).
In the second round, your opponent will choose Paper (B), and you should choose Rock (X). This ends in a loss for you with a score of 1 (1 + 0).
The third round is a draw with both players choosing Scissors, giving you a score of 3 + 3 = 6.
In this example, if you were to follow the strategy guide, you would get a total score of 15 (8 + 1 + 6).
What would your total score be if everything goes exactly according to your strategy guide?
Your puzzle answer was 14827.
--- Part Two ---
The Elf finishes helping with the tent and sneaks back over to you. "Anyway, the second column says how the round needs to end: X means you need to lose, Y means you need to end the round in a draw, and Z means you need to win. Good luck!"
The total score is still calculated in the same way, but now you need to figure out what shape to choose so the round ends as indicated. The example above now goes like this:
In the first round, your opponent will choose Rock (A), and you need the round to end in a draw (Y), so you also choose Rock. This gives you a score of 1 + 3 = 4.
In the second round, your opponent will choose Paper (B), and you choose Rock so you lose (X) with a score of 1 + 0 = 1.
In the third round, you will defeat your opponent's Scissors with Rock for a score of 1 + 6 = 7.
Now that you're correctly decrypting the ultra top secret strategy guide, you would get a total score of 12.
Following the Elf's instructions for the second column, what would your total score be if everything goes exactly according to your strategy guide?
| 334
|
--- Day 1: Calorie Counting ---
Santa's reindeer typically eat regular reindeer food, but they need a lot of magical energy to deliver presents on Christmas. For that, their favorite snack is a special type of star fruit that only grows deep in the jungle. The Elves have brought you on their annual expedition to the grove where the fruit grows.
To supply enough magical energy, the expedition needs to retrieve a minimum of fifty stars by December 25th. Although the Elves assure you that the grove has plenty of fruit, you decide to grab any fruit you see along the way, just in case.
Collect stars by solving puzzles. Two puzzles will be made available on each day in the Advent calendar; the second puzzle is unlocked when you complete the first. Each puzzle grants one star. Good luck!
The jungle must be too overgrown and difficult to navigate in vehicles or access from the air; the Elves' expedition traditionally goes on foot. As your boats approach land, the Elves begin taking inventory of their supplies. One important consideration is food - in particular, the number of Calories each Elf is carrying (your puzzle input).
The Elves take turns writing down the number of Calories contained by the various meals, snacks, rations, etc. that they've brought with them, one item per line. Each Elf separates their own inventory from the previous Elf's inventory (if any) by a blank line.
For example, suppose the Elves finish writing their items' Calories and end up with the following list:
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
This list represents the Calories of the food carried by five Elves:
The first Elf is carrying food with 1000, 2000, and 3000 Calories, a total of 6000 Calories.
The second Elf is carrying one food item with 4000 Calories.
The third Elf is carrying food with 5000 and 6000 Calories, a total of 11000 Calories.
The fourth Elf is carrying food with 7000, 8000, and 9000 Calories, a total of 24000 Calories.
The fifth Elf is carrying one food item with 10000 Calories.
In case the Elves get hungry and need extra snacks, they need to know which Elf to ask: they'd like to know how many Calories are being carried by the Elf carrying the most Calories. In the example above, this is 24000 (carried by the fourth Elf).
Find the Elf carrying the most Calories. How many total Calories is that Elf carrying?
| 335
|
--- Day 19: Tractor Beam ---
Unsure of the state of Santa's ship, you borrowed the tractor beam technology from Triton. Time to test it out.
When you're safely away from anything else, you activate the tractor beam, but nothing happens. It's hard to tell whether it's working if there's nothing to use it on. Fortunately, your ship's drone system can be configured to deploy a drone to specific coordinates and then check whether it's being pulled. There's even an Intcode program (your puzzle input) that gives you access to the drone system.
The program uses two input instructions to request the X and Y position to which the drone should be deployed. Negative numbers are invalid and will confuse the drone; all numbers should be zero or positive.
Then, the program will output whether the drone is stationary (0) or being pulled by something (1). For example, the coordinate X=0, Y=0 is directly in front of the tractor beam emitter, so the drone control program will always report 1 at that location.
To better understand the tractor beam, it is important to get a good picture of the beam itself. For example, suppose you scan the 10x10 grid of points closest to the emitter:
X
0-> 9
0#.........
|.#........
v..##......
...###....
....###...
Y .....####.
......####
......####
.......###
9........##
In this example, the number of points affected by the tractor beam in the 10x10 area closest to the emitter is 27.
However, you'll need to scan a larger area to understand the shape of the beam. How many points are affected by the tractor beam in the 50x50 area closest to the emitter? (For each of X and Y, this will be 0 through 49.)
Your puzzle answer was 186.
--- Part Two ---
You aren't sure how large Santa's ship is. You aren't even sure if you'll need to use this thing on Santa's ship, but it doesn't hurt to be prepared. You figure Santa's ship might fit in a 100x100 square.
The beam gets wider as it travels away from the emitter; you'll need to be a minimum distance away to fit a square of that size into the beam fully. (Don't rotate the square; it should be aligned to the same axes as the drone grid.)
For example, suppose you have the following tractor beam readings:
#.......................................
.#......................................
..##....................................
...###..................................
....###.................................
.....####...............................
......#####.............................
......######............................
.......#######..........................
........########........................
.........#########......................
..........#########.....................
...........##########...................
...........############.................
............############................
.............#############..............
..............##############............
...............###############..........
................###############.........
................#################.......
.................########OOOOOOOOOO.....
..................#######OOOOOOOOOO#....
...................######OOOOOOOOOO###..
....................#####OOOOOOOOOO#####
.....................####OOOOOOOOOO#####
.....................####OOOOOOOOOO#####
......................###OOOOOOOOOO#####
.......................##OOOOOOOOOO#####
........................#OOOOOOOOOO#####
.........................OOOOOOOOOO#####
..........................##############
..........................##############
...........................#############
............................############
.............................###########
In this example, the 10x10 square closest to the emitter that fits entirely within the tractor beam has been marked O. Within it, the point closest to the emitter (the only highlighted O) is at X=25, Y=20.
Find the 100x100 square closest to the emitter that fits entirely within the tractor beam; within that square, find the point closest to the emitter. What value do you get if you take that point's X coordinate, multiply it by 10000, then add the point's Y coordinate? (In the example above, this would be 250020.)
| 336
|
--- Day 9: Disk Fragmenter ---
Another push of the button leaves you in the familiar hallways of some friendly amphipods! Good thing you each somehow got your own personal mini submarine. The Historians jet away in search of the Chief, mostly by driving directly into walls.
While The Historians quickly figure out how to pilot these things, you notice an amphipod in the corner struggling with his computer. He's trying to make more contiguous free space by compacting all of the files, but his program isn't working; you offer to help.
He shows you the disk map (your puzzle input) he's already generated. For example:
2333133121414131402
The disk map uses a dense format to represent the layout of files and free space on the disk. The digits alternate between indicating the length of a file and the length of free space.
So, a disk map like 12345 would represent a one-block file, two blocks of free space, a three-block file, four blocks of free space, and then a five-block file. A disk map like 90909 would represent three nine-block files in a row (with no free space between them).
Each file on disk also has an ID number based on the order of the files as they appear before they are rearranged, starting with ID 0. So, the disk map 12345 has three files: a one-block file with ID 0, a three-block file with ID 1, and a five-block file with ID 2. Using one character for each block where digits are the file ID and . is free space, the disk map 12345 represents these individual blocks:
0..111....22222
The first example above, 2333133121414131402, represents these individual blocks:
00...111...2...333.44.5555.6666.777.888899
The amphipod would like to move file blocks one at a time from the end of the disk to the leftmost free space block (until there are no gaps remaining between file blocks). For the disk map 12345, the process looks like this:
0..111....22222
02.111....2222.
022111....222..
0221112...22...
02211122..2....
022111222......
The first example requires a few more steps:
00...111...2...333.44.5555.6666.777.888899
009..111...2...333.44.5555.6666.777.88889.
0099.111...2...333.44.5555.6666.777.8888..
00998111...2...333.44.5555.6666.777.888...
009981118..2...333.44.5555.6666.777.88....
0099811188.2...333.44.5555.6666.777.8.....
009981118882...333.44.5555.6666.777.......
0099811188827..333.44.5555.6666.77........
00998111888277.333.44.5555.6666.7.........
009981118882777333.44.5555.6666...........
009981118882777333644.5555.666............
00998111888277733364465555.66.............
0099811188827773336446555566..............
The final step of this file-compacting process is to update the filesystem checksum. To calculate the checksum, add up the result of multiplying each of these blocks' position with the file ID number it contains. The leftmost block is in position 0. If a block contains free space, skip it instead.
Continuing the first example, the first few blocks' position multiplied by its file ID number are 0 * 0 = 0, 1 * 0 = 0, 2 * 9 = 18, 3 * 9 = 27, 4 * 8 = 32, and so on. In this example, the checksum is the sum of these, 1928.
Compact the amphipod's hard drive using the process he requested. What is the resulting filesystem checksum? (Be careful copy/pasting the input for this puzzle; it is a single, very long line.)
| 337
|
--- Day 19: Go With The Flow ---
With the Elves well on their way constructing the North Pole base, you turn your attention back to understanding the inner workings of programming the device.
You can't help but notice that the device's opcodes don't contain any flow control like jump instructions. The device's manual goes on to explain:
"In programs where flow control is required, the instruction pointer can be bound to a register so that it can be manipulated directly. This way, setr/seti can function as absolute jumps, addr/addi can function as relative jumps, and other opcodes can cause truly fascinating effects."
This mechanism is achieved through a declaration like #ip 1, which would modify register 1 so that accesses to it let the program indirectly access the instruction pointer itself. To compensate for this kind of binding, there are now six registers (numbered 0 through 5); the five not bound to the instruction pointer behave as normal. Otherwise, the same rules apply as the last time you worked with this device.
When the instruction pointer is bound to a register, its value is written to that register just before each instruction is executed, and the value of that register is written back to the instruction pointer immediately after each instruction finishes execution. Afterward, move to the next instruction by adding one to the instruction pointer, even if the value in the instruction pointer was just updated by an instruction. (Because of this, instructions must effectively set the instruction pointer to the instruction before the one they want executed next.)
The instruction pointer is 0 during the first instruction, 1 during the second, and so on. If the instruction pointer ever causes the device to attempt to load an instruction outside the instructions defined in the program, the program instead immediately halts. The instruction pointer starts at 0.
It turns out that this new information is already proving useful: the CPU in the device is not very powerful, and a background process is occupying most of its time. You dump the background process' declarations and instructions to a file (your puzzle input), making sure to use the names of the opcodes rather than the numbers.
For example, suppose you have the following program:
#ip 0
seti 5 0 1
seti 6 0 2
addi 0 1 0
addr 1 2 3
setr 1 0 0
seti 8 0 4
seti 9 0 5
When executed, the following instructions are executed. Each line contains the value of the instruction pointer at the time the instruction started, the values of the six registers before executing the instructions (in square brackets), the instruction itself, and the values of the six registers after executing the instruction (also in square brackets).
ip=0 [0, 0, 0, 0, 0, 0] seti 5 0 1 [0, 5, 0, 0, 0, 0]
ip=1 [1, 5, 0, 0, 0, 0] seti 6 0 2 [1, 5, 6, 0, 0, 0]
ip=2 [2, 5, 6, 0, 0, 0] addi 0 1 0 [3, 5, 6, 0, 0, 0]
ip=4 [4, 5, 6, 0, 0, 0] setr 1 0 0 [5, 5, 6, 0, 0, 0]
ip=6 [6, 5, 6, 0, 0, 0] seti 9 0 5 [6, 5, 6, 0, 0, 9]
In detail, when running this program, the following events occur:
The first line (#ip 0) indicates that the instruction pointer should be bound to register 0 in this program. This is not an instruction, and so the value of the instruction pointer does not change during the processing of this line.
The instruction pointer contains 0, and so the first instruction is executed (seti 5 0 1). It updates register 0 to the current instruction pointer value (0), sets register 1 to 5, sets the instruction pointer to the value of register 0 (which has no effect, as the instruction did not modify register 0), and then adds one to the instruction pointer.
The instruction pointer contains 1, and so the second instruction, seti 6 0 2, is executed. This is very similar to the instruction before it: 6 is stored in register 2, and the instruction pointer is left with the value 2.
The instruction pointer is 2, which points at the instruction addi 0 1 0. This is like a relative jump: the value of the instruction pointer, 2, is loaded into register 0. Then, addi finds the result of adding the value in register 0 and the value 1, storing the result, 3, back in register 0. Register 0 is then copied back to the instruction pointer, which will cause it to end up 1 larger than it would have otherwise and skip the next instruction (addr 1 2 3) entirely. Finally, 1 is added to the instruction pointer.
The instruction pointer is 4, so the instruction setr 1 0 0 is run. This is like an absolute jump: it copies the value contained in register 1, 5, into register 0, which causes it to end up in the instruction pointer. The instruction pointer is then incremented, leaving it at 6.
The instruction pointer is 6, so the instruction seti 9 0 5 stores 9 into register 5. The instruction pointer is incremented, causing it to point outside the program, and so the program ends.
What value is left in register 0 when the background process halts?
| 338
|
--- Day 18: Boiling Boulders ---
You and the elephants finally reach fresh air. You've emerged near the base of a large volcano that seems to be actively erupting! Fortunately, the lava seems to be flowing away from you and toward the ocean.
Bits of lava are still being ejected toward you, so you're sheltering in the cavern exit a little longer. Outside the cave, you can see the lava landing in a pond and hear it loudly hissing as it solidifies.
Depending on the specific compounds in the lava and speed at which it cools, it might be forming obsidian! The cooling rate should be based on the surface area of the lava droplets, so you take a quick scan of a droplet as it flies past you (your puzzle input).
Because of how quickly the lava is moving, the scan isn't very good; its resolution is quite low and, as a result, it approximates the shape of the lava droplet with 1x1x1 cubes on a 3D grid, each given as its x,y,z position.
To approximate the surface area, count the number of sides of each cube that are not immediately connected to another cube. So, if your scan were only two adjacent cubes like 1,1,1 and 2,1,1, each cube would have a single side covered and five sides exposed, a total surface area of 10 sides.
Here's a larger example:
2,2,2
1,2,2
3,2,2
2,1,2
2,3,2
2,2,1
2,2,3
2,2,4
2,2,6
1,2,5
3,2,5
2,1,5
2,3,5
In the above example, after counting up all the sides that aren't connected to another cube, the total surface area is 64.
What is the surface area of your scanned lava droplet?
Your puzzle answer was 4314.
--- Part Two ---
Something seems off about your calculation. The cooling rate depends on exterior surface area, but your calculation also included the surface area of air pockets trapped in the lava droplet.
Instead, consider only cube sides that could be reached by the water and steam as the lava droplet tumbles into the pond. The steam will expand to reach as much as possible, completely displacing any air on the outside of the lava droplet but never expanding diagonally.
In the larger example above, exactly one cube of air is trapped within the lava droplet (at 2,2,5), so the exterior surface area of the lava droplet is 58.
What is the exterior surface area of your scanned lava droplet?
| 339
|
--- Day 13: Knights of the Dinner Table ---
In years past, the holiday feast with your family hasn't gone so well. Not everyone gets along! This year, you resolve, will be different. You're going to find the optimal seating arrangement and avoid all those awkward conversations.
You start by writing up a list of everyone invited and the amount their happiness would increase or decrease if they were to find themselves sitting next to each other person. You have a circular table that will be just big enough to fit everyone comfortably, and so each person will have exactly two neighbors.
For example, suppose you have only four attendees planned, and you calculate their potential happiness as follows:
Alice would gain 54 happiness units by sitting next to Bob.
Alice would lose 79 happiness units by sitting next to Carol.
Alice would lose 2 happiness units by sitting next to David.
Bob would gain 83 happiness units by sitting next to Alice.
Bob would lose 7 happiness units by sitting next to Carol.
Bob would lose 63 happiness units by sitting next to David.
Carol would lose 62 happiness units by sitting next to Alice.
Carol would gain 60 happiness units by sitting next to Bob.
Carol would gain 55 happiness units by sitting next to David.
David would gain 46 happiness units by sitting next to Alice.
David would lose 7 happiness units by sitting next to Bob.
David would gain 41 happiness units by sitting next to Carol.
Then, if you seat Alice next to David, Alice would lose 2 happiness units (because David talks so much), but David would gain 46 happiness units (because Alice is such a good listener), for a total change of 44.
If you continue around the table, you could then seat Bob next to Alice (Bob gains 83, Alice gains 54). Finally, seat Carol, who sits next to Bob (Carol gains 60, Bob loses 7) and David (Carol gains 55, David gains 41). The arrangement looks like this:
+41 +46
+55 David -2
Carol Alice
+60 Bob +54
-7 +83
After trying every other seating arrangement in this hypothetical scenario, you find that this one is the most optimal, with a total change in happiness of 330.
What is the total change in happiness for the optimal seating arrangement of the actual guest list?
Your puzzle answer was 709.
--- Part Two ---
In all the commotion, you realize that you forgot to seat yourself. At this point, you're pretty apathetic toward the whole thing, and your happiness wouldn't really go up or down regardless of who you sit next to. You assume everyone else would be just as ambivalent about sitting next to you, too.
So, add yourself to the list, and give all happiness relationships that involve you a score of 0.
What is the total change in happiness for the optimal seating arrangement that actually includes yourself?
| 340
|
--- Day 23: Opening the Turing Lock ---
Little Jane Marie just got her very first computer for Christmas from some unknown benefactor. It comes with instructions and an example program, but the computer itself seems to be malfunctioning. She's curious what the program does, and would like you to help her run it.
The manual explains that the computer supports two registers and six instructions (truly, it goes on to remind the reader, a state-of-the-art technology). The registers are named a and b, can hold any non-negative integer, and begin with a value of 0. The instructions are as follows:
hlf r sets register r to half its current value, then continues with the next instruction.
tpl r sets register r to triple its current value, then continues with the next instruction.
inc r increments register r, adding 1 to it, then continues with the next instruction.
jmp offset is a jump; it continues with the instruction offset away relative to itself.
jie r, offset is like jmp, but only jumps if register r is even ("jump if even").
jio r, offset is like jmp, but only jumps if register r is 1 ("jump if one", not odd).
All three jump instructions work with an offset relative to that instruction. The offset is always written with a prefix + or - to indicate the direction of the jump (forward or backward, respectively). For example, jmp +1 would simply continue with the next instruction, while jmp +0 would continuously jump back to itself forever.
The program exits when it tries to run an instruction beyond the ones defined.
For example, this program sets a to 2, because the jio instruction causes it to skip the tpl instruction:
inc a
jio a, +2
tpl a
inc a
What is the value in register b when the program in your puzzle input is finished executing?
Your puzzle answer was 170.
--- Part Two ---
The unknown benefactor is very thankful for releasi-- er, helping little Jane Marie with her computer. Definitely not to distract you, what is the value in register b after the program is finished executing if register a starts as 1 instead?
| 341
|
--- Day 8: Haunted Wasteland ---
You're still riding a camel across Desert Island when you spot a sandstorm quickly approaching. When you turn to warn the Elf, she disappears before your eyes! To be fair, she had just finished warning you about ghosts a few minutes ago.
One of the camel's pouches is labeled "maps" - sure enough, it's full of documents (your puzzle input) about how to navigate the desert. At least, you're pretty sure that's what they are; one of the documents contains a list of left/right instructions, and the rest of the documents seem to describe some kind of network of labeled nodes.
It seems like you're meant to use the left/right instructions to navigate the network. Perhaps if you have the camel follow the same instructions, you can escape the haunted wasteland!
After examining the maps for a bit, two nodes stick out: AAA and ZZZ. You feel like AAA is where you are now, and you have to follow the left/right instructions until you reach ZZZ.
This format defines each node of the network individually. For example:
RL
AAA = (BBB, CCC)
BBB = (DDD, EEE)
CCC = (ZZZ, GGG)
DDD = (DDD, DDD)
EEE = (EEE, EEE)
GGG = (GGG, GGG)
ZZZ = (ZZZ, ZZZ)
Starting with AAA, you need to look up the next element based on the next left/right instruction in your input. In this example, start with AAA and go right (R) by choosing the right element of AAA, CCC. Then, L means to choose the left element of CCC, ZZZ. By following the left/right instructions, you reach ZZZ in 2 steps.
Of course, you might not find ZZZ right away. If you run out of left/right instructions, repeat the whole sequence of instructions as necessary: RL really means RLRLRLRLRLRLRLRL... and so on. For example, here is a situation that takes 6 steps to reach ZZZ:
LLR
AAA = (BBB, BBB)
BBB = (AAA, ZZZ)
ZZZ = (ZZZ, ZZZ)
Starting at AAA, follow the left/right instructions. How many steps are required to reach ZZZ?
| 342
|
--- Day 24: Arithmetic Logic Unit ---
Magic smoke starts leaking from the submarine's arithmetic logic unit (ALU). Without the ability to perform basic arithmetic and logic functions, the submarine can't produce cool patterns with its Christmas lights!
It also can't navigate. Or run the oxygen system.
Don't worry, though - you probably have enough oxygen left to give you enough time to build a new ALU.
The ALU is a four-dimensional processing unit: it has integer variables w, x, y, and z. These variables all start with the value 0. The ALU also supports six instructions:
inp a - Read an input value and write it to variable a.
add a b - Add the value of a to the value of b, then store the result in variable a.
mul a b - Multiply the value of a by the value of b, then store the result in variable a.
div a b - Divide the value of a by the value of b, truncate the result to an integer, then store the result in variable a. (Here, "truncate" means to round the value toward zero.)
mod a b - Divide the value of a by the value of b, then store the remainder in variable a. (This is also called the modulo operation.)
eql a b - If the value of a and b are equal, then store the value 1 in variable a. Otherwise, store the value 0 in variable a.
In all of these instructions, a and b are placeholders; a will always be the variable where the result of the operation is stored (one of w, x, y, or z), while b can be either a variable or a number. Numbers can be positive or negative, but will always be integers.
The ALU has no jump instructions; in an ALU program, every instruction is run exactly once in order from top to bottom. The program halts after the last instruction has finished executing.
(Program authors should be especially cautious; attempting to execute div with b=0 or attempting to execute mod with a<0 or b<=0 will cause the program to crash and might even damage the ALU. These operations are never intended in any serious ALU program.)
For example, here is an ALU program which takes an input number, negates it, and stores it in x:
inp x
mul x -1
Here is an ALU program which takes two input numbers, then sets z to 1 if the second input number is three times larger than the first input number, or sets z to 0 otherwise:
inp z
inp x
mul z 3
eql z x
Here is an ALU program which takes a non-negative integer as input, converts it into binary, and stores the lowest (1's) bit in z, the second-lowest (2's) bit in y, the third-lowest (4's) bit in x, and the fourth-lowest (8's) bit in w:
inp w
add z w
mod z 2
div w 2
add y w
mod y 2
div w 2
add x w
mod x 2
div w 2
mod w 2
Once you have built a replacement ALU, you can install it in the submarine, which will immediately resume what it was doing when the ALU failed: validating the submarine's model number. To do this, the ALU will run the MOdel Number Automatic Detector program (MONAD, your puzzle input).
Submarine model numbers are always fourteen-digit numbers consisting only of digits 1 through 9. The digit 0 cannot appear in a model number.
When MONAD checks a hypothetical fourteen-digit model number, it uses fourteen separate inp instructions, each expecting a single digit of the model number in order of most to least significant. (So, to check the model number 13579246899999, you would give 1 to the first inp instruction, 3 to the second inp instruction, 5 to the third inp instruction, and so on.) This means that when operating MONAD, each input instruction should only ever be given an integer value of at least 1 and at most 9.
Then, after MONAD has finished running all of its instructions, it will indicate that the model number was valid by leaving a 0 in variable z. However, if the model number was invalid, it will leave some other non-zero value in z.
MONAD imposes additional, mysterious restrictions on model numbers, and legend says the last copy of the MONAD documentation was eaten by a tanuki. You'll need to figure out what MONAD does some other way.
To enable as many submarine features as possible, find the largest valid fourteen-digit model number that contains no 0 digits. What is the largest model number accepted by MONAD?
Your puzzle answer was 94399898949959.
--- Part Two ---
As the submarine starts booting up things like the Retro Encabulator, you realize that maybe you don't need all these submarine features after all.
What is the smallest model number accepted by MONAD?
| 343
|
--- Day 6: Probably a Fire Hazard ---
Because your neighbors keep defeating you in the holiday house decorating contest year after year, you've decided to deploy one million lights in a 1000x1000 grid.
Furthermore, because you've been especially nice this year, Santa has mailed you instructions on how to display the ideal lighting configuration.
Lights in your grid are numbered from 0 to 999 in each direction; the lights at each corner are at 0,0, 0,999, 999,999, and 999,0. The instructions include whether to turn on, turn off, or toggle various inclusive ranges given as coordinate pairs. Each coordinate pair represents opposite corners of a rectangle, inclusive; a coordinate pair like 0,0 through 2,2 therefore refers to 9 lights in a 3x3 square. The lights all start turned off.
To defeat your neighbors this year, all you have to do is set up your lights by doing the instructions Santa sent you in order.
For example:
turn on 0,0 through 999,999 would turn on (or leave on) every light.
toggle 0,0 through 999,0 would toggle the first line of 1000 lights, turning off the ones that were on, and turning on the ones that were off.
turn off 499,499 through 500,500 would turn off (or leave off) the middle four lights.
After following the instructions, how many lights are lit?
Your puzzle answer was 569999.
--- Part Two ---
You just finish implementing your winning light pattern when you realize you mistranslated Santa's message from Ancient Nordic Elvish.
The light grid you bought actually has individual brightness controls; each light can have a brightness of zero or more. The lights all start at zero.
The phrase turn on actually means that you should increase the brightness of those lights by 1.
The phrase turn off actually means that you should decrease the brightness of those lights by 1, to a minimum of zero.
The phrase toggle actually means that you should increase the brightness of those lights by 2.
What is the total brightness of all lights combined after following Santa's instructions?
For example:
turn on 0,0 through 0,0 would increase the total brightness by 1.
toggle 0,0 through 999,999 would increase the total brightness by 2000000.
| 344
|
--- Day 15: Warehouse Woes ---
You appear back inside your own mini submarine! Each Historian drives their mini submarine in a different direction; maybe the Chief has his own submarine down here somewhere as well?
You look up to see a vast school of lanternfish swimming past you. On closer inspection, they seem quite anxious, so you drive your mini submarine over to see if you can help.
Because lanternfish populations grow rapidly, they need a lot of food, and that food needs to be stored somewhere. That's why these lanternfish have built elaborate warehouse complexes operated by robots!
These lanternfish seem so anxious because they have lost control of the robot that operates one of their most important warehouses! It is currently running amok, pushing around boxes in the warehouse with no regard for lanternfish logistics or lanternfish inventory management strategies.
Right now, none of the lanternfish are brave enough to swim up to an unpredictable robot so they could shut it off. However, if you could anticipate the robot's movements, maybe they could find a safe option.
The lanternfish already have a map of the warehouse and a list of movements the robot will attempt to make (your puzzle input). The problem is that the movements will sometimes fail as boxes are shifted around, making the actual movements of the robot difficult to predict.
For example:
##########
#..O..O.O#
#......O.#
#.OO..O.O#
#[email protected].#
#O#..O...#
#O..O..O.#
#.OO.O.OO#
#....O...#
##########
<vv>^<v^>v>^vv^v>v<>v^v<v<^vv<<<^><<><>>v<vvv<>^v^>^<<<><<v<<<v^vv^v>^
vvv<<^>^v^^><<>>><>^<<><^vv^^<>vvv<>><^^v>^>vv<>v<<<<v<^v>^<^^>>>^<v<v
><>vv>v^v^<>><>>>><^^>vv>v<^^^>>v^v^<^^>v^^>v^<^v>v<>>v^v^<v>v^^<^^vv<
<<v<^>>^^^^>>>v^<>vvv^><v<<<>^^^vv^<vvv>^>v<^^^^v<>^>vvvv><>>v^<<^^^^^
^><^><>>><>^^<<^^v>>><^<v>^<vv>>v>>>^v><>^v><<<<v>>v<v<v>vvv>^<><<>^><
^>><>^v<><^vvv<^^<><v<<<<<><^v<<<><<<^^<v<^^^><^>>^<v^><<<^>>^v<v^v<v^
>^>>^v>vv>^<<^v<>><<><<v<<v><>v<^vv<<<>^^v^>^^>>><<^v>>v^v><^^>>^<>vv^
<><^^>^^^<><vvvvv^v<v<<>^v<v>v<<^><<><<><<<^^<<<^<<>><<><^^^>^^<>^>v<>
^^>vv<^v^v<vv>^<><v<^v>^^^>>>^^vvv^>vvv<>>>^<^>>>>>^<<^v>^vvv<>^<><<v>
v^^>>><<^^<>>^v^<v^vv<>v^<<>^<^v^v><^<<<><<^<v><v<>vv>>v><v^<vv<>v^<<^
As the robot (@) attempts to move, if there are any boxes (O) in the way, the robot will also attempt to push those boxes. However, if this action would cause the robot or a box to move into a wall (#), nothing moves instead, including the robot. The initial positions of these are shown on the map at the top of the document the lanternfish gave you.
The rest of the document describes the moves (^ for up, v for down, < for left, > for right) that the robot will attempt to make, in order. (The moves form a single giant sequence; they are broken into multiple lines just to make copy-pasting easier. Newlines within the move sequence should be ignored.)
Here is a smaller example to get started:
########
#..O.O.#
##@.O..#
#...O..#
#.#.O..#
#...O..#
#......#
########
<^^>>>vv<v>>v<<
Were the robot to attempt the given sequence of moves, it would push around the boxes as follows:
Initial state:
########
#..O.O.#
##@.O..#
#...O..#
#.#.O..#
#...O..#
#......#
########
Move <:
########
#..O.O.#
##@.O..#
#...O..#
#.#.O..#
#...O..#
#......#
########
Move ^:
########
#[email protected].#
##..O..#
#...O..#
#.#.O..#
#...O..#
#......#
########
Move ^:
########
#[email protected].#
##..O..#
#...O..#
#.#.O..#
#...O..#
#......#
########
Move >:
########
#..@OO.#
##..O..#
#...O..#
#.#.O..#
#...O..#
#......#
########
Move >:
########
#...@OO#
##..O..#
#...O..#
#.#.O..#
#...O..#
#......#
########
Move >:
########
#...@OO#
##..O..#
#...O..#
#.#.O..#
#...O..#
#......#
########
Move v:
########
#....OO#
##..@..#
#...O..#
#.#.O..#
#...O..#
#...O..#
########
Move v:
########
#....OO#
##..@..#
#...O..#
#.#.O..#
#...O..#
#...O..#
########
Move <:
########
#....OO#
##.@...#
#...O..#
#.#.O..#
#...O..#
#...O..#
########
Move v:
########
#....OO#
##.....#
#..@O..#
#.#.O..#
#...O..#
#...O..#
########
Move >:
########
#....OO#
##.....#
#...@O.#
#.#.O..#
#...O..#
#...O..#
########
Move >:
########
#....OO#
##.....#
#....@O#
#.#.O..#
#...O..#
#...O..#
########
Move v:
########
#....OO#
##.....#
#.....O#
#.#.O@.#
#...O..#
#...O..#
########
Move <:
########
#....OO#
##.....#
#.....O#
#.#O@..#
#...O..#
#...O..#
########
Move <:
########
#....OO#
##.....#
#.....O#
#.#O@..#
#...O..#
#...O..#
########
The larger example has many more moves; after the robot has finished those moves, the warehouse would look like this:
##########
#.O.O.OOO#
#........#
#OO......#
#OO@.....#
#O#.....O#
#O.....OO#
#O.....OO#
#OO....OO#
##########
The lanternfish use their own custom Goods Positioning System (GPS for short) to track the locations of the boxes. The GPS coordinate of a box is equal to 100 times its distance from the top edge of the map plus its distance from the left edge of the map. (This process does not stop at wall tiles; measure all the way to the edges of the map.)
So, the box shown below has a distance of 1 from the top edge of the map and 4 from the left edge of the map, resulting in a GPS coordinate of 100 * 1 + 4 = 104.
#######
#...O..
#......
The lanternfish would like to know the sum of all boxes' GPS coordinates after the robot finishes moving. In the larger example, the sum of all boxes' GPS coordinates is 10092. In the smaller example, the sum is 2028.
Predict the motion of the robot and boxes in the warehouse. After the robot is finished moving, what is the sum of all boxes' GPS coordinates?
Your puzzle answer was 1505963.
The first half of this puzzle is complete! It provides one gold star: *
--- Part Two ---
The lanternfish use your information to find a safe moment to swim in and turn off the malfunctioning robot! Just as they start preparing a festival in your honor, reports start coming in that a second warehouse's robot is also malfunctioning.
This warehouse's layout is surprisingly similar to the one you just helped. There is one key difference: everything except the robot is twice as wide! The robot's list of movements doesn't change.
To get the wider warehouse's map, start with your original map and, for each tile, make the following changes:
If the tile is #, the new map contains ## instead.
If the tile is O, the new map contains [] instead.
If the tile is ., the new map contains .. instead.
If the tile is @, the new map contains @. instead.
This will produce a new warehouse map which is twice as wide and with wide boxes that are represented by []. (The robot does not change size.)
The larger example from before would now look like this:
####################
##....[]....[]..[]##
##............[]..##
##..[][]....[]..[]##
##....[]@.....[]..##
##[]##....[]......##
##[]....[]....[]..##
##..[][]..[]..[][]##
##........[]......##
####################
Because boxes are now twice as wide but the robot is still the same size and speed, boxes can be aligned such that they directly push two other boxes at once. For example, consider this situation:
#######
#...#.#
#.....#
#..OO@#
#..O..#
#.....#
#######
<vv<<^^<<^^
After appropriately resizing this map, the robot would push around these boxes as follows:
Initial state:
##############
##......##..##
##..........##
##....[][]@.##
##....[]....##
##..........##
##############
Move <:
##############
##......##..##
##..........##
##...[][]@..##
##....[]....##
##..........##
##############
Move v:
##############
##......##..##
##..........##
##...[][]...##
##....[].@..##
##..........##
##############
Move v:
##############
##......##..##
##..........##
##...[][]...##
##....[]....##
##.......@..##
##############
Move <:
##############
##......##..##
##..........##
##...[][]...##
##....[]....##
##......@...##
##############
Move <:
##############
##......##..##
##..........##
##...[][]...##
##....[]....##
##.....@....##
##############
Move ^:
##############
##......##..##
##...[][]...##
##....[]....##
##.....@....##
##..........##
##############
Move ^:
##############
##......##..##
##...[][]...##
##....[]....##
##.....@....##
##..........##
##############
Move <:
##############
##......##..##
##...[][]...##
##....[]....##
##....@.....##
##..........##
##############
Move <:
##############
##......##..##
##...[][]...##
##....[]....##
##...@......##
##..........##
##############
Move ^:
##############
##......##..##
##...[][]...##
##...@[]....##
##..........##
##..........##
##############
Move ^:
##############
##...[].##..##
##...@.[]...##
##....[]....##
##..........##
##..........##
##############
This warehouse also uses GPS to locate the boxes. For these larger boxes, distances are measured from the edge of the map to the closest edge of the box in question. So, the box shown below has a distance of 1 from the top edge of the map and 5 from the left edge of the map, resulting in a GPS coordinate of 100 * 1 + 5 = 105.
##########
##...[]...
##........
In the scaled-up version of the larger example from above, after the robot has finished all of its moves, the warehouse would look like this:
####################
##[].......[].[][]##
##[]...........[].##
##[]........[][][]##
##[]......[]....[]##
##..##......[]....##
##..[]............##
##..@......[].[][]##
##......[][]..[]..##
####################
The sum of these boxes' GPS coordinates is 9021.
Predict the motion of the robot and boxes in this new, scaled-up warehouse. What is the sum of all boxes' final GPS coordinates?
| 345
|
--- Day 23: Experimental Emergency Teleportation ---
Using your torch to search the darkness of the rocky cavern, you finally locate the man's friend: a small reindeer.
You're not sure how it got so far in this cave. It looks sick - too sick to walk - and too heavy for you to carry all the way back. Sleighs won't be invented for another 1500 years, of course.
The only option is experimental emergency teleportation.
You hit the "experimental emergency teleportation" button on the device and push I accept the risk on no fewer than 18 different warning messages. Immediately, the device deploys hundreds of tiny nanobots which fly around the cavern, apparently assembling themselves into a very specific formation. The device lists the X,Y,Z position (pos) for each nanobot as well as its signal radius (r) on its tiny screen (your puzzle input).
Each nanobot can transmit signals to any integer coordinate which is a distance away from it less than or equal to its signal radius (as measured by Manhattan distance). Coordinates a distance away of less than or equal to a nanobot's signal radius are said to be in range of that nanobot.
Before you start the teleportation process, you should determine which nanobot is the strongest (that is, which has the largest signal radius) and then, for that nanobot, the total number of nanobots that are in range of it, including itself.
For example, given the following nanobots:
pos=<0,0,0>, r=4
pos=<1,0,0>, r=1
pos=<4,0,0>, r=3
pos=<0,2,0>, r=1
pos=<0,5,0>, r=3
pos=<0,0,3>, r=1
pos=<1,1,1>, r=1
pos=<1,1,2>, r=1
pos=<1,3,1>, r=1
The strongest nanobot is the first one (position 0,0,0) because its signal radius, 4 is the largest. Using that nanobot's location and signal radius, the following nanobots are in or out of range:
The nanobot at 0,0,0 is distance 0 away, and so it is in range.
The nanobot at 1,0,0 is distance 1 away, and so it is in range.
The nanobot at 4,0,0 is distance 4 away, and so it is in range.
The nanobot at 0,2,0 is distance 2 away, and so it is in range.
The nanobot at 0,5,0 is distance 5 away, and so it is not in range.
The nanobot at 0,0,3 is distance 3 away, and so it is in range.
The nanobot at 1,1,1 is distance 3 away, and so it is in range.
The nanobot at 1,1,2 is distance 4 away, and so it is in range.
The nanobot at 1,3,1 is distance 5 away, and so it is not in range.
In this example, in total, 7 nanobots are in range of the nanobot with the largest signal radius.
Find the nanobot with the largest signal radius. How many nanobots are in range of its signals?
Your puzzle answer was 619.
--- Part Two ---
Now, you just need to figure out where to position yourself so that you're actually teleported when the nanobots activate.
To increase the probability of success, you need to find the coordinate which puts you in range of the largest number of nanobots. If there are multiple, choose one closest to your position (0,0,0, measured by manhattan distance).
For example, given the following nanobot formation:
pos=<10,12,12>, r=2
pos=<12,14,12>, r=2
pos=<16,12,12>, r=4
pos=<14,14,14>, r=6
pos=<50,50,50>, r=200
pos=<10,10,10>, r=5
Many coordinates are in range of some of the nanobots in this formation. However, only the coordinate 12,12,12 is in range of the most nanobots: it is in range of the first five, but is not in range of the nanobot at 10,10,10. (All other coordinates are in range of fewer than five nanobots.) This coordinate's distance from 0,0,0 is 36.
Find the coordinates that are in range of the largest number of nanobots. What is the shortest manhattan distance between any of those points and 0,0,0?
| 346
|
--- Day 20: Trench Map ---
With the scanners fully deployed, you turn their attention to mapping the floor of the ocean trench.
When you get back the image from the scanners, it seems to just be random noise. Perhaps you can combine an image enhancement algorithm and the input image (your puzzle input) to clean it up a little.
For example:
..#.#..#####.#.#.#.###.##.....###.##.#..###.####..#####..#....#..#..##..##
#..######.###...####..#..#####..##..#.#####...##.#.#..#.##..#.#......#.###
.######.###.####...#.##.##..#..#..#####.....#.#....###..#.##......#.....#.
.#..#..##..#...##.######.####.####.#.#...#.......#..#.#.#...####.##.#.....
.#..#...##.#.##..#...##.#.##..###.#......#.#.......#.#.#.####.###.##...#..
...####.#..#..#.##.#....##..#.####....##...##..#...#......#.#.......#.....
..##..####..#...#.#.#...##..#.#..###..#####........#..####......#..#
#..#.
#....
##..#
..#..
..###
The first section is the image enhancement algorithm. It is normally given on a single line, but it has been wrapped to multiple lines in this example for legibility. The second section is the input image, a two-dimensional grid of light pixels (#) and dark pixels (.).
The image enhancement algorithm describes how to enhance an image by simultaneously converting all pixels in the input image into an output image. Each pixel of the output image is determined by looking at a 3x3 square of pixels centered on the corresponding input image pixel. So, to determine the value of the pixel at (5,10) in the output image, nine pixels from the input image need to be considered: (4,9), (4,10), (4,11), (5,9), (5,10), (5,11), (6,9), (6,10), and (6,11). These nine input pixels are combined into a single binary number that is used as an index in the image enhancement algorithm string.
For example, to determine the output pixel that corresponds to the very middle pixel of the input image, the nine pixels marked by [...] would need to be considered:
# . . # .
#[. . .].
#[# . .]#
.[. # .].
. . # # #
Starting from the top-left and reading across each row, these pixels are ..., then #.., then .#.; combining these forms ...#...#.. By turning dark pixels (.) into 0 and light pixels (#) into 1, the binary number 000100010 can be formed, which is 34 in decimal.
The image enhancement algorithm string is exactly 512 characters long, enough to match every possible 9-bit binary number. The first few characters of the string (numbered starting from zero) are as follows:
0 10 20 30 34 40 50 60 70
| | | | | | | | |
..#.#..#####.#.#.#.###.##.....###.##.#..###.####..#####..#....#..#..##..##
In the middle of this first group of characters, the character at index 34 can be found: #. So, the output pixel in the center of the output image should be #, a light pixel.
This process can then be repeated to calculate every pixel of the output image.
Through advances in imaging technology, the images being operated on here are infinite in size. Every pixel of the infinite output image needs to be calculated exactly based on the relevant pixels of the input image. The small input image you have is only a small region of the actual infinite input image; the rest of the input image consists of dark pixels (.). For the purposes of the example, to save on space, only a portion of the infinite-sized input and output images will be shown.
The starting input image, therefore, looks something like this, with more dark pixels (.) extending forever in every direction not shown here:
...............
...............
...............
...............
...............
.....#..#......
.....#.........
.....##..#.....
.......#.......
.......###.....
...............
...............
...............
...............
...............
By applying the image enhancement algorithm to every pixel simultaneously, the following output image can be obtained:
...............
...............
...............
...............
.....##.##.....
....#..#.#.....
....##.#..#....
....####..#....
.....#..##.....
......##..#....
.......#.#.....
...............
...............
...............
...............
Through further advances in imaging technology, the above output image can also be used as an input image! This allows it to be enhanced a second time:
...............
...............
...............
..........#....
....#..#.#.....
...#.#...###...
...#...##.#....
...#.....#.#...
....#.#####....
.....#.#####...
......##.##....
.......###.....
...............
...............
...............
Truly incredible - now the small details are really starting to come through. After enhancing the original input image twice, 35 pixels are lit.
Start with the original input image and apply the image enhancement algorithm twice, being careful to account for the infinite size of the images. How many pixels are lit in the resulting image?
Your puzzle answer was 5464.
--- Part Two ---
You still can't quite make out the details in the image. Maybe you just didn't enhance it enough.
If you enhance the starting input image in the above example a total of 50 times, 3351 pixels are lit in the final output image.
Start again with the original input image and apply the image enhancement algorithm 50 times. How many pixels are lit in the resulting image?
| 347
|
--- Day 21: Monkey Math ---
The monkeys are back! You're worried they're going to try to steal your stuff again, but it seems like they're just holding their ground and making various monkey noises at you.
Eventually, one of the elephants realizes you don't speak monkey and comes over to interpret. As it turns out, they overheard you talking about trying to find the grove; they can show you a shortcut if you answer their riddle.
Each monkey is given a job: either to yell a specific number or to yell the result of a math operation. All of the number-yelling monkeys know their number from the start; however, the math operation monkeys need to wait for two other monkeys to yell a number, and those two other monkeys might also be waiting on other monkeys.
Your job is to work out the number the monkey named root will yell before the monkeys figure it out themselves.
For example:
root: pppw + sjmn
dbpl: 5
cczh: sllz + lgvd
zczc: 2
ptdq: humn - dvpt
dvpt: 3
lfqf: 4
humn: 5
ljgn: 2
sjmn: drzm * dbpl
sllz: 4
pppw: cczh / lfqf
lgvd: ljgn * ptdq
drzm: hmdt - zczc
hmdt: 32
Each line contains the name of a monkey, a colon, and then the job of that monkey:
A lone number means the monkey's job is simply to yell that number.
A job like aaaa + bbbb means the monkey waits for monkeys aaaa and bbbb to yell each of their numbers; the monkey then yells the sum of those two numbers.
aaaa - bbbb means the monkey yells aaaa's number minus bbbb's number.
Job aaaa * bbbb will yell aaaa's number multiplied by bbbb's number.
Job aaaa / bbbb will yell aaaa's number divided by bbbb's number.
So, in the above example, monkey drzm has to wait for monkeys hmdt and zczc to yell their numbers. Fortunately, both hmdt and zczc have jobs that involve simply yelling a single number, so they do this immediately: 32 and 2. Monkey drzm can then yell its number by finding 32 minus 2: 30.
Then, monkey sjmn has one of its numbers (30, from monkey drzm), and already has its other number, 5, from dbpl. This allows it to yell its own number by finding 30 multiplied by 5: 150.
This process continues until root yells a number: 152.
However, your actual situation involves considerably more monkeys. What number will the monkey named root yell?
Your puzzle answer was 56490240862410.
--- Part Two ---
Due to some kind of monkey-elephant-human mistranslation, you seem to have misunderstood a few key details about the riddle.
First, you got the wrong job for the monkey named root; specifically, you got the wrong math operation. The correct operation for monkey root should be =, which means that it still listens for two numbers (from the same two monkeys as before), but now checks that the two numbers match.
Second, you got the wrong monkey for the job starting with humn:. It isn't a monkey - it's you. Actually, you got the job wrong, too: you need to figure out what number you need to yell so that root's equality check passes. (The number that appears after humn: in your input is now irrelevant.)
In the above example, the number you need to yell to pass root's equality test is 301. (This causes root to get the same number, 150, from both of its monkeys.)
What number do you yell to pass root's equality test?
| 348
|
--- Day 11: Plutonian Pebbles ---
The ancient civilization on Pluto was known for its ability to manipulate spacetime, and while The Historians explore their infinite corridors, you've noticed a strange set of physics-defying stones.
At first glance, they seem like normal stones: they're arranged in a perfectly straight line, and each stone has a number engraved on it.
The strange part is that every time you blink, the stones change.
Sometimes, the number engraved on a stone changes. Other times, a stone might split in two, causing all the other stones to shift over a bit to make room in their perfectly straight line.
As you observe them for a while, you find that the stones have a consistent behavior. Every time you blink, the stones each simultaneously change according to the first applicable rule in this list:
If the stone is engraved with the number 0, it is replaced by a stone engraved with the number 1.
If the stone is engraved with a number that has an even number of digits, it is replaced by two stones. The left half of the digits are engraved on the new left stone, and the right half of the digits are engraved on the new right stone. (The new numbers don't keep extra leading zeroes: 1000 would become stones 10 and 0.)
If none of the other rules apply, the stone is replaced by a new stone; the old stone's number multiplied by 2024 is engraved on the new stone.
No matter how the stones change, their order is preserved, and they stay on their perfectly straight line.
How will the stones evolve if you keep blinking at them? You take a note of the number engraved on each stone in the line (your puzzle input).
If you have an arrangement of five stones engraved with the numbers 0 1 10 99 999 and you blink once, the stones transform as follows:
The first stone, 0, becomes a stone marked 1.
The second stone, 1, is multiplied by 2024 to become 2024.
The third stone, 10, is split into a stone marked 1 followed by a stone marked 0.
The fourth stone, 99, is split into two stones marked 9.
The fifth stone, 999, is replaced by a stone marked 2021976.
So, after blinking once, your five stones would become an arrangement of seven stones engraved with the numbers 1 2024 1 0 9 9 2021976.
Here is a longer example:
Initial arrangement:
125 17
After 1 blink:
253000 1 7
After 2 blinks:
253 0 2024 14168
After 3 blinks:
512072 1 20 24 28676032
After 4 blinks:
512 72 2024 2 0 2 4 2867 6032
After 5 blinks:
1036288 7 2 20 24 4048 1 4048 8096 28 67 60 32
After 6 blinks:
2097446912 14168 4048 2 0 2 4 40 48 2024 40 48 80 96 2 8 6 7 6 0 3 2
In this example, after blinking six times, you would have 22 stones. After blinking 25 times, you would have 55312 stones!
Consider the arrangement of stones in front of you. How many stones will you have after blinking 25 times?
| 349
|
--- Day 20: Donut Maze ---
You notice a strange pattern on the surface of Pluto and land nearby to get a closer look. Upon closer inspection, you realize you've come across one of the famous space-warping mazes of the long-lost Pluto civilization!
Because there isn't much space on Pluto, the civilization that used to live here thrived by inventing a method for folding spacetime. Although the technology is no longer understood, mazes like this one provide a small glimpse into the daily life of an ancient Pluto citizen.
This maze is shaped like a donut. Portals along the inner and outer edge of the donut can instantly teleport you from one side to the other. For example:
A
A
#######.#########
#######.........#
#######.#######.#
#######.#######.#
#######.#######.#
##### B ###.#
BC...## C ###.#
##.## ###.#
##...DE F ###.#
##### G ###.#
#########.#####.#
DE..#######...###.#
#.#########.###.#
FG..#########.....#
###########.#####
Z
Z
This map of the maze shows solid walls (#) and open passages (.). Every maze on Pluto has a start (the open tile next to AA) and an end (the open tile next to ZZ). Mazes on Pluto also have portals; this maze has three pairs of portals: BC, DE, and FG. When on an open tile next to one of these labels, a single step can take you to the other tile with the same label. (You can only walk on . tiles; labels and empty space are not traversable.)
One path through the maze doesn't require any portals. Starting at AA, you could go down 1, right 8, down 12, left 4, and down 1 to reach ZZ, a total of 26 steps.
However, there is a shorter path: You could walk from AA to the inner BC portal (4 steps), warp to the outer BC portal (1 step), walk to the inner DE (6 steps), warp to the outer DE (1 step), walk to the outer FG (4 steps), warp to the inner FG (1 step), and finally walk to ZZ (6 steps). In total, this is only 23 steps.
Here is a larger example:
A
A
#################.#############
#.#...#...................#.#.#
#.#.#.###.###.###.#########.#.#
#.#.#.......#...#.....#.#.#...#
#.#########.###.#####.#.#.###.#
#.............#.#.....#.......#
###.###########.###.#####.#.#.#
#.....# A C #.#.#.#
####### S P #####.#
#.#...# #......VT
#.#.#.# #.#####
#...#.# YN....#.#
#.###.# #####.#
DI....#.# #.....#
#####.# #.###.#
ZZ......# QG....#..AS
###.### #######
JO..#.#.# #.....#
#.#.#.# ###.#.#
#...#..DI BU....#..LF
#####.# #.#####
YN......# VT..#....QG
#.###.# #.###.#
#.#...# #.....#
###.### J L J #.#.###
#.....# O F P #.#...#
#.###.#####.#.#####.#####.###.#
#...#.#.#...#.....#.....#.#...#
#.#####.###.###.#.#.#########.#
#...#.#.....#...#.#.#.#.....#.#
#.###.#####.###.###.#.#.#######
#.#.........#...#.............#
#########.###.###.#############
B J C
U P P
Here, AA has no direct path to ZZ, but it does connect to AS and CP. By passing through AS, QG, BU, and JO, you can reach ZZ in 58 steps.
In your maze, how many steps does it take to get from the open tile marked AA to the open tile marked ZZ?
Your puzzle answer was 714.
--- Part Two ---
Strangely, the exit isn't open when you reach it. Then, you remember: the ancient Plutonians were famous for building recursive spaces.
The marked connections in the maze aren't portals: they physically connect to a larger or smaller copy of the maze. Specifically, the labeled tiles around the inside edge actually connect to a smaller copy of the same maze, and the smaller copy's inner labeled tiles connect to yet a smaller copy, and so on.
When you enter the maze, you are at the outermost level; when at the outermost level, only the outer labels AA and ZZ function (as the start and end, respectively); all other outer labeled tiles are effectively walls. At any other level, AA and ZZ count as walls, but the other outer labeled tiles bring you one level outward.
Your goal is to find a path through the maze that brings you back to ZZ at the outermost level of the maze.
In the first example above, the shortest path is now the loop around the right side. If the starting level is 0, then taking the previously-shortest path would pass through BC (to level 1), DE (to level 2), and FG (back to level 1). Because this is not the outermost level, ZZ is a wall, and the only option is to go back around to BC, which would only send you even deeper into the recursive maze.
In the second example above, there is no path that brings you to ZZ at the outermost level.
Here is a more interesting example:
Z L X W C
Z P Q B K
###########.#.#.#.#######.###############
#...#.......#.#.......#.#.......#.#.#...#
###.#.#.#.#.#.#.#.###.#.#.#######.#.#.###
#.#...#.#.#...#.#.#...#...#...#.#.......#
#.###.#######.###.###.#.###.###.#.#######
#...#.......#.#...#...#.............#...#
#.#########.#######.#.#######.#######.###
#...#.# F R I Z #.#.#.#
#.###.# D E C H #.#.#.#
#.#...# #...#.#
#.###.# #.###.#
#.#....OA WB..#.#..ZH
#.###.# #.#.#.#
CJ......# #.....#
####### #######
#.#....CK #......IC
#.###.# #.###.#
#.....# #...#.#
###.### #.#.#.#
XF....#.# RF..#.#.#
#####.# #######
#......CJ NM..#...#
###.#.# #.###.#
RE....#.# #......RF
###.### X X L #.#.#.#
#.....# F Q P #.#.#.#
###.###########.###.#######.#########.###
#.....#...#.....#.......#...#.....#.#...#
#####.#.###.#######.#######.###.###.#.#.#
#.......#.......#.#.#.#.#...#...#...#.#.#
#####.###.#####.#.#.#.#.###.###.#.###.###
#.......#.....#.#...#...............#...#
#############.#.#.###.###################
A O F N
A A D M
One shortest path through the maze is the following:
Walk from AA to XF (16 steps)
Recurse into level 1 through XF (1 step)
Walk from XF to CK (10 steps)
Recurse into level 2 through CK (1 step)
Walk from CK to ZH (14 steps)
Recurse into level 3 through ZH (1 step)
Walk from ZH to WB (10 steps)
Recurse into level 4 through WB (1 step)
Walk from WB to IC (10 steps)
Recurse into level 5 through IC (1 step)
Walk from IC to RF (10 steps)
Recurse into level 6 through RF (1 step)
Walk from RF to NM (8 steps)
Recurse into level 7 through NM (1 step)
Walk from NM to LP (12 steps)
Recurse into level 8 through LP (1 step)
Walk from LP to FD (24 steps)
Recurse into level 9 through FD (1 step)
Walk from FD to XQ (8 steps)
Recurse into level 10 through XQ (1 step)
Walk from XQ to WB (4 steps)
Return to level 9 through WB (1 step)
Walk from WB to ZH (10 steps)
Return to level 8 through ZH (1 step)
Walk from ZH to CK (14 steps)
Return to level 7 through CK (1 step)
Walk from CK to XF (10 steps)
Return to level 6 through XF (1 step)
Walk from XF to OA (14 steps)
Return to level 5 through OA (1 step)
Walk from OA to CJ (8 steps)
Return to level 4 through CJ (1 step)
Walk from CJ to RE (8 steps)
Return to level 3 through RE (1 step)
Walk from RE to IC (4 steps)
Recurse into level 4 through IC (1 step)
Walk from IC to RF (10 steps)
Recurse into level 5 through RF (1 step)
Walk from RF to NM (8 steps)
Recurse into level 6 through NM (1 step)
Walk from NM to LP (12 steps)
Recurse into level 7 through LP (1 step)
Walk from LP to FD (24 steps)
Recurse into level 8 through FD (1 step)
Walk from FD to XQ (8 steps)
Recurse into level 9 through XQ (1 step)
Walk from XQ to WB (4 steps)
Return to level 8 through WB (1 step)
Walk from WB to ZH (10 steps)
Return to level 7 through ZH (1 step)
Walk from ZH to CK (14 steps)
Return to level 6 through CK (1 step)
Walk from CK to XF (10 steps)
Return to level 5 through XF (1 step)
Walk from XF to OA (14 steps)
Return to level 4 through OA (1 step)
Walk from OA to CJ (8 steps)
Return to level 3 through CJ (1 step)
Walk from CJ to RE (8 steps)
Return to level 2 through RE (1 step)
Walk from RE to XQ (14 steps)
Return to level 1 through XQ (1 step)
Walk from XQ to FD (8 steps)
Return to level 0 through FD (1 step)
Walk from FD to ZZ (18 steps)
This path takes a total of 396 steps to move from AA at the outermost layer to ZZ at the outermost layer.
In your maze, when accounting for recursion, how many steps does it take to get from the open tile marked AA to the open tile marked ZZ, both at the outermost layer?
| 350
|
--- Day 12: Hill Climbing Algorithm ---
You try contacting the Elves using your handheld device, but the river you're following must be too low to get a decent signal.
You ask the device for a heightmap of the surrounding area (your puzzle input). The heightmap shows the local area from above broken into a grid; the elevation of each square of the grid is given by a single lowercase letter, where a is the lowest elevation, b is the next-lowest, and so on up to the highest elevation, z.
Also included on the heightmap are marks for your current position (S) and the location that should get the best signal (E). Your current position (S) has elevation a, and the location that should get the best signal (E) has elevation z.
You'd like to reach E, but to save energy, you should do it in as few steps as possible. During each step, you can move exactly one square up, down, left, or right. To avoid needing to get out your climbing gear, the elevation of the destination square can be at most one higher than the elevation of your current square; that is, if your current elevation is m, you could step to elevation n, but not to elevation o. (This also means that the elevation of the destination square can be much lower than the elevation of your current square.)
For example:
Sabqponm
abcryxxl
accszExk
acctuvwj
abdefghi
Here, you start in the top-left corner; your goal is near the middle. You could start by moving down or right, but eventually you'll need to head toward the e at the bottom. From there, you can spiral around to the goal:
v..v<<<<
>v.vv<<^
.>vv>E^^
..v>>>^^
..>>>>>^
In the above diagram, the symbols indicate whether the path exits each square moving up (^), down (v), left (<), or right (>). The location that should get the best signal is still E, and . marks unvisited squares.
This path reaches the goal in 31 steps, the fewest possible.
What is the fewest steps required to move from your current position to the location that should get the best signal?
Your puzzle answer was 423.
--- Part Two ---
As you walk up the hill, you suspect that the Elves will want to turn this into a hiking trail. The beginning isn't very scenic, though; perhaps you can find a better starting point.
To maximize exercise while hiking, the trail should start as low as possible: elevation a. The goal is still the square marked E. However, the trail should still be direct, taking the fewest steps to reach its goal. So, you'll need to find the shortest path from any square at elevation a to the square marked E.
Again consider the example from above:
Sabqponm
abcryxxl
accszExk
acctuvwj
abdefghi
Now, there are six choices for starting position (five marked a, plus the square marked S that counts as being at elevation a). If you start at the bottom-left square, you can reach the goal most quickly:
...v<<<<
...vv<<^
...v>E^^
.>v>>>^^
>^>>>>>^
This path reaches the goal in only 29 steps, the fewest possible.
What is the fewest steps required to move starting from any square with elevation a to the location that should get the best signal?
| 351
|
--- Day 17: Two Steps Forward ---
You're trying to access a secure vault protected by a 4x4 grid of small rooms connected by doors. You start in the top-left room (marked S), and you can access the vault (marked V) once you reach the bottom-right room:
#########
#S| | | #
#-#-#-#-#
# | | | #
#-#-#-#-#
# | | | #
#-#-#-#-#
# | | |
####### V
Fixed walls are marked with #, and doors are marked with - or |.
The doors in your current room are either open or closed (and locked) based on the hexadecimal MD5 hash of a passcode (your puzzle input) followed by a sequence of uppercase characters representing the path you have taken so far (U for up, D for down, L for left, and R for right).
Only the first four characters of the hash are used; they represent, respectively, the doors up, down, left, and right from your current position. Any b, c, d, e, or f means that the corresponding door is open; any other character (any number or a) means that the corresponding door is closed and locked.
To access the vault, all you need to do is reach the bottom-right room; reaching this room opens the vault and all doors in the maze.
For example, suppose the passcode is hijkl. Initially, you have taken no steps, and so your path is empty: you simply find the MD5 hash of hijkl alone. The first four characters of this hash are ced9, which indicate that up is open (c), down is open (e), left is open (d), and right is closed and locked (9). Because you start in the top-left corner, there are no "up" or "left" doors to be open, so your only choice is down.
Next, having gone only one step (down, or D), you find the hash of hijklD. This produces f2bc, which indicates that you can go back up, left (but that's a wall), or right. Going right means hashing hijklDR to get 5745 - all doors closed and locked. However, going up instead is worthwhile: even though it returns you to the room you started in, your path would then be DU, opening a different set of doors.
After going DU (and then hashing hijklDU to get 528e), only the right door is open; after going DUR, all doors lock. (Fortunately, your actual passcode is not hijkl).
Passcodes actually used by Easter Bunny Vault Security do allow access to the vault if you know the right path. For example:
If your passcode were ihgpwlah, the shortest path would be DDRRRD.
With kglvqrro, the shortest path would be DDUDRLRRUDRD.
With ulqzkmiv, the shortest would be DRURDRUDDLLDLUURRDULRLDUUDDDRR.
Given your vault's passcode, what is the shortest path (the actual path, not just the length) to reach the vault?
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--- Day 7: The Sum of Its Parts ---
You find yourself standing on a snow-covered coastline; apparently, you landed a little off course. The region is too hilly to see the North Pole from here, but you do spot some Elves that seem to be trying to unpack something that washed ashore. It's quite cold out, so you decide to risk creating a paradox by asking them for directions.
"Oh, are you the search party?" Somehow, you can understand whatever Elves from the year 1018 speak; you assume it's Ancient Nordic Elvish. Could the device on your wrist also be a translator? "Those clothes don't look very warm; take this." They hand you a heavy coat.
"We do need to find our way back to the North Pole, but we have higher priorities at the moment. You see, believe it or not, this box contains something that will solve all of Santa's transportation problems - at least, that's what it looks like from the pictures in the instructions." It doesn't seem like they can read whatever language it's in, but you can: "Sleigh kit. Some assembly required."
"'Sleigh'? What a wonderful name! You must help us assemble this 'sleigh' at once!" They start excitedly pulling more parts out of the box.
The instructions specify a series of steps and requirements about which steps must be finished before others can begin (your puzzle input). Each step is designated by a single letter. For example, suppose you have the following instructions:
Step C must be finished before step A can begin.
Step C must be finished before step F can begin.
Step A must be finished before step B can begin.
Step A must be finished before step D can begin.
Step B must be finished before step E can begin.
Step D must be finished before step E can begin.
Step F must be finished before step E can begin.
Visually, these requirements look like this:
-->A--->B--
/ C -->D----->E
/
---->F-----
Your first goal is to determine the order in which the steps should be completed. If more than one step is ready, choose the step which is first alphabetically. In this example, the steps would be completed as follows:
Only C is available, and so it is done first.
Next, both A and F are available. A is first alphabetically, so it is done next.
Then, even though F was available earlier, steps B and D are now also available, and B is the first alphabetically of the three.
After that, only D and F are available. E is not available because only some of its prerequisites are complete. Therefore, D is completed next.
F is the only choice, so it is done next.
Finally, E is completed.
So, in this example, the correct order is CABDFE.
In what order should the steps in your instructions be completed?
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--- Day 12: The N-Body Problem ---
The space near Jupiter is not a very safe place; you need to be careful of a big distracting red spot, extreme radiation, and a whole lot of moons swirling around. You decide to start by tracking the four largest moons: Io, Europa, Ganymede, and Callisto.
After a brief scan, you calculate the position of each moon (your puzzle input). You just need to simulate their motion so you can avoid them.
Each moon has a 3-dimensional position (x, y, and z) and a 3-dimensional velocity. The position of each moon is given in your scan; the x, y, and z velocity of each moon starts at 0.
Simulate the motion of the moons in time steps. Within each time step, first update the velocity of every moon by applying gravity. Then, once all moons' velocities have been updated, update the position of every moon by applying velocity. Time progresses by one step once all of the positions are updated.
To apply gravity, consider every pair of moons. On each axis (x, y, and z), the velocity of each moon changes by exactly +1 or -1 to pull the moons together. For example, if Ganymede has an x position of 3, and Callisto has a x position of 5, then Ganymede's x velocity changes by +1 (because 5 > 3) and Callisto's x velocity changes by -1 (because 3 < 5). However, if the positions on a given axis are the same, the velocity on that axis does not change for that pair of moons.
Once all gravity has been applied, apply velocity: simply add the velocity of each moon to its own position. For example, if Europa has a position of x=1, y=2, z=3 and a velocity of x=-2, y=0,z=3, then its new position would be x=-1, y=2, z=6. This process does not modify the velocity of any moon.
For example, suppose your scan reveals the following positions:
<x=-1, y=0, z=2>
<x=2, y=-10, z=-7>
<x=4, y=-8, z=8>
<x=3, y=5, z=-1>
Simulating the motion of these moons would produce the following:
After 0 steps:
pos=<x=-1, y= 0, z= 2>, vel=<x= 0, y= 0, z= 0>
pos=<x= 2, y=-10, z=-7>, vel=<x= 0, y= 0, z= 0>
pos=<x= 4, y= -8, z= 8>, vel=<x= 0, y= 0, z= 0>
pos=<x= 3, y= 5, z=-1>, vel=<x= 0, y= 0, z= 0>
After 1 step:
pos=<x= 2, y=-1, z= 1>, vel=<x= 3, y=-1, z=-1>
pos=<x= 3, y=-7, z=-4>, vel=<x= 1, y= 3, z= 3>
pos=<x= 1, y=-7, z= 5>, vel=<x=-3, y= 1, z=-3>
pos=<x= 2, y= 2, z= 0>, vel=<x=-1, y=-3, z= 1>
After 2 steps:
pos=<x= 5, y=-3, z=-1>, vel=<x= 3, y=-2, z=-2>
pos=<x= 1, y=-2, z= 2>, vel=<x=-2, y= 5, z= 6>
pos=<x= 1, y=-4, z=-1>, vel=<x= 0, y= 3, z=-6>
pos=<x= 1, y=-4, z= 2>, vel=<x=-1, y=-6, z= 2>
After 3 steps:
pos=<x= 5, y=-6, z=-1>, vel=<x= 0, y=-3, z= 0>
pos=<x= 0, y= 0, z= 6>, vel=<x=-1, y= 2, z= 4>
pos=<x= 2, y= 1, z=-5>, vel=<x= 1, y= 5, z=-4>
pos=<x= 1, y=-8, z= 2>, vel=<x= 0, y=-4, z= 0>
After 4 steps:
pos=<x= 2, y=-8, z= 0>, vel=<x=-3, y=-2, z= 1>
pos=<x= 2, y= 1, z= 7>, vel=<x= 2, y= 1, z= 1>
pos=<x= 2, y= 3, z=-6>, vel=<x= 0, y= 2, z=-1>
pos=<x= 2, y=-9, z= 1>, vel=<x= 1, y=-1, z=-1>
After 5 steps:
pos=<x=-1, y=-9, z= 2>, vel=<x=-3, y=-1, z= 2>
pos=<x= 4, y= 1, z= 5>, vel=<x= 2, y= 0, z=-2>
pos=<x= 2, y= 2, z=-4>, vel=<x= 0, y=-1, z= 2>
pos=<x= 3, y=-7, z=-1>, vel=<x= 1, y= 2, z=-2>
After 6 steps:
pos=<x=-1, y=-7, z= 3>, vel=<x= 0, y= 2, z= 1>
pos=<x= 3, y= 0, z= 0>, vel=<x=-1, y=-1, z=-5>
pos=<x= 3, y=-2, z= 1>, vel=<x= 1, y=-4, z= 5>
pos=<x= 3, y=-4, z=-2>, vel=<x= 0, y= 3, z=-1>
After 7 steps:
pos=<x= 2, y=-2, z= 1>, vel=<x= 3, y= 5, z=-2>
pos=<x= 1, y=-4, z=-4>, vel=<x=-2, y=-4, z=-4>
pos=<x= 3, y=-7, z= 5>, vel=<x= 0, y=-5, z= 4>
pos=<x= 2, y= 0, z= 0>, vel=<x=-1, y= 4, z= 2>
After 8 steps:
pos=<x= 5, y= 2, z=-2>, vel=<x= 3, y= 4, z=-3>
pos=<x= 2, y=-7, z=-5>, vel=<x= 1, y=-3, z=-1>
pos=<x= 0, y=-9, z= 6>, vel=<x=-3, y=-2, z= 1>
pos=<x= 1, y= 1, z= 3>, vel=<x=-1, y= 1, z= 3>
After 9 steps:
pos=<x= 5, y= 3, z=-4>, vel=<x= 0, y= 1, z=-2>
pos=<x= 2, y=-9, z=-3>, vel=<x= 0, y=-2, z= 2>
pos=<x= 0, y=-8, z= 4>, vel=<x= 0, y= 1, z=-2>
pos=<x= 1, y= 1, z= 5>, vel=<x= 0, y= 0, z= 2>
After 10 steps:
pos=<x= 2, y= 1, z=-3>, vel=<x=-3, y=-2, z= 1>
pos=<x= 1, y=-8, z= 0>, vel=<x=-1, y= 1, z= 3>
pos=<x= 3, y=-6, z= 1>, vel=<x= 3, y= 2, z=-3>
pos=<x= 2, y= 0, z= 4>, vel=<x= 1, y=-1, z=-1>
Then, it might help to calculate the total energy in the system. The total energy for a single moon is its potential energy multiplied by its kinetic energy. A moon's potential energy is the sum of the absolute values of its x, y, and z position coordinates. A moon's kinetic energy is the sum of the absolute values of its velocity coordinates. Below, each line shows the calculations for a moon's potential energy (pot), kinetic energy (kin), and total energy:
Energy after 10 steps:
pot: 2 + 1 + 3 = 6; kin: 3 + 2 + 1 = 6; total: 6 * 6 = 36
pot: 1 + 8 + 0 = 9; kin: 1 + 1 + 3 = 5; total: 9 * 5 = 45
pot: 3 + 6 + 1 = 10; kin: 3 + 2 + 3 = 8; total: 10 * 8 = 80
pot: 2 + 0 + 4 = 6; kin: 1 + 1 + 1 = 3; total: 6 * 3 = 18
Sum of total energy: 36 + 45 + 80 + 18 = 179
In the above example, adding together the total energy for all moons after 10 steps produces the total energy in the system, 179.
Here's a second example:
<x=-8, y=-10, z=0>
<x=5, y=5, z=10>
<x=2, y=-7, z=3>
<x=9, y=-8, z=-3>
Every ten steps of simulation for 100 steps produces:
After 0 steps:
pos=<x= -8, y=-10, z= 0>, vel=<x= 0, y= 0, z= 0>
pos=<x= 5, y= 5, z= 10>, vel=<x= 0, y= 0, z= 0>
pos=<x= 2, y= -7, z= 3>, vel=<x= 0, y= 0, z= 0>
pos=<x= 9, y= -8, z= -3>, vel=<x= 0, y= 0, z= 0>
After 10 steps:
pos=<x= -9, y=-10, z= 1>, vel=<x= -2, y= -2, z= -1>
pos=<x= 4, y= 10, z= 9>, vel=<x= -3, y= 7, z= -2>
pos=<x= 8, y=-10, z= -3>, vel=<x= 5, y= -1, z= -2>
pos=<x= 5, y=-10, z= 3>, vel=<x= 0, y= -4, z= 5>
After 20 steps:
pos=<x=-10, y= 3, z= -4>, vel=<x= -5, y= 2, z= 0>
pos=<x= 5, y=-25, z= 6>, vel=<x= 1, y= 1, z= -4>
pos=<x= 13, y= 1, z= 1>, vel=<x= 5, y= -2, z= 2>
pos=<x= 0, y= 1, z= 7>, vel=<x= -1, y= -1, z= 2>
After 30 steps:
pos=<x= 15, y= -6, z= -9>, vel=<x= -5, y= 4, z= 0>
pos=<x= -4, y=-11, z= 3>, vel=<x= -3, y=-10, z= 0>
pos=<x= 0, y= -1, z= 11>, vel=<x= 7, y= 4, z= 3>
pos=<x= -3, y= -2, z= 5>, vel=<x= 1, y= 2, z= -3>
After 40 steps:
pos=<x= 14, y=-12, z= -4>, vel=<x= 11, y= 3, z= 0>
pos=<x= -1, y= 18, z= 8>, vel=<x= -5, y= 2, z= 3>
pos=<x= -5, y=-14, z= 8>, vel=<x= 1, y= -2, z= 0>
pos=<x= 0, y=-12, z= -2>, vel=<x= -7, y= -3, z= -3>
After 50 steps:
pos=<x=-23, y= 4, z= 1>, vel=<x= -7, y= -1, z= 2>
pos=<x= 20, y=-31, z= 13>, vel=<x= 5, y= 3, z= 4>
pos=<x= -4, y= 6, z= 1>, vel=<x= -1, y= 1, z= -3>
pos=<x= 15, y= 1, z= -5>, vel=<x= 3, y= -3, z= -3>
After 60 steps:
pos=<x= 36, y=-10, z= 6>, vel=<x= 5, y= 0, z= 3>
pos=<x=-18, y= 10, z= 9>, vel=<x= -3, y= -7, z= 5>
pos=<x= 8, y=-12, z= -3>, vel=<x= -2, y= 1, z= -7>
pos=<x=-18, y= -8, z= -2>, vel=<x= 0, y= 6, z= -1>
After 70 steps:
pos=<x=-33, y= -6, z= 5>, vel=<x= -5, y= -4, z= 7>
pos=<x= 13, y= -9, z= 2>, vel=<x= -2, y= 11, z= 3>
pos=<x= 11, y= -8, z= 2>, vel=<x= 8, y= -6, z= -7>
pos=<x= 17, y= 3, z= 1>, vel=<x= -1, y= -1, z= -3>
After 80 steps:
pos=<x= 30, y= -8, z= 3>, vel=<x= 3, y= 3, z= 0>
pos=<x= -2, y= -4, z= 0>, vel=<x= 4, y=-13, z= 2>
pos=<x=-18, y= -7, z= 15>, vel=<x= -8, y= 2, z= -2>
pos=<x= -2, y= -1, z= -8>, vel=<x= 1, y= 8, z= 0>
After 90 steps:
pos=<x=-25, y= -1, z= 4>, vel=<x= 1, y= -3, z= 4>
pos=<x= 2, y= -9, z= 0>, vel=<x= -3, y= 13, z= -1>
pos=<x= 32, y= -8, z= 14>, vel=<x= 5, y= -4, z= 6>
pos=<x= -1, y= -2, z= -8>, vel=<x= -3, y= -6, z= -9>
After 100 steps:
pos=<x= 8, y=-12, z= -9>, vel=<x= -7, y= 3, z= 0>
pos=<x= 13, y= 16, z= -3>, vel=<x= 3, y=-11, z= -5>
pos=<x=-29, y=-11, z= -1>, vel=<x= -3, y= 7, z= 4>
pos=<x= 16, y=-13, z= 23>, vel=<x= 7, y= 1, z= 1>
Energy after 100 steps:
pot: 8 + 12 + 9 = 29; kin: 7 + 3 + 0 = 10; total: 29 * 10 = 290
pot: 13 + 16 + 3 = 32; kin: 3 + 11 + 5 = 19; total: 32 * 19 = 608
pot: 29 + 11 + 1 = 41; kin: 3 + 7 + 4 = 14; total: 41 * 14 = 574
pot: 16 + 13 + 23 = 52; kin: 7 + 1 + 1 = 9; total: 52 * 9 = 468
Sum of total energy: 290 + 608 + 574 + 468 = 1940
What is the total energy in the system after simulating the moons given in your scan for 1000 steps?
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--- Day 2: 1202 Program Alarm ---
On the way to your gravity assist around the Moon, your ship computer beeps angrily about a "1202 program alarm". On the radio, an Elf is already explaining how to handle the situation: "Don't worry, that's perfectly norma--" The ship computer bursts into flames.
You notify the Elves that the computer's magic smoke seems to have escaped. "That computer ran Intcode programs like the gravity assist program it was working on; surely there are enough spare parts up there to build a new Intcode computer!"
An Intcode program is a list of integers separated by commas (like 1,0,0,3,99). To run one, start by looking at the first integer (called position 0). Here, you will find an opcode - either 1, 2, or 99. The opcode indicates what to do; for example, 99 means that the program is finished and should immediately halt. Encountering an unknown opcode means something went wrong.
Opcode 1 adds together numbers read from two positions and stores the result in a third position. The three integers immediately after the opcode tell you these three positions - the first two indicate the positions from which you should read the input values, and the third indicates the position at which the output should be stored.
For example, if your Intcode computer encounters 1,10,20,30, it should read the values at positions 10 and 20, add those values, and then overwrite the value at position 30 with their sum.
Opcode 2 works exactly like opcode 1, except it multiplies the two inputs instead of adding them. Again, the three integers after the opcode indicate where the inputs and outputs are, not their values.
Once you're done processing an opcode, move to the next one by stepping forward 4 positions.
For example, suppose you have the following program:
1,9,10,3,2,3,11,0,99,30,40,50
For the purposes of illustration, here is the same program split into multiple lines:
1,9,10,3,
2,3,11,0,
99,
30,40,50
The first four integers, 1,9,10,3, are at positions 0, 1, 2, and 3. Together, they represent the first opcode (1, addition), the positions of the two inputs (9 and 10), and the position of the output (3). To handle this opcode, you first need to get the values at the input positions: position 9 contains 30, and position 10 contains 40. Add these numbers together to get 70. Then, store this value at the output position; here, the output position (3) is at position 3, so it overwrites itself. Afterward, the program looks like this:
1,9,10,70,
2,3,11,0,
99,
30,40,50
Step forward 4 positions to reach the next opcode, 2. This opcode works just like the previous, but it multiplies instead of adding. The inputs are at positions 3 and 11; these positions contain 70 and 50 respectively. Multiplying these produces 3500; this is stored at position 0:
3500,9,10,70,
2,3,11,0,
99,
30,40,50
Stepping forward 4 more positions arrives at opcode 99, halting the program.
Here are the initial and final states of a few more small programs:
1,0,0,0,99 becomes 2,0,0,0,99 (1 + 1 = 2).
2,3,0,3,99 becomes 2,3,0,6,99 (3 * 2 = 6).
2,4,4,5,99,0 becomes 2,4,4,5,99,9801 (99 * 99 = 9801).
1,1,1,4,99,5,6,0,99 becomes 30,1,1,4,2,5,6,0,99.
Once you have a working computer, the first step is to restore the gravity assist program (your puzzle input) to the "1202 program alarm" state it had just before the last computer caught fire. To do this, before running the program, replace position 1 with the value 12 and replace position 2 with the value 2. What value is left at position 0 after the program halts?
Your puzzle answer was 4714701.
--- Part Two ---
"Good, the new computer seems to be working correctly! Keep it nearby during this mission - you'll probably use it again. Real Intcode computers support many more features than your new one, but we'll let you know what they are as you need them."
"However, your current priority should be to complete your gravity assist around the Moon. For this mission to succeed, we should settle on some terminology for the parts you've already built."
Intcode programs are given as a list of integers; these values are used as the initial state for the computer's memory. When you run an Intcode program, make sure to start by initializing memory to the program's values. A position in memory is called an address (for example, the first value in memory is at "address 0").
Opcodes (like 1, 2, or 99) mark the beginning of an instruction. The values used immediately after an opcode, if any, are called the instruction's parameters. For example, in the instruction 1,2,3,4, 1 is the opcode; 2, 3, and 4 are the parameters. The instruction 99 contains only an opcode and has no parameters.
The address of the current instruction is called the instruction pointer; it starts at 0. After an instruction finishes, the instruction pointer increases by the number of values in the instruction; until you add more instructions to the computer, this is always 4 (1 opcode + 3 parameters) for the add and multiply instructions. (The halt instruction would increase the instruction pointer by 1, but it halts the program instead.)
"With terminology out of the way, we're ready to proceed. To complete the gravity assist, you need to determine what pair of inputs produces the output 19690720."
The inputs should still be provided to the program by replacing the values at addresses 1 and 2, just like before. In this program, the value placed in address 1 is called the noun, and the value placed in address 2 is called the verb. Each of the two input values will be between 0 and 99, inclusive.
Once the program has halted, its output is available at address 0, also just like before. Each time you try a pair of inputs, make sure you first reset the computer's memory to the values in the program (your puzzle input) - in other words, don't reuse memory from a previous attempt.
Find the input noun and verb that cause the program to produce the output 19690720. What is 100 * noun + verb? (For example, if noun=12 and verb=2, the answer would be 1202.)
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--- Day 5: Print Queue ---
Satisfied with their search on Ceres, the squadron of scholars suggests subsequently scanning the stationery stacks of sub-basement 17.
The North Pole printing department is busier than ever this close to Christmas, and while The Historians continue their search of this historically significant facility, an Elf operating a very familiar printer beckons you over.
The Elf must recognize you, because they waste no time explaining that the new sleigh launch safety manual updates won't print correctly. Failure to update the safety manuals would be dire indeed, so you offer your services.
Safety protocols clearly indicate that new pages for the safety manuals must be printed in a very specific order. The notation X|Y means that if both page number X and page number Y are to be produced as part of an update, page number X must be printed at some point before page number Y.
The Elf has for you both the page ordering rules and the pages to produce in each update (your puzzle input), but can't figure out whether each update has the pages in the right order.
For example:
47|53
97|13
97|61
97|47
75|29
61|13
75|53
29|13
97|29
53|29
61|53
97|53
61|29
47|13
75|47
97|75
47|61
75|61
47|29
75|13
53|13
75,47,61,53,29
97,61,53,29,13
75,29,13
75,97,47,61,53
61,13,29
97,13,75,29,47
The first section specifies the page ordering rules, one per line. The first rule, 47|53, means that if an update includes both page number 47 and page number 53, then page number 47 must be printed at some point before page number 53. (47 doesn't necessarily need to be immediately before 53; other pages are allowed to be between them.)
The second section specifies the page numbers of each update. Because most safety manuals are different, the pages needed in the updates are different too. The first update, 75,47,61,53,29, means that the update consists of page numbers 75, 47, 61, 53, and 29.
To get the printers going as soon as possible, start by identifying which updates are already in the right order.
In the above example, the first update (75,47,61,53,29) is in the right order:
75 is correctly first because there are rules that put each other page after it: 75|47, 75|61, 75|53, and 75|29.
47 is correctly second because 75 must be before it (75|47) and every other page must be after it according to 47|61, 47|53, and 47|29.
61 is correctly in the middle because 75 and 47 are before it (75|61 and 47|61) and 53 and 29 are after it (61|53 and 61|29).
53 is correctly fourth because it is before page number 29 (53|29).
29 is the only page left and so is correctly last.
Because the first update does not include some page numbers, the ordering rules involving those missing page numbers are ignored.
The second and third updates are also in the correct order according to the rules. Like the first update, they also do not include every page number, and so only some of the ordering rules apply - within each update, the ordering rules that involve missing page numbers are not used.
The fourth update, 75,97,47,61,53, is not in the correct order: it would print 75 before 97, which violates the rule 97|75.
The fifth update, 61,13,29, is also not in the correct order, since it breaks the rule 29|13.
The last update, 97,13,75,29,47, is not in the correct order due to breaking several rules.
For some reason, the Elves also need to know the middle page number of each update being printed. Because you are currently only printing the correctly-ordered updates, you will need to find the middle page number of each correctly-ordered update. In the above example, the correctly-ordered updates are:
75,47,61,53,29
97,61,53,29,13
75,29,13
These have middle page numbers of 61, 53, and 29 respectively. Adding these page numbers together gives 143.
Of course, you'll need to be careful: the actual list of page ordering rules is bigger and more complicated than the above example.
Determine which updates are already in the correct order. What do you get if you add up the middle page number from those correctly-ordered updates?
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--- Day 15: Lens Library ---
The newly-focused parabolic reflector dish is sending all of the collected light to a point on the side of yet another mountain - the largest mountain on Lava Island. As you approach the mountain, you find that the light is being collected by the wall of a large facility embedded in the mountainside.
You find a door under a large sign that says "Lava Production Facility" and next to a smaller sign that says "Danger - Personal Protective Equipment required beyond this point".
As you step inside, you are immediately greeted by a somewhat panicked reindeer wearing goggles and a loose-fitting hard hat. The reindeer leads you to a shelf of goggles and hard hats (you quickly find some that fit) and then further into the facility. At one point, you pass a button with a faint snout mark and the label "PUSH FOR HELP". No wonder you were loaded into that trebuchet so quickly!
You pass through a final set of doors surrounded with even more warning signs and into what must be the room that collects all of the light from outside. As you admire the large assortment of lenses available to further focus the light, the reindeer brings you a book titled "Initialization Manual".
"Hello!", the book cheerfully begins, apparently unaware of the concerned reindeer reading over your shoulder. "This procedure will let you bring the Lava Production Facility online - all without burning or melting anything unintended!"
"Before you begin, please be prepared to use the Holiday ASCII String Helper algorithm (appendix 1A)." You turn to appendix 1A. The reindeer leans closer with interest.
The HASH algorithm is a way to turn any string of characters into a single number in the range 0 to 255. To run the HASH algorithm on a string, start with a current value of 0. Then, for each character in the string starting from the beginning:
Determine the ASCII code for the current character of the string.
Increase the current value by the ASCII code you just determined.
Set the current value to itself multiplied by 17.
Set the current value to the remainder of dividing itself by 256.
After following these steps for each character in the string in order, the current value is the output of the HASH algorithm.
So, to find the result of running the HASH algorithm on the string HASH:
The current value starts at 0.
The first character is H; its ASCII code is 72.
The current value increases to 72.
The current value is multiplied by 17 to become 1224.
The current value becomes 200 (the remainder of 1224 divided by 256).
The next character is A; its ASCII code is 65.
The current value increases to 265.
The current value is multiplied by 17 to become 4505.
The current value becomes 153 (the remainder of 4505 divided by 256).
The next character is S; its ASCII code is 83.
The current value increases to 236.
The current value is multiplied by 17 to become 4012.
The current value becomes 172 (the remainder of 4012 divided by 256).
The next character is H; its ASCII code is 72.
The current value increases to 244.
The current value is multiplied by 17 to become 4148.
The current value becomes 52 (the remainder of 4148 divided by 256).
So, the result of running the HASH algorithm on the string HASH is 52.
The initialization sequence (your puzzle input) is a comma-separated list of steps to start the Lava Production Facility. Ignore newline characters when parsing the initialization sequence. To verify that your HASH algorithm is working, the book offers the sum of the result of running the HASH algorithm on each step in the initialization sequence.
For example:
rn=1,cm-,qp=3,cm=2,qp-,pc=4,ot=9,ab=5,pc-,pc=6,ot=7
This initialization sequence specifies 11 individual steps; the result of running the HASH algorithm on each of the steps is as follows:
rn=1 becomes 30.
cm- becomes 253.
qp=3 becomes 97.
cm=2 becomes 47.
qp- becomes 14.
pc=4 becomes 180.
ot=9 becomes 9.
ab=5 becomes 197.
pc- becomes 48.
pc=6 becomes 214.
ot=7 becomes 231.
In this example, the sum of these results is 1320. Unfortunately, the reindeer has stolen the page containing the expected verification number and is currently running around the facility with it excitedly.
Run the HASH algorithm on each step in the initialization sequence. What is the sum of the results? (The initialization sequence is one long line; be careful when copy-pasting it.)
| 357
|
--- Day 22: Reactor Reboot ---
Operating at these extreme ocean depths has overloaded the submarine's reactor; it needs to be rebooted.
The reactor core is made up of a large 3-dimensional grid made up entirely of cubes, one cube per integer 3-dimensional coordinate (x,y,z). Each cube can be either on or off; at the start of the reboot process, they are all off. (Could it be an old model of a reactor you've seen before?)
To reboot the reactor, you just need to set all of the cubes to either on or off by following a list of reboot steps (your puzzle input). Each step specifies a cuboid (the set of all cubes that have coordinates which fall within ranges for x, y, and z) and whether to turn all of the cubes in that cuboid on or off.
For example, given these reboot steps:
on x=10..12,y=10..12,z=10..12
on x=11..13,y=11..13,z=11..13
off x=9..11,y=9..11,z=9..11
on x=10..10,y=10..10,z=10..10
The first step (on x=10..12,y=10..12,z=10..12) turns on a 3x3x3 cuboid consisting of 27 cubes:
10,10,10
10,10,11
10,10,12
10,11,10
10,11,11
10,11,12
10,12,10
10,12,11
10,12,12
11,10,10
11,10,11
11,10,12
11,11,10
11,11,11
11,11,12
11,12,10
11,12,11
11,12,12
12,10,10
12,10,11
12,10,12
12,11,10
12,11,11
12,11,12
12,12,10
12,12,11
12,12,12
The second step (on x=11..13,y=11..13,z=11..13) turns on a 3x3x3 cuboid that overlaps with the first. As a result, only 19 additional cubes turn on; the rest are already on from the previous step:
11,11,13
11,12,13
11,13,11
11,13,12
11,13,13
12,11,13
12,12,13
12,13,11
12,13,12
12,13,13
13,11,11
13,11,12
13,11,13
13,12,11
13,12,12
13,12,13
13,13,11
13,13,12
13,13,13
The third step (off x=9..11,y=9..11,z=9..11) turns off a 3x3x3 cuboid that overlaps partially with some cubes that are on, ultimately turning off 8 cubes:
10,10,10
10,10,11
10,11,10
10,11,11
11,10,10
11,10,11
11,11,10
11,11,11
The final step (on x=10..10,y=10..10,z=10..10) turns on a single cube, 10,10,10. After this last step, 39 cubes are on.
The initialization procedure only uses cubes that have x, y, and z positions of at least -50 and at most 50. For now, ignore cubes outside this region.
Here is a larger example:
on x=-20..26,y=-36..17,z=-47..7
on x=-20..33,y=-21..23,z=-26..28
on x=-22..28,y=-29..23,z=-38..16
on x=-46..7,y=-6..46,z=-50..-1
on x=-49..1,y=-3..46,z=-24..28
on x=2..47,y=-22..22,z=-23..27
on x=-27..23,y=-28..26,z=-21..29
on x=-39..5,y=-6..47,z=-3..44
on x=-30..21,y=-8..43,z=-13..34
on x=-22..26,y=-27..20,z=-29..19
off x=-48..-32,y=26..41,z=-47..-37
on x=-12..35,y=6..50,z=-50..-2
off x=-48..-32,y=-32..-16,z=-15..-5
on x=-18..26,y=-33..15,z=-7..46
off x=-40..-22,y=-38..-28,z=23..41
on x=-16..35,y=-41..10,z=-47..6
off x=-32..-23,y=11..30,z=-14..3
on x=-49..-5,y=-3..45,z=-29..18
off x=18..30,y=-20..-8,z=-3..13
on x=-41..9,y=-7..43,z=-33..15
on x=-54112..-39298,y=-85059..-49293,z=-27449..7877
on x=967..23432,y=45373..81175,z=27513..53682
The last two steps are fully outside the initialization procedure area; all other steps are fully within it. After executing these steps in the initialization procedure region, 590784 cubes are on.
Execute the reboot steps. Afterward, considering only cubes in the region x=-50..50,y=-50..50,z=-50..50, how many cubes are on?
| 358
|
--- Day 12: Garden Groups ---
Why not search for the Chief Historian near the gardener and his massive farm? There's plenty of food, so The Historians grab something to eat while they search.
You're about to settle near a complex arrangement of garden plots when some Elves ask if you can lend a hand. They'd like to set up fences around each region of garden plots, but they can't figure out how much fence they need to order or how much it will cost. They hand you a map (your puzzle input) of the garden plots.
Each garden plot grows only a single type of plant and is indicated by a single letter on your map. When multiple garden plots are growing the same type of plant and are touching (horizontally or vertically), they form a region. For example:
AAAA
BBCD
BBCC
EEEC
This 4x4 arrangement includes garden plots growing five different types of plants (labeled A, B, C, D, and E), each grouped into their own region.
In order to accurately calculate the cost of the fence around a single region, you need to know that region's area and perimeter.
The area of a region is simply the number of garden plots the region contains. The above map's type A, B, and C plants are each in a region of area 4. The type E plants are in a region of area 3; the type D plants are in a region of area 1.
Each garden plot is a square and so has four sides. The perimeter of a region is the number of sides of garden plots in the region that do not touch another garden plot in the same region. The type A and C plants are each in a region with perimeter 10. The type B and E plants are each in a region with perimeter 8. The lone D plot forms its own region with perimeter 4.
Visually indicating the sides of plots in each region that contribute to the perimeter using - and |, the above map's regions' perimeters are measured as follows:
+-+-+-+-+
|A A A A|
+-+-+-+-+ +-+
|D|
+-+-+ +-+ +-+
|B B| |C|
+ + + +-+
|B B| |C C|
+-+-+ +-+ +
|C|
+-+-+-+ +-+
|E E E|
+-+-+-+
Plants of the same type can appear in multiple separate regions, and regions can even appear within other regions. For example:
OOOOO
OXOXO
OOOOO
OXOXO
OOOOO
The above map contains five regions, one containing all of the O garden plots, and the other four each containing a single X plot.
The four X regions each have area 1 and perimeter 4. The region containing 21 type O plants is more complicated; in addition to its outer edge contributing a perimeter of 20, its boundary with each X region contributes an additional 4 to its perimeter, for a total perimeter of 36.
Due to "modern" business practices, the price of fence required for a region is found by multiplying that region's area by its perimeter. The total price of fencing all regions on a map is found by adding together the price of fence for every region on the map.
In the first example, region A has price 4 * 10 = 40, region B has price 4 * 8 = 32, region C has price 4 * 10 = 40, region D has price 1 * 4 = 4, and region E has price 3 * 8 = 24. So, the total price for the first example is 140.
In the second example, the region with all of the O plants has price 21 * 36 = 756, and each of the four smaller X regions has price 1 * 4 = 4, for a total price of 772 (756 + 4 + 4 + 4 + 4).
Here's a larger example:
RRRRIICCFF
RRRRIICCCF
VVRRRCCFFF
VVRCCCJFFF
VVVVCJJCFE
VVIVCCJJEE
VVIIICJJEE
MIIIIIJJEE
MIIISIJEEE
MMMISSJEEE
It contains:
A region of R plants with price 12 * 18 = 216.
A region of I plants with price 4 * 8 = 32.
A region of C plants with price 14 * 28 = 392.
A region of F plants with price 10 * 18 = 180.
A region of V plants with price 13 * 20 = 260.
A region of J plants with price 11 * 20 = 220.
A region of C plants with price 1 * 4 = 4.
A region of E plants with price 13 * 18 = 234.
A region of I plants with price 14 * 22 = 308.
A region of M plants with price 5 * 12 = 60.
A region of S plants with price 3 * 8 = 24.
So, it has a total price of 1930.
What is the total price of fencing all regions on your map?
Your puzzle answer was 1456082.
The first half of this puzzle is complete! It provides one gold star: *
--- Part Two ---
Fortunately, the Elves are trying to order so much fence that they qualify for a bulk discount!
Under the bulk discount, instead of using the perimeter to calculate the price, you need to use the number of sides each region has. Each straight section of fence counts as a side, regardless of how long it is.
Consider this example again:
AAAA
BBCD
BBCC
EEEC
The region containing type A plants has 4 sides, as does each of the regions containing plants of type B, D, and E. However, the more complex region containing the plants of type C has 8 sides!
Using the new method of calculating the per-region price by multiplying the region's area by its number of sides, regions A through E have prices 16, 16, 32, 4, and 12, respectively, for a total price of 80.
The second example above (full of type X and O plants) would have a total price of 436.
Here's a map that includes an E-shaped region full of type E plants:
EEEEE
EXXXX
EEEEE
EXXXX
EEEEE
The E-shaped region has an area of 17 and 12 sides for a price of 204. Including the two regions full of type X plants, this map has a total price of 236.
This map has a total price of 368:
AAAAAA
AAABBA
AAABBA
ABBAAA
ABBAAA
AAAAAA
It includes two regions full of type B plants (each with 4 sides) and a single region full of type A plants (with 4 sides on the outside and 8 more sides on the inside, a total of 12 sides). Be especially careful when counting the fence around regions like the one full of type A plants; in particular, each section of fence has an in-side and an out-side, so the fence does not connect across the middle of the region (where the two B regions touch diagonally). (The Elves would have used the Möbius Fencing Company instead, but their contract terms were too one-sided.)
The larger example from before now has the following updated prices:
A region of R plants with price 12 * 10 = 120.
A region of I plants with price 4 * 4 = 16.
A region of C plants with price 14 * 22 = 308.
A region of F plants with price 10 * 12 = 120.
A region of V plants with price 13 * 10 = 130.
A region of J plants with price 11 * 12 = 132.
A region of C plants with price 1 * 4 = 4.
A region of E plants with price 13 * 8 = 104.
A region of I plants with price 14 * 16 = 224.
A region of M plants with price 5 * 6 = 30.
A region of S plants with price 3 * 6 = 18.
Adding these together produces its new total price of 1206.
What is the new total price of fencing all regions on your map?
| 359
|
--- Day 22: Sand Slabs ---
Enough sand has fallen; it can finally filter water for Snow Island.
Well, almost.
The sand has been falling as large compacted bricks of sand, piling up to form an impressive stack here near the edge of Island Island. In order to make use of the sand to filter water, some of the bricks will need to be broken apart - nay, disintegrated - back into freely flowing sand.
The stack is tall enough that you'll have to be careful about choosing which bricks to disintegrate; if you disintegrate the wrong brick, large portions of the stack could topple, which sounds pretty dangerous.
The Elves responsible for water filtering operations took a snapshot of the bricks while they were still falling (your puzzle input) which should let you work out which bricks are safe to disintegrate. For example:
1,0,1~1,2,1
0,0,2~2,0,2
0,2,3~2,2,3
0,0,4~0,2,4
2,0,5~2,2,5
0,1,6~2,1,6
1,1,8~1,1,9
Each line of text in the snapshot represents the position of a single brick at the time the snapshot was taken. The position is given as two x,y,z coordinates - one for each end of the brick - separated by a tilde (~). Each brick is made up of a single straight line of cubes, and the Elves were even careful to choose a time for the snapshot that had all of the free-falling bricks at integer positions above the ground, so the whole snapshot is aligned to a three-dimensional cube grid.
A line like 2,2,2~2,2,2 means that both ends of the brick are at the same coordinate - in other words, that the brick is a single cube.
Lines like 0,0,10~1,0,10 or 0,0,10~0,1,10 both represent bricks that are two cubes in volume, both oriented horizontally. The first brick extends in the x direction, while the second brick extends in the y direction.
A line like 0,0,1~0,0,10 represents a ten-cube brick which is oriented vertically. One end of the brick is the cube located at 0,0,1, while the other end of the brick is located directly above it at 0,0,10.
The ground is at z=0 and is perfectly flat; the lowest z value a brick can have is therefore 1. So, 5,5,1~5,6,1 and 0,2,1~0,2,5 are both resting on the ground, but 3,3,2~3,3,3 was above the ground at the time of the snapshot.
Because the snapshot was taken while the bricks were still falling, some bricks will still be in the air; you'll need to start by figuring out where they will end up. Bricks are magically stabilized, so they never rotate, even in weird situations like where a long horizontal brick is only supported on one end. Two bricks cannot occupy the same position, so a falling brick will come to rest upon the first other brick it encounters.
Here is the same example again, this time with each brick given a letter so it can be marked in diagrams:
1,0,1~1,2,1 <- A
0,0,2~2,0,2 <- B
0,2,3~2,2,3 <- C
0,0,4~0,2,4 <- D
2,0,5~2,2,5 <- E
0,1,6~2,1,6 <- F
1,1,8~1,1,9 <- G
At the time of the snapshot, from the side so the x axis goes left to right, these bricks are arranged like this:
x
012
.G. 9
.G. 8
... 7
FFF 6
..E 5 z
D.. 4
CCC 3
BBB 2
.A. 1
--- 0
Rotating the perspective 90 degrees so the y axis now goes left to right, the same bricks are arranged like this:
y
012
.G. 9
.G. 8
... 7
.F. 6
EEE 5 z
DDD 4
..C 3
B.. 2
AAA 1
--- 0
Once all of the bricks fall downward as far as they can go, the stack looks like this, where ? means bricks are hidden behind other bricks at that location:
x
012
.G. 6
.G. 5
FFF 4
D.E 3 z
??? 2
.A. 1
--- 0
Again from the side:
y
012
.G. 6
.G. 5
.F. 4
??? 3 z
B.C 2
AAA 1
--- 0
Now that all of the bricks have settled, it becomes easier to tell which bricks are supporting which other bricks:
Brick A is the only brick supporting bricks B and C.
Brick B is one of two bricks supporting brick D and brick E.
Brick C is the other brick supporting brick D and brick E.
Brick D supports brick F.
Brick E also supports brick F.
Brick F supports brick G.
Brick G isn't supporting any bricks.
Your first task is to figure out which bricks are safe to disintegrate. A brick can be safely disintegrated if, after removing it, no other bricks would fall further directly downward. Don't actually disintegrate any bricks - just determine what would happen if, for each brick, only that brick were disintegrated. Bricks can be disintegrated even if they're completely surrounded by other bricks; you can squeeze between bricks if you need to.
In this example, the bricks can be disintegrated as follows:
Brick A cannot be disintegrated safely; if it were disintegrated, bricks B and C would both fall.
Brick B can be disintegrated; the bricks above it (D and E) would still be supported by brick C.
Brick C can be disintegrated; the bricks above it (D and E) would still be supported by brick B.
Brick D can be disintegrated; the brick above it (F) would still be supported by brick E.
Brick E can be disintegrated; the brick above it (F) would still be supported by brick D.
Brick F cannot be disintegrated; the brick above it (G) would fall.
Brick G can be disintegrated; it does not support any other bricks.
So, in this example, 5 bricks can be safely disintegrated.
Figure how the blocks will settle based on the snapshot. Once they've settled, consider disintegrating a single brick; how many bricks could be safely chosen as the one to get disintegrated?
Your puzzle answer was 519.
--- Part Two ---
Disintegrating bricks one at a time isn't going to be fast enough. While it might sound dangerous, what you really need is a chain reaction.
You'll need to figure out the best brick to disintegrate. For each brick, determine how many other bricks would fall if that brick were disintegrated.
Using the same example as above:
Disintegrating brick A would cause all 6 other bricks to fall.
Disintegrating brick F would cause only 1 other brick, G, to fall.
Disintegrating any other brick would cause no other bricks to fall. So, in this example, the sum of the number of other bricks that would fall as a result of disintegrating each brick is 7.
For each brick, determine how many other bricks would fall if that brick were disintegrated. What is the sum of the number of other bricks that would fall?
| 360
|
--- Day 4: Giant Squid ---
You're already almost 1.5km (almost a mile) below the surface of the ocean, already so deep that you can't see any sunlight. What you can see, however, is a giant squid that has attached itself to the outside of your submarine.
Maybe it wants to play bingo?
Bingo is played on a set of boards each consisting of a 5x5 grid of numbers. Numbers are chosen at random, and the chosen number is marked on all boards on which it appears. (Numbers may not appear on all boards.) If all numbers in any row or any column of a board are marked, that board wins. (Diagonals don't count.)
The submarine has a bingo subsystem to help passengers (currently, you and the giant squid) pass the time. It automatically generates a random order in which to draw numbers and a random set of boards (your puzzle input). For example:
7,4,9,5,11,17,23,2,0,14,21,24,10,16,13,6,15,25,12,22,18,20,8,19,3,26,1
22 13 17 11 0
8 2 23 4 24
21 9 14 16 7
6 10 3 18 5
1 12 20 15 19
3 15 0 2 22
9 18 13 17 5
19 8 7 25 23
20 11 10 24 4
14 21 16 12 6
14 21 17 24 4
10 16 15 9 19
18 8 23 26 20
22 11 13 6 5
2 0 12 3 7
After the first five numbers are drawn (7, 4, 9, 5, and 11), there are no winners, but the boards are marked as follows (shown here adjacent to each other to save space):
22 13 17 11 0 3 15 0 2 22 14 21 17 24 4
8 2 23 4 24 9 18 13 17 5 10 16 15 9 19
21 9 14 16 7 19 8 7 25 23 18 8 23 26 20
6 10 3 18 5 20 11 10 24 4 22 11 13 6 5
1 12 20 15 19 14 21 16 12 6 2 0 12 3 7
After the next six numbers are drawn (17, 23, 2, 0, 14, and 21), there are still no winners:
22 13 17 11 0 3 15 0 2 22 14 21 17 24 4
8 2 23 4 24 9 18 13 17 5 10 16 15 9 19
21 9 14 16 7 19 8 7 25 23 18 8 23 26 20
6 10 3 18 5 20 11 10 24 4 22 11 13 6 5
1 12 20 15 19 14 21 16 12 6 2 0 12 3 7
Finally, 24 is drawn:
22 13 17 11 0 3 15 0 2 22 14 21 17 24 4
8 2 23 4 24 9 18 13 17 5 10 16 15 9 19
21 9 14 16 7 19 8 7 25 23 18 8 23 26 20
6 10 3 18 5 20 11 10 24 4 22 11 13 6 5
1 12 20 15 19 14 21 16 12 6 2 0 12 3 7
At this point, the third board wins because it has at least one complete row or column of marked numbers (in this case, the entire top row is marked: 14 21 17 24 4).
The score of the winning board can now be calculated. Start by finding the sum of all unmarked numbers on that board; in this case, the sum is 188. Then, multiply that sum by the number that was just called when the board won, 24, to get the final score, 188 * 24 = 4512.
To guarantee victory against the giant squid, figure out which board will win first. What will your final score be if you choose that board?
Your puzzle answer was 27027.
--- Part Two ---
On the other hand, it might be wise to try a different strategy: let the giant squid win.
You aren't sure how many bingo boards a giant squid could play at once, so rather than waste time counting its arms, the safe thing to do is to figure out which board will win last and choose that one. That way, no matter which boards it picks, it will win for sure.
In the above example, the second board is the last to win, which happens after 13 is eventually called and its middle column is completely marked. If you were to keep playing until this point, the second board would have a sum of unmarked numbers equal to 148 for a final score of 148 * 13 = 1924.
Figure out which board will win last. Once it wins, what would its final score be?
| 361
|
--- Day 17: Spinlock ---
Suddenly, whirling in the distance, you notice what looks like a massive, pixelated hurricane: a deadly spinlock. This spinlock isn't just consuming computing power, but memory, too; vast, digital mountains are being ripped from the ground and consumed by the vortex.
If you don't move quickly, fixing that printer will be the least of your problems.
This spinlock's algorithm is simple but efficient, quickly consuming everything in its path. It starts with a circular buffer containing only the value 0, which it marks as the current position. It then steps forward through the circular buffer some number of steps (your puzzle input) before inserting the first new value, 1, after the value it stopped on. The inserted value becomes the current position. Then, it steps forward from there the same number of steps, and wherever it stops, inserts after it the second new value, 2, and uses that as the new current position again.
It repeats this process of stepping forward, inserting a new value, and using the location of the inserted value as the new current position a total of 2017 times, inserting 2017 as its final operation, and ending with a total of 2018 values (including 0) in the circular buffer.
For example, if the spinlock were to step 3 times per insert, the circular buffer would begin to evolve like this (using parentheses to mark the current position after each iteration of the algorithm):
(0), the initial state before any insertions.
0 (1): the spinlock steps forward three times (0, 0, 0), and then inserts the first value, 1, after it. 1 becomes the current position.
0 (2) 1: the spinlock steps forward three times (0, 1, 0), and then inserts the second value, 2, after it. 2 becomes the current position.
0 2 (3) 1: the spinlock steps forward three times (1, 0, 2), and then inserts the third value, 3, after it. 3 becomes the current position.
And so on:
0 2 (4) 3 1
0 (5) 2 4 3 1
0 5 2 4 3 (6) 1
0 5 (7) 2 4 3 6 1
0 5 7 2 4 3 (8) 6 1
0 (9) 5 7 2 4 3 8 6 1
Eventually, after 2017 insertions, the section of the circular buffer near the last insertion looks like this:
1512 1134 151 (2017) 638 1513 851
Perhaps, if you can identify the value that will ultimately be after the last value written (2017), you can short-circuit the spinlock. In this example, that would be 638.
What is the value after 2017 in your completed circular buffer?
Your puzzle answer was 1914.
--- Part Two ---
The spinlock does not short-circuit. Instead, it gets more angry. At least, you assume that's what happened; it's spinning significantly faster than it was a moment ago.
You have good news and bad news.
The good news is that you have improved calculations for how to stop the spinlock. They indicate that you actually need to identify the value after 0 in the current state of the circular buffer.
The bad news is that while you were determining this, the spinlock has just finished inserting its fifty millionth value (50000000).
What is the value after 0 the moment 50000000 is inserted?
| 362
|
--- Day 5: How About a Nice Game of Chess? ---
You are faced with a security door designed by Easter Bunny engineers that seem to have acquired most of their security knowledge by watching hacking movies.
The eight-character password for the door is generated one character at a time by finding the MD5 hash of some Door ID (your puzzle input) and an increasing integer index (starting with 0).
A hash indicates the next character in the password if its hexadecimal representation starts with five zeroes. If it does, the sixth character in the hash is the next character of the password.
For example, if the Door ID is abc:
The first index which produces a hash that starts with five zeroes is 3231929, which we find by hashing abc3231929; the sixth character of the hash, and thus the first character of the password, is 1.
5017308 produces the next interesting hash, which starts with 000008f82..., so the second character of the password is 8.
The third time a hash starts with five zeroes is for abc5278568, discovering the character f.
In this example, after continuing this search a total of eight times, the password is 18f47a30.
Given the actual Door ID, what is the password?
Your puzzle answer was 4543c154.
--- Part Two ---
As the door slides open, you are presented with a second door that uses a slightly more inspired security mechanism. Clearly unimpressed by the last version (in what movie is the password decrypted in order?!), the Easter Bunny engineers have worked out a better solution.
Instead of simply filling in the password from left to right, the hash now also indicates the position within the password to fill. You still look for hashes that begin with five zeroes; however, now, the sixth character represents the position (0-7), and the seventh character is the character to put in that position.
A hash result of 000001f means that f is the second character in the password. Use only the first result for each position, and ignore invalid positions.
For example, if the Door ID is abc:
The first interesting hash is from abc3231929, which produces 0000015...; so, 5 goes in position 1: _5______.
In the previous method, 5017308 produced an interesting hash; however, it is ignored, because it specifies an invalid position (8).
The second interesting hash is at index 5357525, which produces 000004e...; so, e goes in position 4: _5__e___.
You almost choke on your popcorn as the final character falls into place, producing the password 05ace8e3.
Given the actual Door ID and this new method, what is the password? Be extra proud of your solution if it uses a cinematic "decrypting" animation.
| 363
|
--- Day 20: Donut Maze ---
You notice a strange pattern on the surface of Pluto and land nearby to get a closer look. Upon closer inspection, you realize you've come across one of the famous space-warping mazes of the long-lost Pluto civilization!
Because there isn't much space on Pluto, the civilization that used to live here thrived by inventing a method for folding spacetime. Although the technology is no longer understood, mazes like this one provide a small glimpse into the daily life of an ancient Pluto citizen.
This maze is shaped like a donut. Portals along the inner and outer edge of the donut can instantly teleport you from one side to the other. For example:
A
A
#######.#########
#######.........#
#######.#######.#
#######.#######.#
#######.#######.#
##### B ###.#
BC...## C ###.#
##.## ###.#
##...DE F ###.#
##### G ###.#
#########.#####.#
DE..#######...###.#
#.#########.###.#
FG..#########.....#
###########.#####
Z
Z
This map of the maze shows solid walls (#) and open passages (.). Every maze on Pluto has a start (the open tile next to AA) and an end (the open tile next to ZZ). Mazes on Pluto also have portals; this maze has three pairs of portals: BC, DE, and FG. When on an open tile next to one of these labels, a single step can take you to the other tile with the same label. (You can only walk on . tiles; labels and empty space are not traversable.)
One path through the maze doesn't require any portals. Starting at AA, you could go down 1, right 8, down 12, left 4, and down 1 to reach ZZ, a total of 26 steps.
However, there is a shorter path: You could walk from AA to the inner BC portal (4 steps), warp to the outer BC portal (1 step), walk to the inner DE (6 steps), warp to the outer DE (1 step), walk to the outer FG (4 steps), warp to the inner FG (1 step), and finally walk to ZZ (6 steps). In total, this is only 23 steps.
Here is a larger example:
A
A
#################.#############
#.#...#...................#.#.#
#.#.#.###.###.###.#########.#.#
#.#.#.......#...#.....#.#.#...#
#.#########.###.#####.#.#.###.#
#.............#.#.....#.......#
###.###########.###.#####.#.#.#
#.....# A C #.#.#.#
####### S P #####.#
#.#...# #......VT
#.#.#.# #.#####
#...#.# YN....#.#
#.###.# #####.#
DI....#.# #.....#
#####.# #.###.#
ZZ......# QG....#..AS
###.### #######
JO..#.#.# #.....#
#.#.#.# ###.#.#
#...#..DI BU....#..LF
#####.# #.#####
YN......# VT..#....QG
#.###.# #.###.#
#.#...# #.....#
###.### J L J #.#.###
#.....# O F P #.#...#
#.###.#####.#.#####.#####.###.#
#...#.#.#...#.....#.....#.#...#
#.#####.###.###.#.#.#########.#
#...#.#.....#...#.#.#.#.....#.#
#.###.#####.###.###.#.#.#######
#.#.........#...#.............#
#########.###.###.#############
B J C
U P P
Here, AA has no direct path to ZZ, but it does connect to AS and CP. By passing through AS, QG, BU, and JO, you can reach ZZ in 58 steps.
In your maze, how many steps does it take to get from the open tile marked AA to the open tile marked ZZ?
| 364
|
--- Day 1: Inverse Captcha ---
The night before Christmas, one of Santa's Elves calls you in a panic. "The printer's broken! We can't print the Naughty or Nice List!" By the time you make it to sub-basement 17, there are only a few minutes until midnight. "We have a big problem," she says; "there must be almost fifty bugs in this system, but nothing else can print The List. Stand in this square, quick! There's no time to explain; if you can convince them to pay you in stars, you'll be able to--" She pulls a lever and the world goes blurry.
When your eyes can focus again, everything seems a lot more pixelated than before. She must have sent you inside the computer! You check the system clock: 25 milliseconds until midnight. With that much time, you should be able to collect all fifty stars by December 25th.
Collect stars by solving puzzles. Two puzzles will be made available on each day millisecond in the Advent calendar; the second puzzle is unlocked when you complete the first. Each puzzle grants one star. Good luck!
You're standing in a room with "digitization quarantine" written in LEDs along one wall. The only door is locked, but it includes a small interface. "Restricted Area - Strictly No Digitized Users Allowed."
It goes on to explain that you may only leave by solving a captcha to prove you're not a human. Apparently, you only get one millisecond to solve the captcha: too fast for a normal human, but it feels like hours to you.
The captcha requires you to review a sequence of digits (your puzzle input) and find the sum of all digits that match the next digit in the list. The list is circular, so the digit after the last digit is the first digit in the list.
For example:
1122 produces a sum of 3 (1 + 2) because the first digit (1) matches the second digit and the third digit (2) matches the fourth digit.
1111 produces 4 because each digit (all 1) matches the next.
1234 produces 0 because no digit matches the next.
91212129 produces 9 because the only digit that matches the next one is the last digit, 9.
What is the solution to your captcha?
| 365
|
--- Day 3: Toboggan Trajectory ---
With the toboggan login problems resolved, you set off toward the airport. While travel by toboggan might be easy, it's certainly not safe: there's very minimal steering and the area is covered in trees. You'll need to see which angles will take you near the fewest trees.
Due to the local geology, trees in this area only grow on exact integer coordinates in a grid. You make a map (your puzzle input) of the open squares (.) and trees (#) you can see. For example:
..##.......
#...#...#..
.#....#..#.
..#.#...#.#
.#...##..#.
..#.##.....
.#.#.#....#
.#........#
#.##...#...
#...##....#
.#..#...#.#
These aren't the only trees, though; due to something you read about once involving arboreal genetics and biome stability, the same pattern repeats to the right many times:
..##.........##.........##.........##.........##.........##....... --->
#...#...#..#...#...#..#...#...#..#...#...#..#...#...#..#...#...#..
.#....#..#..#....#..#..#....#..#..#....#..#..#....#..#..#....#..#.
..#.#...#.#..#.#...#.#..#.#...#.#..#.#...#.#..#.#...#.#..#.#...#.#
.#...##..#..#...##..#..#...##..#..#...##..#..#...##..#..#...##..#.
..#.##.......#.##.......#.##.......#.##.......#.##.......#.##..... --->
.#.#.#....#.#.#.#....#.#.#.#....#.#.#.#....#.#.#.#....#.#.#.#....#
.#........#.#........#.#........#.#........#.#........#.#........#
#.##...#...#.##...#...#.##...#...#.##...#...#.##...#...#.##...#...
#...##....##...##....##...##....##...##....##...##....##...##....#
.#..#...#.#.#..#...#.#.#..#...#.#.#..#...#.#.#..#...#.#.#..#...#.# --->
You start on the open square (.) in the top-left corner and need to reach the bottom (below the bottom-most row on your map).
The toboggan can only follow a few specific slopes (you opted for a cheaper model that prefers rational numbers); start by counting all the trees you would encounter for the slope right 3, down 1:
From your starting position at the top-left, check the position that is right 3 and down 1. Then, check the position that is right 3 and down 1 from there, and so on until you go past the bottom of the map.
The locations you'd check in the above example are marked here with O where there was an open square and X where there was a tree:
..##.........##.........##.........##.........##.........##....... --->
#..O#...#..#...#...#..#...#...#..#...#...#..#...#...#..#...#...#..
.#....X..#..#....#..#..#....#..#..#....#..#..#....#..#..#....#..#.
..#.#...#O#..#.#...#.#..#.#...#.#..#.#...#.#..#.#...#.#..#.#...#.#
.#...##..#..X...##..#..#...##..#..#...##..#..#...##..#..#...##..#.
..#.##.......#.X#.......#.##.......#.##.......#.##.......#.##..... --->
.#.#.#....#.#.#.#.O..#.#.#.#....#.#.#.#....#.#.#.#....#.#.#.#....#
.#........#.#........X.#........#.#........#.#........#.#........#
#.##...#...#.##...#...#.X#...#...#.##...#...#.##...#...#.##...#...
#...##....##...##....##...#X....##...##....##...##....##...##....#
.#..#...#.#.#..#...#.#.#..#...X.#.#..#...#.#.#..#...#.#.#..#...#.# --->
In this example, traversing the map using this slope would cause you to encounter 7 trees.
Starting at the top-left corner of your map and following a slope of right 3 and down 1, how many trees would you encounter?
| 366
|
--- Day 1: Calorie Counting ---
Santa's reindeer typically eat regular reindeer food, but they need a lot of magical energy to deliver presents on Christmas. For that, their favorite snack is a special type of star fruit that only grows deep in the jungle. The Elves have brought you on their annual expedition to the grove where the fruit grows.
To supply enough magical energy, the expedition needs to retrieve a minimum of fifty stars by December 25th. Although the Elves assure you that the grove has plenty of fruit, you decide to grab any fruit you see along the way, just in case.
Collect stars by solving puzzles. Two puzzles will be made available on each day in the Advent calendar; the second puzzle is unlocked when you complete the first. Each puzzle grants one star. Good luck!
The jungle must be too overgrown and difficult to navigate in vehicles or access from the air; the Elves' expedition traditionally goes on foot. As your boats approach land, the Elves begin taking inventory of their supplies. One important consideration is food - in particular, the number of Calories each Elf is carrying (your puzzle input).
The Elves take turns writing down the number of Calories contained by the various meals, snacks, rations, etc. that they've brought with them, one item per line. Each Elf separates their own inventory from the previous Elf's inventory (if any) by a blank line.
For example, suppose the Elves finish writing their items' Calories and end up with the following list:
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
This list represents the Calories of the food carried by five Elves:
The first Elf is carrying food with 1000, 2000, and 3000 Calories, a total of 6000 Calories.
The second Elf is carrying one food item with 4000 Calories.
The third Elf is carrying food with 5000 and 6000 Calories, a total of 11000 Calories.
The fourth Elf is carrying food with 7000, 8000, and 9000 Calories, a total of 24000 Calories.
The fifth Elf is carrying one food item with 10000 Calories.
In case the Elves get hungry and need extra snacks, they need to know which Elf to ask: they'd like to know how many Calories are being carried by the Elf carrying the most Calories. In the example above, this is 24000 (carried by the fourth Elf).
Find the Elf carrying the most Calories. How many total Calories is that Elf carrying?
Your puzzle answer was 68292.
--- Part Two ---
By the time you calculate the answer to the Elves' question, they've already realized that the Elf carrying the most Calories of food might eventually run out of snacks.
To avoid this unacceptable situation, the Elves would instead like to know the total Calories carried by the top three Elves carrying the most Calories. That way, even if one of those Elves runs out of snacks, they still have two backups.
In the example above, the top three Elves are the fourth Elf (with 24000 Calories), then the third Elf (with 11000 Calories), then the fifth Elf (with 10000 Calories). The sum of the Calories carried by these three elves is 45000.
Find the top three Elves carrying the most Calories. How many Calories are those Elves carrying in total?
| 367
|
--- Day 7: Recursive Circus ---
Wandering further through the circuits of the computer, you come upon a tower of programs that have gotten themselves into a bit of trouble. A recursive algorithm has gotten out of hand, and now they're balanced precariously in a large tower.
One program at the bottom supports the entire tower. It's holding a large disc, and on the disc are balanced several more sub-towers. At the bottom of these sub-towers, standing on the bottom disc, are other programs, each holding their own disc, and so on. At the very tops of these sub-sub-sub-...-towers, many programs stand simply keeping the disc below them balanced but with no disc of their own.
You offer to help, but first you need to understand the structure of these towers. You ask each program to yell out their name, their weight, and (if they're holding a disc) the names of the programs immediately above them balancing on that disc. You write this information down (your puzzle input). Unfortunately, in their panic, they don't do this in an orderly fashion; by the time you're done, you're not sure which program gave which information.
For example, if your list is the following:
pbga (66)
xhth (57)
ebii (61)
havc (66)
ktlj (57)
fwft (72) -> ktlj, cntj, xhth
qoyq (66)
padx (45) -> pbga, havc, qoyq
tknk (41) -> ugml, padx, fwft
jptl (61)
ugml (68) -> gyxo, ebii, jptl
gyxo (61)
cntj (57)
...then you would be able to recreate the structure of the towers that looks like this:
gyxo
/
ugml - ebii
/
| jptl
|
| pbga
/ /
tknk --- padx - havc
| qoyq
|
| ktlj
/
fwft - cntj
xhth
In this example, tknk is at the bottom of the tower (the bottom program), and is holding up ugml, padx, and fwft. Those programs are, in turn, holding up other programs; in this example, none of those programs are holding up any other programs, and are all the tops of their own towers. (The actual tower balancing in front of you is much larger.)
Before you're ready to help them, you need to make sure your information is correct. What is the name of the bottom program?
Your puzzle answer was dtacyn.
--- Part Two ---
The programs explain the situation: they can't get down. Rather, they could get down, if they weren't expending all of their energy trying to keep the tower balanced. Apparently, one program has the wrong weight, and until it's fixed, they're stuck here.
For any program holding a disc, each program standing on that disc forms a sub-tower. Each of those sub-towers are supposed to be the same weight, or the disc itself isn't balanced. The weight of a tower is the sum of the weights of the programs in that tower.
In the example above, this means that for ugml's disc to be balanced, gyxo, ebii, and jptl must all have the same weight, and they do: 61.
However, for tknk to be balanced, each of the programs standing on its disc and all programs above it must each match. This means that the following sums must all be the same:
ugml + (gyxo + ebii + jptl) = 68 + (61 + 61 + 61) = 251
padx + (pbga + havc + qoyq) = 45 + (66 + 66 + 66) = 243
fwft + (ktlj + cntj + xhth) = 72 + (57 + 57 + 57) = 243
As you can see, tknk's disc is unbalanced: ugml's stack is heavier than the other two. Even though the nodes above ugml are balanced, ugml itself is too heavy: it needs to be 8 units lighter for its stack to weigh 243 and keep the towers balanced. If this change were made, its weight would be 60.
Given that exactly one program is the wrong weight, what would its weight need to be to balance the entire tower?
| 368
|
--- Day 9: Stream Processing ---
A large stream blocks your path. According to the locals, it's not safe to cross the stream at the moment because it's full of garbage. You look down at the stream; rather than water, you discover that it's a stream of characters.
You sit for a while and record part of the stream (your puzzle input). The characters represent groups - sequences that begin with { and end with }. Within a group, there are zero or more other things, separated by commas: either another group or garbage. Since groups can contain other groups, a } only closes the most-recently-opened unclosed group - that is, they are nestable. Your puzzle input represents a single, large group which itself contains many smaller ones.
Sometimes, instead of a group, you will find garbage. Garbage begins with < and ends with >. Between those angle brackets, almost any character can appear, including { and }. Within garbage, < has no special meaning.
In a futile attempt to clean up the garbage, some program has canceled some of the characters within it using !: inside garbage, any character that comes after ! should be ignored, including <, >, and even another !.
You don't see any characters that deviate from these rules. Outside garbage, you only find well-formed groups, and garbage always terminates according to the rules above.
Here are some self-contained pieces of garbage:
<>, empty garbage.
<random characters>, garbage containing random characters.
<<<<>, because the extra < are ignored.
<{!>}>, because the first > is canceled.
<!!>, because the second ! is canceled, allowing the > to terminate the garbage.
<!!!>>, because the second ! and the first > are canceled.
<{o"i!a,<{i<a>, which ends at the first >.
Here are some examples of whole streams and the number of groups they contain:
{}, 1 group.
{{{}}}, 3 groups.
{{},{}}, also 3 groups.
{{{},{},{{}}}}, 6 groups.
{<{},{},{{}}>}, 1 group (which itself contains garbage).
{<a>,<a>,<a>,<a>}, 1 group.
{{<a>},{<a>},{<a>},{<a>}}, 5 groups.
{{<!>},{<!>},{<!>},{<a>}}, 2 groups (since all but the last > are canceled).
Your goal is to find the total score for all groups in your input. Each group is assigned a score which is one more than the score of the group that immediately contains it. (The outermost group gets a score of 1.)
{}, score of 1.
{{{}}}, score of 1 + 2 + 3 = 6.
{{},{}}, score of 1 + 2 + 2 = 5.
{{{},{},{{}}}}, score of 1 + 2 + 3 + 3 + 3 + 4 = 16.
{<a>,<a>,<a>,<a>}, score of 1.
{{<ab>},{<ab>},{<ab>},{<ab>}}, score of 1 + 2 + 2 + 2 + 2 = 9.
{{<!!>},{<!!>},{<!!>},{<!!>}}, score of 1 + 2 + 2 + 2 + 2 = 9.
{{<a!>},{<a!>},{<a!>},{<ab>}}, score of 1 + 2 = 3.
What is the total score for all groups in your input?
| 369
|
--- Day 21: RPG Simulator 20XX ---
Little Henry Case got a new video game for Christmas. It's an RPG, and he's stuck on a boss. He needs to know what equipment to buy at the shop. He hands you the controller.
In this game, the player (you) and the enemy (the boss) take turns attacking. The player always goes first. Each attack reduces the opponent's hit points by at least 1. The first character at or below 0 hit points loses.
Damage dealt by an attacker each turn is equal to the attacker's damage score minus the defender's armor score. An attacker always does at least 1 damage. So, if the attacker has a damage score of 8, and the defender has an armor score of 3, the defender loses 5 hit points. If the defender had an armor score of 300, the defender would still lose 1 hit point.
Your damage score and armor score both start at zero. They can be increased by buying items in exchange for gold. You start with no items and have as much gold as you need. Your total damage or armor is equal to the sum of those stats from all of your items. You have 100 hit points.
Here is what the item shop is selling:
Weapons: Cost Damage Armor
Dagger 8 4 0
Shortsword 10 5 0
Warhammer 25 6 0
Longsword 40 7 0
Greataxe 74 8 0
Armor: Cost Damage Armor
Leather 13 0 1
Chainmail 31 0 2
Splintmail 53 0 3
Bandedmail 75 0 4
Platemail 102 0 5
Rings: Cost Damage Armor
Damage +1 25 1 0
Damage +2 50 2 0
Damage +3 100 3 0
Defense +1 20 0 1
Defense +2 40 0 2
Defense +3 80 0 3
You must buy exactly one weapon; no dual-wielding. Armor is optional, but you can't use more than one. You can buy 0-2 rings (at most one for each hand). You must use any items you buy. The shop only has one of each item, so you can't buy, for example, two rings of Damage +3.
For example, suppose you have 8 hit points, 5 damage, and 5 armor, and that the boss has 12 hit points, 7 damage, and 2 armor:
The player deals 5-2 = 3 damage; the boss goes down to 9 hit points.
The boss deals 7-5 = 2 damage; the player goes down to 6 hit points.
The player deals 5-2 = 3 damage; the boss goes down to 6 hit points.
The boss deals 7-5 = 2 damage; the player goes down to 4 hit points.
The player deals 5-2 = 3 damage; the boss goes down to 3 hit points.
The boss deals 7-5 = 2 damage; the player goes down to 2 hit points.
The player deals 5-2 = 3 damage; the boss goes down to 0 hit points.
In this scenario, the player wins! (Barely.)
You have 100 hit points. The boss's actual stats are in your puzzle input. What is the least amount of gold you can spend and still win the fight?
Your puzzle answer was 121.
--- Part Two ---
Turns out the shopkeeper is working with the boss, and can persuade you to buy whatever items he wants. The other rules still apply, and he still only has one of each item.
What is the most amount of gold you can spend and still lose the fight?
| 370
|
--- Day 17: Trick Shot ---
You finally decode the Elves' message. HI, the message says. You continue searching for the sleigh keys.
Ahead of you is what appears to be a large ocean trench. Could the keys have fallen into it? You'd better send a probe to investigate.
The probe launcher on your submarine can fire the probe with any integer velocity in the x (forward) and y (upward, or downward if negative) directions. For example, an initial x,y velocity like 0,10 would fire the probe straight up, while an initial velocity like 10,-1 would fire the probe forward at a slight downward angle.
The probe's x,y position starts at 0,0. Then, it will follow some trajectory by moving in steps. On each step, these changes occur in the following order:
The probe's x position increases by its x velocity.
The probe's y position increases by its y velocity.
Due to drag, the probe's x velocity changes by 1 toward the value 0; that is, it decreases by 1 if it is greater than 0, increases by 1 if it is less than 0, or does not change if it is already 0.
Due to gravity, the probe's y velocity decreases by 1.
For the probe to successfully make it into the trench, the probe must be on some trajectory that causes it to be within a target area after any step. The submarine computer has already calculated this target area (your puzzle input). For example:
target area: x=20..30, y=-10..-5
This target area means that you need to find initial x,y velocity values such that after any step, the probe's x position is at least 20 and at most 30, and the probe's y position is at least -10 and at most -5.
Given this target area, one initial velocity that causes the probe to be within the target area after any step is 7,2:
.............#....#............
.......#..............#........
...............................
S........................#.....
...............................
...............................
...........................#...
...............................
....................TTTTTTTTTTT
....................TTTTTTTTTTT
....................TTTTTTTT#TT
....................TTTTTTTTTTT
....................TTTTTTTTTTT
....................TTTTTTTTTTT
In this diagram, S is the probe's initial position, 0,0. The x coordinate increases to the right, and the y coordinate increases upward. In the bottom right, positions that are within the target area are shown as T. After each step (until the target area is reached), the position of the probe is marked with #. (The bottom-right # is both a position the probe reaches and a position in the target area.)
Another initial velocity that causes the probe to be within the target area after any step is 6,3:
...............#..#............
...........#........#..........
...............................
......#..............#.........
...............................
...............................
S....................#.........
...............................
...............................
...............................
.....................#.........
....................TTTTTTTTTTT
....................TTTTTTTTTTT
....................TTTTTTTTTTT
....................TTTTTTTTTTT
....................T#TTTTTTTTT
....................TTTTTTTTTTT
Another one is 9,0:
S........#.....................
.................#.............
...............................
........................#......
...............................
....................TTTTTTTTTTT
....................TTTTTTTTTT#
....................TTTTTTTTTTT
....................TTTTTTTTTTT
....................TTTTTTTTTTT
....................TTTTTTTTTTT
One initial velocity that doesn't cause the probe to be within the target area after any step is 17,-4:
S..............................................................
...............................................................
...............................................................
...............................................................
.................#.............................................
....................TTTTTTTTTTT................................
....................TTTTTTTTTTT................................
....................TTTTTTTTTTT................................
....................TTTTTTTTTTT................................
....................TTTTTTTTTTT..#.............................
....................TTTTTTTTTTT................................
...............................................................
...............................................................
...............................................................
...............................................................
................................................#..............
...............................................................
...............................................................
...............................................................
...............................................................
...............................................................
...............................................................
..............................................................#
The probe appears to pass through the target area, but is never within it after any step. Instead, it continues down and to the right - only the first few steps are shown.
If you're going to fire a highly scientific probe out of a super cool probe launcher, you might as well do it with style. How high can you make the probe go while still reaching the target area?
In the above example, using an initial velocity of 6,9 is the best you can do, causing the probe to reach a maximum y position of 45. (Any higher initial y velocity causes the probe to overshoot the target area entirely.)
Find the initial velocity that causes the probe to reach the highest y position and still eventually be within the target area after any step. What is the highest y position it reaches on this trajectory?
| 371
|
--- Day 10: Elves Look, Elves Say ---
Today, the Elves are playing a game called look-and-say. They take turns making sequences by reading aloud the previous sequence and using that reading as the next sequence. For example, 211 is read as "one two, two ones", which becomes 1221 (1 2, 2 1s).
Look-and-say sequences are generated iteratively, using the previous value as input for the next step. For each step, take the previous value, and replace each run of digits (like 111) with the number of digits (3) followed by the digit itself (1).
For example:
1 becomes 11 (1 copy of digit 1).
11 becomes 21 (2 copies of digit 1).
21 becomes 1211 (one 2 followed by one 1).
1211 becomes 111221 (one 1, one 2, and two 1s).
111221 becomes 312211 (three 1s, two 2s, and one 1).
Starting with the digits in your puzzle input, apply this process 40 times. What is the length of the result?
Your puzzle answer was 252594.
--- Part Two ---
Neat, right? You might also enjoy hearing John Conway talking about this sequence (that's Conway of Conway's Game of Life fame).
Now, starting again with the digits in your puzzle input, apply this process 50 times. What is the length of the new result?
| 372
|
--- Day 25: Four-Dimensional Adventure ---
The reindeer's symptoms are getting worse, and neither you nor the white-bearded man have a solution. At least the reindeer has a warm place to rest: a small bed near where you're sitting.
As you reach down, the reindeer looks up at you, accidentally bumping a button on your wrist-mounted device with its nose in the process - a button labeled "help".
"Hello, and welcome to the Time Travel Support Hotline! If you are lost in time and space, press 1. If you are trapped in a time paradox, press 2. If you need help caring for a sick reindeer, press 3. If you--"
Beep.
A few seconds later, you hear a new voice. "Hello; please state the nature of your reindeer." You try to describe the situation.
"Just a moment, I think I can remotely run a diagnostic scan." A beam of light projects from the device and sweeps over the reindeer a few times.
"Okay, it looks like your reindeer is very low on magical energy; it should fully recover if we can fix that. Let me check your timeline for a source.... Got one. There's actually a powerful source of magical energy about 1000 years forward from you, and at roughly your position, too! It looks like... hot chocolate? Anyway, you should be able to travel there to pick some up; just don't forget a mug! Is there anything else I can help you with today?"
You explain that your device isn't capable of going forward in time. "I... see. That's tricky. Well, according to this information, your device should have the necessary hardware to open a small portal and send some hot chocolate back to you. You'll need a list of fixed points in spacetime; I'm transmitting it to you now."
"You just need to align your device to the constellations of fixed points so that it can lock on to the destination and open the portal. Let me look up how much hot chocolate that breed of reindeer needs."
"It says here that your particular reindeer is-- this can't be right, it says there's only one like that in the universe! But THAT means that you're--" You disconnect the call.
The list of fixed points in spacetime (your puzzle input) is a set of four-dimensional coordinates. To align your device, acquire the hot chocolate, and save the reindeer, you just need to find the number of constellations of points in the list.
Two points are in the same constellation if their manhattan distance apart is no more than 3 or if they can form a chain of points, each a manhattan distance no more than 3 from the last, between the two of them. (That is, if a point is close enough to a constellation, it "joins" that constellation.) For example:
0,0,0,0
3,0,0,0
0,3,0,0
0,0,3,0
0,0,0,3
0,0,0,6
9,0,0,0
12,0,0,0
In the above list, the first six points form a single constellation: 0,0,0,0 is exactly distance 3 from the next four, and the point at 0,0,0,6 is connected to the others by being 3 away from 0,0,0,3, which is already in the constellation. The bottom two points, 9,0,0,0 and 12,0,0,0 are in a separate constellation because no point is close enough to connect them to the first constellation. So, in the above list, the number of constellations is 2. (If a point at 6,0,0,0 were present, it would connect 3,0,0,0 and 9,0,0,0, merging all of the points into a single giant constellation instead.)
In this example, the number of constellations is 4:
-1,2,2,0
0,0,2,-2
0,0,0,-2
-1,2,0,0
-2,-2,-2,2
3,0,2,-1
-1,3,2,2
-1,0,-1,0
0,2,1,-2
3,0,0,0
In this one, it's 3:
1,-1,0,1
2,0,-1,0
3,2,-1,0
0,0,3,1
0,0,-1,-1
2,3,-2,0
-2,2,0,0
2,-2,0,-1
1,-1,0,-1
3,2,0,2
Finally, in this one, it's 8:
1,-1,-1,-2
-2,-2,0,1
0,2,1,3
-2,3,-2,1
0,2,3,-2
-1,-1,1,-2
0,-2,-1,0
-2,2,3,-1
1,2,2,0
-1,-2,0,-2
The portly man nervously strokes his white beard. It's time to get that hot chocolate.
How many constellations are formed by the fixed points in spacetime?
| 373
|
--- Day 4: Camp Cleanup ---
Space needs to be cleared before the last supplies can be unloaded from the ships, and so several Elves have been assigned the job of cleaning up sections of the camp. Every section has a unique ID number, and each Elf is assigned a range of section IDs.
However, as some of the Elves compare their section assignments with each other, they've noticed that many of the assignments overlap. To try to quickly find overlaps and reduce duplicated effort, the Elves pair up and make a big list of the section assignments for each pair (your puzzle input).
For example, consider the following list of section assignment pairs:
2-4,6-8
2-3,4-5
5-7,7-9
2-8,3-7
6-6,4-6
2-6,4-8
For the first few pairs, this list means:
Within the first pair of Elves, the first Elf was assigned sections 2-4 (sections 2, 3, and 4), while the second Elf was assigned sections 6-8 (sections 6, 7, 8).
The Elves in the second pair were each assigned two sections.
The Elves in the third pair were each assigned three sections: one got sections 5, 6, and 7, while the other also got 7, plus 8 and 9.
This example list uses single-digit section IDs to make it easier to draw; your actual list might contain larger numbers. Visually, these pairs of section assignments look like this:
.234..... 2-4
.....678. 6-8
.23...... 2-3
...45.... 4-5
....567.. 5-7
......789 7-9
.2345678. 2-8
..34567.. 3-7
.....6... 6-6
...456... 4-6
.23456... 2-6
...45678. 4-8
Some of the pairs have noticed that one of their assignments fully contains the other. For example, 2-8 fully contains 3-7, and 6-6 is fully contained by 4-6. In pairs where one assignment fully contains the other, one Elf in the pair would be exclusively cleaning sections their partner will already be cleaning, so these seem like the most in need of reconsideration. In this example, there are 2 such pairs.
In how many assignment pairs does one range fully contain the other?
Your puzzle answer was 526.
--- Part Two ---
It seems like there is still quite a bit of duplicate work planned. Instead, the Elves would like to know the number of pairs that overlap at all.
In the above example, the first two pairs (2-4,6-8 and 2-3,4-5) don't overlap, while the remaining four pairs (5-7,7-9, 2-8,3-7, 6-6,4-6, and 2-6,4-8) do overlap:
5-7,7-9 overlaps in a single section, 7.
2-8,3-7 overlaps all of the sections 3 through 7.
6-6,4-6 overlaps in a single section, 6.
2-6,4-8 overlaps in sections 4, 5, and 6.
So, in this example, the number of overlapping assignment pairs is 4.
In how many assignment pairs do the ranges overlap?
| 374
|
--- Day 13: Claw Contraption ---
Next up: the lobby of a resort on a tropical island. The Historians take a moment to admire the hexagonal floor tiles before spreading out.
Fortunately, it looks like the resort has a new arcade! Maybe you can win some prizes from the claw machines?
The claw machines here are a little unusual. Instead of a joystick or directional buttons to control the claw, these machines have two buttons labeled A and B. Worse, you can't just put in a token and play; it costs 3 tokens to push the A button and 1 token to push the B button.
With a little experimentation, you figure out that each machine's buttons are configured to move the claw a specific amount to the right (along the X axis) and a specific amount forward (along the Y axis) each time that button is pressed.
Each machine contains one prize; to win the prize, the claw must be positioned exactly above the prize on both the X and Y axes.
You wonder: what is the smallest number of tokens you would have to spend to win as many prizes as possible? You assemble a list of every machine's button behavior and prize location (your puzzle input). For example:
Button A: X+94, Y+34
Button B: X+22, Y+67
Prize: X=8400, Y=5400
Button A: X+26, Y+66
Button B: X+67, Y+21
Prize: X=12748, Y=12176
Button A: X+17, Y+86
Button B: X+84, Y+37
Prize: X=7870, Y=6450
Button A: X+69, Y+23
Button B: X+27, Y+71
Prize: X=18641, Y=10279
This list describes the button configuration and prize location of four different claw machines.
For now, consider just the first claw machine in the list:
Pushing the machine's A button would move the claw 94 units along the X axis and 34 units along the Y axis.
Pushing the B button would move the claw 22 units along the X axis and 67 units along the Y axis.
The prize is located at X=8400, Y=5400; this means that from the claw's initial position, it would need to move exactly 8400 units along the X axis and exactly 5400 units along the Y axis to be perfectly aligned with the prize in this machine.
The cheapest way to win the prize is by pushing the A button 80 times and the B button 40 times. This would line up the claw along the X axis (because 80*94 + 40*22 = 8400) and along the Y axis (because 80*34 + 40*67 = 5400). Doing this would cost 80*3 tokens for the A presses and 40*1 for the B presses, a total of 280 tokens.
For the second and fourth claw machines, there is no combination of A and B presses that will ever win a prize.
For the third claw machine, the cheapest way to win the prize is by pushing the A button 38 times and the B button 86 times. Doing this would cost a total of 200 tokens.
So, the most prizes you could possibly win is two; the minimum tokens you would have to spend to win all (two) prizes is 480.
You estimate that each button would need to be pressed no more than 100 times to win a prize. How else would someone be expected to play?
Figure out how to win as many prizes as possible. What is the fewest tokens you would have to spend to win all possible prizes?
| 375
|
--- Day 11: Seating System ---
Your plane lands with plenty of time to spare. The final leg of your journey is a ferry that goes directly to the tropical island where you can finally start your vacation. As you reach the waiting area to board the ferry, you realize you're so early, nobody else has even arrived yet!
By modeling the process people use to choose (or abandon) their seat in the waiting area, you're pretty sure you can predict the best place to sit. You make a quick map of the seat layout (your puzzle input).
The seat layout fits neatly on a grid. Each position is either floor (.), an empty seat (L), or an occupied seat (#). For example, the initial seat layout might look like this:
L.LL.LL.LL
LLLLLLL.LL
L.L.L..L..
LLLL.LL.LL
L.LL.LL.LL
L.LLLLL.LL
..L.L.....
LLLLLLLLLL
L.LLLLLL.L
L.LLLLL.LL
Now, you just need to model the people who will be arriving shortly. Fortunately, people are entirely predictable and always follow a simple set of rules. All decisions are based on the number of occupied seats adjacent to a given seat (one of the eight positions immediately up, down, left, right, or diagonal from the seat). The following rules are applied to every seat simultaneously:
If a seat is empty (L) and there are no occupied seats adjacent to it, the seat becomes occupied.
If a seat is occupied (#) and four or more seats adjacent to it are also occupied, the seat becomes empty.
Otherwise, the seat's state does not change.
Floor (.) never changes; seats don't move, and nobody sits on the floor.
After one round of these rules, every seat in the example layout becomes occupied:
#.##.##.##
#######.##
#.#.#..#..
####.##.##
#.##.##.##
#.#####.##
..#.#.....
##########
#.######.#
#.#####.##
After a second round, the seats with four or more occupied adjacent seats become empty again:
#.LL.L#.##
#LLLLLL.L#
L.L.L..L..
#LLL.LL.L#
#.LL.LL.LL
#.LLLL#.##
..L.L.....
#LLLLLLLL#
#.LLLLLL.L
#.#LLLL.##
This process continues for three more rounds:
#.##.L#.##
#L###LL.L#
L.#.#..#..
#L##.##.L#
#.##.LL.LL
#.###L#.##
..#.#.....
#L######L#
#.LL###L.L
#.#L###.##
#.#L.L#.##
#LLL#LL.L#
L.L.L..#..
#LLL.##.L#
#.LL.LL.LL
#.LL#L#.##
..L.L.....
#L#LLLL#L#
#.LLLLLL.L
#.#L#L#.##
#.#L.L#.##
#LLL#LL.L#
L.#.L..#..
#L##.##.L#
#.#L.LL.LL
#.#L#L#.##
..L.L.....
#L#L##L#L#
#.LLLLLL.L
#.#L#L#.##
At this point, something interesting happens: the chaos stabilizes and further applications of these rules cause no seats to change state! Once people stop moving around, you count 37 occupied seats.
Simulate your seating area by applying the seating rules repeatedly until no seats change state. How many seats end up occupied?
Your puzzle answer was 2126.
--- Part Two ---
As soon as people start to arrive, you realize your mistake. People don't just care about adjacent seats - they care about the first seat they can see in each of those eight directions!
Now, instead of considering just the eight immediately adjacent seats, consider the first seat in each of those eight directions. For example, the empty seat below would see eight occupied seats:
.......#.
...#.....
.#.......
.........
..#L....#
....#....
.........
#........
...#.....
The leftmost empty seat below would only see one empty seat, but cannot see any of the occupied ones:
.............
.L.L.#.#.#.#.
.............
The empty seat below would see no occupied seats:
.##.##.
#.#.#.#
##...##
...L...
##...##
#.#.#.#
.##.##.
Also, people seem to be more tolerant than you expected: it now takes five or more visible occupied seats for an occupied seat to become empty (rather than four or more from the previous rules). The other rules still apply: empty seats that see no occupied seats become occupied, seats matching no rule don't change, and floor never changes.
Given the same starting layout as above, these new rules cause the seating area to shift around as follows:
L.LL.LL.LL
LLLLLLL.LL
L.L.L..L..
LLLL.LL.LL
L.LL.LL.LL
L.LLLLL.LL
..L.L.....
LLLLLLLLLL
L.LLLLLL.L
L.LLLLL.LL
#.##.##.##
#######.##
#.#.#..#..
####.##.##
#.##.##.##
#.#####.##
..#.#.....
##########
#.######.#
#.#####.##
#.LL.LL.L#
#LLLLLL.LL
L.L.L..L..
LLLL.LL.LL
L.LL.LL.LL
L.LLLLL.LL
..L.L.....
LLLLLLLLL#
#.LLLLLL.L
#.LLLLL.L#
#.L#.##.L#
#L#####.LL
L.#.#..#..
##L#.##.##
#.##.#L.##
#.#####.#L
..#.#.....
LLL####LL#
#.L#####.L
#.L####.L#
#.L#.L#.L#
#LLLLLL.LL
L.L.L..#..
##LL.LL.L#
L.LL.LL.L#
#.LLLLL.LL
..L.L.....
LLLLLLLLL#
#.LLLLL#.L
#.L#LL#.L#
#.L#.L#.L#
#LLLLLL.LL
L.L.L..#..
##L#.#L.L#
L.L#.#L.L#
#.L####.LL
..#.#.....
LLL###LLL#
#.LLLLL#.L
#.L#LL#.L#
#.L#.L#.L#
#LLLLLL.LL
L.L.L..#..
##L#.#L.L#
L.L#.LL.L#
#.LLLL#.LL
..#.L.....
LLL###LLL#
#.LLLLL#.L
#.L#LL#.L#
Again, at this point, people stop shifting around and the seating area reaches equilibrium. Once this occurs, you count 26 occupied seats.
Given the new visibility method and the rule change for occupied seats becoming empty, once equilibrium is reached, how many seats end up occupied?
| 376
|
--- Day 21: Keypad Conundrum ---
As you teleport onto Santa's Reindeer-class starship, The Historians begin to panic: someone from their search party is missing. A quick life-form scan by the ship's computer reveals that when the missing Historian teleported, he arrived in another part of the ship.
The door to that area is locked, but the computer can't open it; it can only be opened by physically typing the door codes (your puzzle input) on the numeric keypad on the door.
The numeric keypad has four rows of buttons: 789, 456, 123, and finally an empty gap followed by 0A. Visually, they are arranged like this:
+---+---+---+
| 7 | 8 | 9 |
+---+---+---+
| 4 | 5 | 6 |
+---+---+---+
| 1 | 2 | 3 |
+---+---+---+
| 0 | A |
+---+---+
Unfortunately, the area outside the door is currently depressurized and nobody can go near the door. A robot needs to be sent instead.
The robot has no problem navigating the ship and finding the numeric keypad, but it's not designed for button pushing: it can't be told to push a specific button directly. Instead, it has a robotic arm that can be controlled remotely via a directional keypad.
The directional keypad has two rows of buttons: a gap / ^ (up) / A (activate) on the first row and < (left) / v (down) / > (right) on the second row. Visually, they are arranged like this:
+---+---+
| ^ | A |
+---+---+---+
| < | v | > |
+---+---+---+
When the robot arrives at the numeric keypad, its robotic arm is pointed at the A button in the bottom right corner. After that, this directional keypad remote control must be used to maneuver the robotic arm: the up / down / left / right buttons cause it to move its arm one button in that direction, and the A button causes the robot to briefly move forward, pressing the button being aimed at by the robotic arm.
For example, to make the robot type 029A on the numeric keypad, one sequence of inputs on the directional keypad you could use is:
< to move the arm from A (its initial position) to 0.
A to push the 0 button.
^A to move the arm to the 2 button and push it.
>^^A to move the arm to the 9 button and push it.
vvvA to move the arm to the A button and push it.
In total, there are three shortest possible sequences of button presses on this directional keypad that would cause the robot to type 029A: <A^A>^^AvvvA, <A^A^>^AvvvA, and <A^A^^>AvvvA.
Unfortunately, the area containing this directional keypad remote control is currently experiencing high levels of radiation and nobody can go near it. A robot needs to be sent instead.
When the robot arrives at the directional keypad, its robot arm is pointed at the A button in the upper right corner. After that, a second, different directional keypad remote control is used to control this robot (in the same way as the first robot, except that this one is typing on a directional keypad instead of a numeric keypad).
There are multiple shortest possible sequences of directional keypad button presses that would cause this robot to tell the first robot to type 029A on the door. One such sequence is v<<A>>^A<A>AvA<^AA>A<vAAA>^A.
Unfortunately, the area containing this second directional keypad remote control is currently -40 degrees! Another robot will need to be sent to type on that directional keypad, too.
There are many shortest possible sequences of directional keypad button presses that would cause this robot to tell the second robot to tell the first robot to eventually type 029A on the door. One such sequence is <vA<AA>>^AvAA<^A>A<v<A>>^AvA^A<vA>^A<v<A>^A>AAvA^A<v<A>A>^AAAvA<^A>A.
Unfortunately, the area containing this third directional keypad remote control is currently full of Historians, so no robots can find a clear path there. Instead, you will have to type this sequence yourself.
Were you to choose this sequence of button presses, here are all of the buttons that would be pressed on your directional keypad, the two robots' directional keypads, and the numeric keypad:
<vA<AA>>^AvAA<^A>A<v<A>>^AvA^A<vA>^A<v<A>^A>AAvA^A<v<A>A>^AAAvA<^A>A
v<<A>>^A<A>AvA<^AA>A<vAAA>^A
<A^A>^^AvvvA
029A
In summary, there are the following keypads:
One directional keypad that you are using.
Two directional keypads that robots are using.
One numeric keypad (on a door) that a robot is using.
It is important to remember that these robots are not designed for button pushing. In particular, if a robot arm is ever aimed at a gap where no button is present on the keypad, even for an instant, the robot will panic unrecoverably. So, don't do that. All robots will initially aim at the keypad's A key, wherever it is.
To unlock the door, five codes will need to be typed on its numeric keypad. For example:
029A
980A
179A
456A
379A
For each of these, here is a shortest sequence of button presses you could type to cause the desired code to be typed on the numeric keypad:
029A: <vA<AA>>^AvAA<^A>A<v<A>>^AvA^A<vA>^A<v<A>^A>AAvA^A<v<A>A>^AAAvA<^A>A
980A: <v<A>>^AAAvA^A<vA<AA>>^AvAA<^A>A<v<A>A>^AAAvA<^A>A<vA>^A<A>A
179A: <v<A>>^A<vA<A>>^AAvAA<^A>A<v<A>>^AAvA^A<vA>^AA<A>A<v<A>A>^AAAvA<^A>A
456A: <v<A>>^AA<vA<A>>^AAvAA<^A>A<vA>^A<A>A<vA>^A<A>A<v<A>A>^AAvA<^A>A
379A: <v<A>>^AvA^A<vA<AA>>^AAvA<^A>AAvA^A<vA>^AA<A>A<v<A>A>^AAAvA<^A>A
The Historians are getting nervous; the ship computer doesn't remember whether the missing Historian is trapped in the area containing a giant electromagnet or molten lava. You'll need to make sure that for each of the five codes, you find the shortest sequence of button presses necessary.
The complexity of a single code (like 029A) is equal to the result of multiplying these two values:
The length of the shortest sequence of button presses you need to type on your directional keypad in order to cause the code to be typed on the numeric keypad; for 029A, this would be 68.
The numeric part of the code (ignoring leading zeroes); for 029A, this would be 29.
In the above example, complexity of the five codes can be found by calculating 68 * 29, 60 * 980, 68 * 179, 64 * 456, and 64 * 379. Adding these together produces 126384.
Find the fewest number of button presses you'll need to perform in order to cause the robot in front of the door to type each code. What is the sum of the complexities of the five codes on your list?
| 377
|
--- Day 4: Security Through Obscurity ---
Finally, you come across an information kiosk with a list of rooms. Of course, the list is encrypted and full of decoy data, but the instructions to decode the list are barely hidden nearby. Better remove the decoy data first.
Each room consists of an encrypted name (lowercase letters separated by dashes) followed by a dash, a sector ID, and a checksum in square brackets.
A room is real (not a decoy) if the checksum is the five most common letters in the encrypted name, in order, with ties broken by alphabetization. For example:
aaaaa-bbb-z-y-x-123[abxyz] is a real room because the most common letters are a (5), b (3), and then a tie between x, y, and z, which are listed alphabetically.
a-b-c-d-e-f-g-h-987[abcde] is a real room because although the letters are all tied (1 of each), the first five are listed alphabetically.
not-a-real-room-404[oarel] is a real room.
totally-real-room-200[decoy] is not.
Of the real rooms from the list above, the sum of their sector IDs is 1514.
What is the sum of the sector IDs of the real rooms?
| 378
|
--- Day 16: Flawed Frequency Transmission ---
You're 3/4ths of the way through the gas giants. Not only do roundtrip signals to Earth take five hours, but the signal quality is quite bad as well. You can clean up the signal with the Flawed Frequency Transmission algorithm, or FFT.
As input, FFT takes a list of numbers. In the signal you received (your puzzle input), each number is a single digit: data like 15243 represents the sequence 1, 5, 2, 4, 3.
FFT operates in repeated phases. In each phase, a new list is constructed with the same length as the input list. This new list is also used as the input for the next phase.
Each element in the new list is built by multiplying every value in the input list by a value in a repeating pattern and then adding up the results. So, if the input list were 9, 8, 7, 6, 5 and the pattern for a given element were 1, 2, 3, the result would be 9*1 + 8*2 + 7*3 + 6*1 + 5*2 (with each input element on the left and each value in the repeating pattern on the right of each multiplication). Then, only the ones digit is kept: 38 becomes 8, -17 becomes 7, and so on.
While each element in the output array uses all of the same input array elements, the actual repeating pattern to use depends on which output element is being calculated. The base pattern is 0, 1, 0, -1. Then, repeat each value in the pattern a number of times equal to the position in the output list being considered. Repeat once for the first element, twice for the second element, three times for the third element, and so on. So, if the third element of the output list is being calculated, repeating the values would produce: 0, 0, 0, 1, 1, 1, 0, 0, 0, -1, -1, -1.
When applying the pattern, skip the very first value exactly once. (In other words, offset the whole pattern left by one.) So, for the second element of the output list, the actual pattern used would be: 0, 1, 1, 0, 0, -1, -1, 0, 0, 1, 1, 0, 0, -1, -1, ....
After using this process to calculate each element of the output list, the phase is complete, and the output list of this phase is used as the new input list for the next phase, if any.
Given the input signal 12345678, below are four phases of FFT. Within each phase, each output digit is calculated on a single line with the result at the far right; each multiplication operation shows the input digit on the left and the pattern value on the right:
Input signal: 12345678
1*1 + 2*0 + 3*-1 + 4*0 + 5*1 + 6*0 + 7*-1 + 8*0 = 4
1*0 + 2*1 + 3*1 + 4*0 + 5*0 + 6*-1 + 7*-1 + 8*0 = 8
1*0 + 2*0 + 3*1 + 4*1 + 5*1 + 6*0 + 7*0 + 8*0 = 2
1*0 + 2*0 + 3*0 + 4*1 + 5*1 + 6*1 + 7*1 + 8*0 = 2
1*0 + 2*0 + 3*0 + 4*0 + 5*1 + 6*1 + 7*1 + 8*1 = 6
1*0 + 2*0 + 3*0 + 4*0 + 5*0 + 6*1 + 7*1 + 8*1 = 1
1*0 + 2*0 + 3*0 + 4*0 + 5*0 + 6*0 + 7*1 + 8*1 = 5
1*0 + 2*0 + 3*0 + 4*0 + 5*0 + 6*0 + 7*0 + 8*1 = 8
After 1 phase: 48226158
4*1 + 8*0 + 2*-1 + 2*0 + 6*1 + 1*0 + 5*-1 + 8*0 = 3
4*0 + 8*1 + 2*1 + 2*0 + 6*0 + 1*-1 + 5*-1 + 8*0 = 4
4*0 + 8*0 + 2*1 + 2*1 + 6*1 + 1*0 + 5*0 + 8*0 = 0
4*0 + 8*0 + 2*0 + 2*1 + 6*1 + 1*1 + 5*1 + 8*0 = 4
4*0 + 8*0 + 2*0 + 2*0 + 6*1 + 1*1 + 5*1 + 8*1 = 0
4*0 + 8*0 + 2*0 + 2*0 + 6*0 + 1*1 + 5*1 + 8*1 = 4
4*0 + 8*0 + 2*0 + 2*0 + 6*0 + 1*0 + 5*1 + 8*1 = 3
4*0 + 8*0 + 2*0 + 2*0 + 6*0 + 1*0 + 5*0 + 8*1 = 8
After 2 phases: 34040438
3*1 + 4*0 + 0*-1 + 4*0 + 0*1 + 4*0 + 3*-1 + 8*0 = 0
3*0 + 4*1 + 0*1 + 4*0 + 0*0 + 4*-1 + 3*-1 + 8*0 = 3
3*0 + 4*0 + 0*1 + 4*1 + 0*1 + 4*0 + 3*0 + 8*0 = 4
3*0 + 4*0 + 0*0 + 4*1 + 0*1 + 4*1 + 3*1 + 8*0 = 1
3*0 + 4*0 + 0*0 + 4*0 + 0*1 + 4*1 + 3*1 + 8*1 = 5
3*0 + 4*0 + 0*0 + 4*0 + 0*0 + 4*1 + 3*1 + 8*1 = 5
3*0 + 4*0 + 0*0 + 4*0 + 0*0 + 4*0 + 3*1 + 8*1 = 1
3*0 + 4*0 + 0*0 + 4*0 + 0*0 + 4*0 + 3*0 + 8*1 = 8
After 3 phases: 03415518
0*1 + 3*0 + 4*-1 + 1*0 + 5*1 + 5*0 + 1*-1 + 8*0 = 0
0*0 + 3*1 + 4*1 + 1*0 + 5*0 + 5*-1 + 1*-1 + 8*0 = 1
0*0 + 3*0 + 4*1 + 1*1 + 5*1 + 5*0 + 1*0 + 8*0 = 0
0*0 + 3*0 + 4*0 + 1*1 + 5*1 + 5*1 + 1*1 + 8*0 = 2
0*0 + 3*0 + 4*0 + 1*0 + 5*1 + 5*1 + 1*1 + 8*1 = 9
0*0 + 3*0 + 4*0 + 1*0 + 5*0 + 5*1 + 1*1 + 8*1 = 4
0*0 + 3*0 + 4*0 + 1*0 + 5*0 + 5*0 + 1*1 + 8*1 = 9
0*0 + 3*0 + 4*0 + 1*0 + 5*0 + 5*0 + 1*0 + 8*1 = 8
After 4 phases: 01029498
Here are the first eight digits of the final output list after 100 phases for some larger inputs:
80871224585914546619083218645595 becomes 24176176.
19617804207202209144916044189917 becomes 73745418.
69317163492948606335995924319873 becomes 52432133.
After 100 phases of FFT, what are the first eight digits in the final output list?
Your puzzle answer was 73127523.
--- Part Two ---
Now that your FFT is working, you can decode the real signal.
The real signal is your puzzle input repeated 10000 times. Treat this new signal as a single input list. Patterns are still calculated as before, and 100 phases of FFT are still applied.
The first seven digits of your initial input signal also represent the message offset. The message offset is the location of the eight-digit message in the final output list. Specifically, the message offset indicates the number of digits to skip before reading the eight-digit message. For example, if the first seven digits of your initial input signal were 1234567, the eight-digit message would be the eight digits after skipping 1,234,567 digits of the final output list. Or, if the message offset were 7 and your final output list were 98765432109876543210, the eight-digit message would be 21098765. (Of course, your real message offset will be a seven-digit number, not a one-digit number like 7.)
Here is the eight-digit message in the final output list after 100 phases. The message offset given in each input has been highlighted. (Note that the inputs given below are repeated 10000 times to find the actual starting input lists.)
03036732577212944063491565474664 becomes 84462026.
02935109699940807407585447034323 becomes 78725270.
03081770884921959731165446850517 becomes 53553731.
After repeating your input signal 10000 times and running 100 phases of FFT, what is the eight-digit message embedded in the final output list?
| 379
|
--- Day 14: Space Stoichiometry ---
As you approach the rings of Saturn, your ship's low fuel indicator turns on. There isn't any fuel here, but the rings have plenty of raw material. Perhaps your ship's Inter-Stellar Refinery Union brand nanofactory can turn these raw materials into fuel.
You ask the nanofactory to produce a list of the reactions it can perform that are relevant to this process (your puzzle input). Every reaction turns some quantities of specific input chemicals into some quantity of an output chemical. Almost every chemical is produced by exactly one reaction; the only exception, ORE, is the raw material input to the entire process and is not produced by a reaction.
You just need to know how much ORE you'll need to collect before you can produce one unit of FUEL.
Each reaction gives specific quantities for its inputs and output; reactions cannot be partially run, so only whole integer multiples of these quantities can be used. (It's okay to have leftover chemicals when you're done, though.) For example, the reaction 1 A, 2 B, 3 C => 2 D means that exactly 2 units of chemical D can be produced by consuming exactly 1 A, 2 B and 3 C. You can run the full reaction as many times as necessary; for example, you could produce 10 D by consuming 5 A, 10 B, and 15 C.
Suppose your nanofactory produces the following list of reactions:
10 ORE => 10 A
1 ORE => 1 B
7 A, 1 B => 1 C
7 A, 1 C => 1 D
7 A, 1 D => 1 E
7 A, 1 E => 1 FUEL
The first two reactions use only ORE as inputs; they indicate that you can produce as much of chemical A as you want (in increments of 10 units, each 10 costing 10 ORE) and as much of chemical B as you want (each costing 1 ORE). To produce 1 FUEL, a total of 31 ORE is required: 1 ORE to produce 1 B, then 30 more ORE to produce the 7 + 7 + 7 + 7 = 28 A (with 2 extra A wasted) required in the reactions to convert the B into C, C into D, D into E, and finally E into FUEL. (30 A is produced because its reaction requires that it is created in increments of 10.)
Or, suppose you have the following list of reactions:
9 ORE => 2 A
8 ORE => 3 B
7 ORE => 5 C
3 A, 4 B => 1 AB
5 B, 7 C => 1 BC
4 C, 1 A => 1 CA
2 AB, 3 BC, 4 CA => 1 FUEL
The above list of reactions requires 165 ORE to produce 1 FUEL:
Consume 45 ORE to produce 10 A.
Consume 64 ORE to produce 24 B.
Consume 56 ORE to produce 40 C.
Consume 6 A, 8 B to produce 2 AB.
Consume 15 B, 21 C to produce 3 BC.
Consume 16 C, 4 A to produce 4 CA.
Consume 2 AB, 3 BC, 4 CA to produce 1 FUEL.
Here are some larger examples:
13312 ORE for 1 FUEL:
157 ORE => 5 NZVS
165 ORE => 6 DCFZ
44 XJWVT, 5 KHKGT, 1 QDVJ, 29 NZVS, 9 GPVTF, 48 HKGWZ => 1 FUEL
12 HKGWZ, 1 GPVTF, 8 PSHF => 9 QDVJ
179 ORE => 7 PSHF
177 ORE => 5 HKGWZ
7 DCFZ, 7 PSHF => 2 XJWVT
165 ORE => 2 GPVTF
3 DCFZ, 7 NZVS, 5 HKGWZ, 10 PSHF => 8 KHKGT
180697 ORE for 1 FUEL:
2 VPVL, 7 FWMGM, 2 CXFTF, 11 MNCFX => 1 STKFG
17 NVRVD, 3 JNWZP => 8 VPVL
53 STKFG, 6 MNCFX, 46 VJHF, 81 HVMC, 68 CXFTF, 25 GNMV => 1 FUEL
22 VJHF, 37 MNCFX => 5 FWMGM
139 ORE => 4 NVRVD
144 ORE => 7 JNWZP
5 MNCFX, 7 RFSQX, 2 FWMGM, 2 VPVL, 19 CXFTF => 3 HVMC
5 VJHF, 7 MNCFX, 9 VPVL, 37 CXFTF => 6 GNMV
145 ORE => 6 MNCFX
1 NVRVD => 8 CXFTF
1 VJHF, 6 MNCFX => 4 RFSQX
176 ORE => 6 VJHF
2210736 ORE for 1 FUEL:
171 ORE => 8 CNZTR
7 ZLQW, 3 BMBT, 9 XCVML, 26 XMNCP, 1 WPTQ, 2 MZWV, 1 RJRHP => 4 PLWSL
114 ORE => 4 BHXH
14 VRPVC => 6 BMBT
6 BHXH, 18 KTJDG, 12 WPTQ, 7 PLWSL, 31 FHTLT, 37 ZDVW => 1 FUEL
6 WPTQ, 2 BMBT, 8 ZLQW, 18 KTJDG, 1 XMNCP, 6 MZWV, 1 RJRHP => 6 FHTLT
15 XDBXC, 2 LTCX, 1 VRPVC => 6 ZLQW
13 WPTQ, 10 LTCX, 3 RJRHP, 14 XMNCP, 2 MZWV, 1 ZLQW => 1 ZDVW
5 BMBT => 4 WPTQ
189 ORE => 9 KTJDG
1 MZWV, 17 XDBXC, 3 XCVML => 2 XMNCP
12 VRPVC, 27 CNZTR => 2 XDBXC
15 KTJDG, 12 BHXH => 5 XCVML
3 BHXH, 2 VRPVC => 7 MZWV
121 ORE => 7 VRPVC
7 XCVML => 6 RJRHP
5 BHXH, 4 VRPVC => 5 LTCX
Given the list of reactions in your puzzle input, what is the minimum amount of ORE required to produce exactly 1 FUEL?
Your puzzle answer was 522031.
--- Part Two ---
After collecting ORE for a while, you check your cargo hold: 1 trillion (1000000000000) units of ORE.
With that much ore, given the examples above:
The 13312 ORE-per-FUEL example could produce 82892753 FUEL.
The 180697 ORE-per-FUEL example could produce 5586022 FUEL.
The 2210736 ORE-per-FUEL example could produce 460664 FUEL.
Given 1 trillion ORE, what is the maximum amount of FUEL you can produce?--- Day 14: Space Stoichiometry ---
As you approach the rings of Saturn, your ship's low fuel indicator turns on. There isn't any fuel here, but the rings have plenty of raw material. Perhaps your ship's Inter-Stellar Refinery Union brand nanofactory can turn these raw materials into fuel.
You ask the nanofactory to produce a list of the reactions it can perform that are relevant to this process (your puzzle input). Every reaction turns some quantities of specific input chemicals into some quantity of an output chemical. Almost every chemical is produced by exactly one reaction; the only exception, ORE, is the raw material input to the entire process and is not produced by a reaction.
You just need to know how much ORE you'll need to collect before you can produce one unit of FUEL.
Each reaction gives specific quantities for its inputs and output; reactions cannot be partially run, so only whole integer multiples of these quantities can be used. (It's okay to have leftover chemicals when you're done, though.) For example, the reaction 1 A, 2 B, 3 C => 2 D means that exactly 2 units of chemical D can be produced by consuming exactly 1 A, 2 B and 3 C. You can run the full reaction as many times as necessary; for example, you could produce 10 D by consuming 5 A, 10 B, and 15 C.
Suppose your nanofactory produces the following list of reactions:
10 ORE => 10 A
1 ORE => 1 B
7 A, 1 B => 1 C
7 A, 1 C => 1 D
7 A, 1 D => 1 E
7 A, 1 E => 1 FUEL
The first two reactions use only ORE as inputs; they indicate that you can produce as much of chemical A as you want (in increments of 10 units, each 10 costing 10 ORE) and as much of chemical B as you want (each costing 1 ORE). To produce 1 FUEL, a total of 31 ORE is required: 1 ORE to produce 1 B, then 30 more ORE to produce the 7 + 7 + 7 + 7 = 28 A (with 2 extra A wasted) required in the reactions to convert the B into C, C into D, D into E, and finally E into FUEL. (30 A is produced because its reaction requires that it is created in increments of 10.)
Or, suppose you have the following list of reactions:
9 ORE => 2 A
8 ORE => 3 B
7 ORE => 5 C
3 A, 4 B => 1 AB
5 B, 7 C => 1 BC
4 C, 1 A => 1 CA
2 AB, 3 BC, 4 CA => 1 FUEL
The above list of reactions requires 165 ORE to produce 1 FUEL:
Consume 45 ORE to produce 10 A.
Consume 64 ORE to produce 24 B.
Consume 56 ORE to produce 40 C.
Consume 6 A, 8 B to produce 2 AB.
Consume 15 B, 21 C to produce 3 BC.
Consume 16 C, 4 A to produce 4 CA.
Consume 2 AB, 3 BC, 4 CA to produce 1 FUEL.
Here are some larger examples:
13312 ORE for 1 FUEL:
157 ORE => 5 NZVS
165 ORE => 6 DCFZ
44 XJWVT, 5 KHKGT, 1 QDVJ, 29 NZVS, 9 GPVTF, 48 HKGWZ => 1 FUEL
12 HKGWZ, 1 GPVTF, 8 PSHF => 9 QDVJ
179 ORE => 7 PSHF
177 ORE => 5 HKGWZ
7 DCFZ, 7 PSHF => 2 XJWVT
165 ORE => 2 GPVTF
3 DCFZ, 7 NZVS, 5 HKGWZ, 10 PSHF => 8 KHKGT
180697 ORE for 1 FUEL:
2 VPVL, 7 FWMGM, 2 CXFTF, 11 MNCFX => 1 STKFG
17 NVRVD, 3 JNWZP => 8 VPVL
53 STKFG, 6 MNCFX, 46 VJHF, 81 HVMC, 68 CXFTF, 25 GNMV => 1 FUEL
22 VJHF, 37 MNCFX => 5 FWMGM
139 ORE => 4 NVRVD
144 ORE => 7 JNWZP
5 MNCFX, 7 RFSQX, 2 FWMGM, 2 VPVL, 19 CXFTF => 3 HVMC
5 VJHF, 7 MNCFX, 9 VPVL, 37 CXFTF => 6 GNMV
145 ORE => 6 MNCFX
1 NVRVD => 8 CXFTF
1 VJHF, 6 MNCFX => 4 RFSQX
176 ORE => 6 VJHF
2210736 ORE for 1 FUEL:
171 ORE => 8 CNZTR
7 ZLQW, 3 BMBT, 9 XCVML, 26 XMNCP, 1 WPTQ, 2 MZWV, 1 RJRHP => 4 PLWSL
114 ORE => 4 BHXH
14 VRPVC => 6 BMBT
6 BHXH, 18 KTJDG, 12 WPTQ, 7 PLWSL, 31 FHTLT, 37 ZDVW => 1 FUEL
6 WPTQ, 2 BMBT, 8 ZLQW, 18 KTJDG, 1 XMNCP, 6 MZWV, 1 RJRHP => 6 FHTLT
15 XDBXC, 2 LTCX, 1 VRPVC => 6 ZLQW
13 WPTQ, 10 LTCX, 3 RJRHP, 14 XMNCP, 2 MZWV, 1 ZLQW => 1 ZDVW
5 BMBT => 4 WPTQ
189 ORE => 9 KTJDG
1 MZWV, 17 XDBXC, 3 XCVML => 2 XMNCP
12 VRPVC, 27 CNZTR => 2 XDBXC
15 KTJDG, 12 BHXH => 5 XCVML
3 BHXH, 2 VRPVC => 7 MZWV
121 ORE => 7 VRPVC
7 XCVML => 6 RJRHP
5 BHXH, 4 VRPVC => 5 LTCX
Given the list of reactions in your puzzle input, what is the minimum amount of ORE required to produce exactly 1 FUEL?
Your puzzle answer was 522031.
--- Part Two ---
After collecting ORE for a while, you check your cargo hold: 1 trillion (1000000000000) units of ORE.
With that much ore, given the examples above:
The 13312 ORE-per-FUEL example could produce 82892753 FUEL.
The 180697 ORE-per-FUEL example could produce 5586022 FUEL.
The 2210736 ORE-per-FUEL example could produce 460664 FUEL.
Given 1 trillion ORE, what is the maximum amount of FUEL you can produce?
| 380
|
--- Day 24: Electromagnetic Moat ---
The CPU itself is a large, black building surrounded by a bottomless pit. Enormous metal tubes extend outward from the side of the building at regular intervals and descend down into the void. There's no way to cross, but you need to get inside.
No way, of course, other than building a bridge out of the magnetic components strewn about nearby.
Each component has two ports, one on each end. The ports come in all different types, and only matching types can be connected. You take an inventory of the components by their port types (your puzzle input). Each port is identified by the number of pins it uses; more pins mean a stronger connection for your bridge. A 3/7 component, for example, has a type-3 port on one side, and a type-7 port on the other.
Your side of the pit is metallic; a perfect surface to connect a magnetic, zero-pin port. Because of this, the first port you use must be of type 0. It doesn't matter what type of port you end with; your goal is just to make the bridge as strong as possible.
The strength of a bridge is the sum of the port types in each component. For example, if your bridge is made of components 0/3, 3/7, and 7/4, your bridge has a strength of 0+3 + 3+7 + 7+4 = 24.
For example, suppose you had the following components:
0/2
2/2
2/3
3/4
3/5
0/1
10/1
9/10
With them, you could make the following valid bridges:
0/1
0/1--10/1
0/1--10/1--9/10
0/2
0/2--2/3
0/2--2/3--3/4
0/2--2/3--3/5
0/2--2/2
0/2--2/2--2/3
0/2--2/2--2/3--3/4
0/2--2/2--2/3--3/5
(Note how, as shown by 10/1, order of ports within a component doesn't matter. However, you may only use each port on a component once.)
Of these bridges, the strongest one is 0/1--10/1--9/10; it has a strength of 0+1 + 1+10 + 10+9 = 31.
What is the strength of the strongest bridge you can make with the components you have available?
Your puzzle answer was 1868.
--- Part Two ---
The bridge you've built isn't long enough; you can't jump the rest of the way.
In the example above, there are two longest bridges:
0/2--2/2--2/3--3/4
0/2--2/2--2/3--3/5
Of them, the one which uses the 3/5 component is stronger; its strength is 0+2 + 2+2 + 2+3 + 3+5 = 19.
What is the strength of the longest bridge you can make? If you can make multiple bridges of the longest length, pick the strongest one.
| 381
|
--- Day 22: Mode Maze ---
This is it, your final stop: the year -483. It's snowing and dark outside; the only light you can see is coming from a small cottage in the distance. You make your way there and knock on the door.
A portly man with a large, white beard answers the door and invites you inside. For someone living near the North Pole in -483, he must not get many visitors, but he doesn't act surprised to see you. Instead, he offers you some milk and cookies.
After talking for a while, he asks a favor of you. His friend hasn't come back in a few hours, and he's not sure where he is. Scanning the region briefly, you discover one life signal in a cave system nearby; his friend must have taken shelter there. The man asks if you can go there to retrieve his friend.
The cave is divided into square regions which are either dominantly rocky, narrow, or wet (called its type). Each region occupies exactly one coordinate in X,Y format where X and Y are integers and zero or greater. (Adjacent regions can be the same type.)
The scan (your puzzle input) is not very detailed: it only reveals the depth of the cave system and the coordinates of the target. However, it does not reveal the type of each region. The mouth of the cave is at 0,0.
The man explains that due to the unusual geology in the area, there is a method to determine any region's type based on its erosion level. The erosion level of a region can be determined from its geologic index. The geologic index can be determined using the first rule that applies from the list below:
The region at 0,0 (the mouth of the cave) has a geologic index of 0.
The region at the coordinates of the target has a geologic index of 0.
If the region's Y coordinate is 0, the geologic index is its X coordinate times 16807.
If the region's X coordinate is 0, the geologic index is its Y coordinate times 48271.
Otherwise, the region's geologic index is the result of multiplying the erosion levels of the regions at X-1,Y and X,Y-1.
A region's erosion level is its geologic index plus the cave system's depth, all modulo 20183. Then:
If the erosion level modulo 3 is 0, the region's type is rocky.
If the erosion level modulo 3 is 1, the region's type is wet.
If the erosion level modulo 3 is 2, the region's type is narrow.
For example, suppose the cave system's depth is 510 and the target's coordinates are 10,10. Using % to represent the modulo operator, the cavern would look as follows:
At 0,0, the geologic index is 0. The erosion level is (0 + 510) % 20183 = 510. The type is 510 % 3 = 0, rocky.
At 1,0, because the Y coordinate is 0, the geologic index is 1 * 16807 = 16807. The erosion level is (16807 + 510) % 20183 = 17317. The type is 17317 % 3 = 1, wet.
At 0,1, because the X coordinate is 0, the geologic index is 1 * 48271 = 48271. The erosion level is (48271 + 510) % 20183 = 8415. The type is 8415 % 3 = 0, rocky.
At 1,1, neither coordinate is 0 and it is not the coordinate of the target, so the geologic index is the erosion level of 0,1 (8415) times the erosion level of 1,0 (17317), 8415 * 17317 = 145722555. The erosion level is (145722555 + 510) % 20183 = 1805. The type is 1805 % 3 = 2, narrow.
At 10,10, because they are the target's coordinates, the geologic index is 0. The erosion level is (0 + 510) % 20183 = 510. The type is 510 % 3 = 0, rocky.
Drawing this same cave system with rocky as ., wet as =, narrow as |, the mouth as M, the target as T, with 0,0 in the top-left corner, X increasing to the right, and Y increasing downward, the top-left corner of the map looks like this:
M=.|=.|.|=.|=|=.
.|=|=|||..|.=...
.==|....||=..|==
=.|....|.==.|==.
=|..==...=.|==..
=||.=.=||=|=..|=
|.=.===|||..=..|
|..==||=.|==|===
.=..===..=|.|||.
.======|||=|=.|=
.===|=|===T===||
=|||...|==..|=.|
=.=|=.=..=.||==|
||=|=...|==.=|==
|=.=||===.|||===
||.|==.|.|.||=||
Before you go in, you should determine the risk level of the area. For the rectangle that has a top-left corner of region 0,0 and a bottom-right corner of the region containing the target, add up the risk level of each individual region: 0 for rocky regions, 1 for wet regions, and 2 for narrow regions.
In the cave system above, because the mouth is at 0,0 and the target is at 10,10, adding up the risk level of all regions with an X coordinate from 0 to 10 and a Y coordinate from 0 to 10, this total is 114.
What is the total risk level for the smallest rectangle that includes 0,0 and the target's coordinates?
| 382
|
--- Day 10: Monitoring Station ---
You fly into the asteroid belt and reach the Ceres monitoring station. The Elves here have an emergency: they're having trouble tracking all of the asteroids and can't be sure they're safe.
The Elves would like to build a new monitoring station in a nearby area of space; they hand you a map of all of the asteroids in that region (your puzzle input).
The map indicates whether each position is empty (.) or contains an asteroid (#). The asteroids are much smaller than they appear on the map, and every asteroid is exactly in the center of its marked position. The asteroids can be described with X,Y coordinates where X is the distance from the left edge and Y is the distance from the top edge (so the top-left corner is 0,0 and the position immediately to its right is 1,0).
Your job is to figure out which asteroid would be the best place to build a new monitoring station. A monitoring station can detect any asteroid to which it has direct line of sight - that is, there cannot be another asteroid exactly between them. This line of sight can be at any angle, not just lines aligned to the grid or diagonally. The best location is the asteroid that can detect the largest number of other asteroids.
For example, consider the following map:
.#..#
.....
#####
....#
...##
The best location for a new monitoring station on this map is the highlighted asteroid at 3,4 because it can detect 8 asteroids, more than any other location. (The only asteroid it cannot detect is the one at 1,0; its view of this asteroid is blocked by the asteroid at 2,2.) All other asteroids are worse locations; they can detect 7 or fewer other asteroids. Here is the number of other asteroids a monitoring station on each asteroid could detect:
.7..7
.....
67775
....7
...87
Here is an asteroid (#) and some examples of the ways its line of sight might be blocked. If there were another asteroid at the location of a capital letter, the locations marked with the corresponding lowercase letter would be blocked and could not be detected:
#.........
...A......
...B..a...
.EDCG....a
..F.c.b...
.....c....
..efd.c.gb
.......c..
....f...c.
...e..d..c
Here are some larger examples:
Best is 5,8 with 33 other asteroids detected:
......#.#.
#..#.#....
..#######.
.#.#.###..
.#..#.....
..#....#.#
#..#....#.
.##.#..###
##...#..#.
.#....####
Best is 1,2 with 35 other asteroids detected:
#.#...#.#.
.###....#.
.#....#...
##.#.#.#.#
....#.#.#.
.##..###.#
..#...##..
..##....##
......#...
.####.###.
Best is 6,3 with 41 other asteroids detected:
.#..#..###
####.###.#
....###.#.
..###.##.#
##.##.#.#.
....###..#
..#.#..#.#
#..#.#.###
.##...##.#
.....#.#..
Best is 11,13 with 210 other asteroids detected:
.#..##.###...#######
##.############..##.
.#.######.########.#
.###.#######.####.#.
#####.##.#.##.###.##
..#####..#.#########
####################
#.####....###.#.#.##
##.#################
#####.##.###..####..
..######..##.#######
####.##.####...##..#
.#####..#.######.###
##...#.##########...
#.##########.#######
.####.#.###.###.#.##
....##.##.###..#####
.#.#.###########.###
#.#.#.#####.####.###
###.##.####.##.#..##
Find the best location for a new monitoring station. How many other asteroids can be detected from that location?
Your puzzle answer was 296.
--- Part Two ---
Once you give them the coordinates, the Elves quickly deploy an Instant Monitoring Station to the location and discover the worst: there are simply too many asteroids.
The only solution is complete vaporization by giant laser.
Fortunately, in addition to an asteroid scanner, the new monitoring station also comes equipped with a giant rotating laser perfect for vaporizing asteroids. The laser starts by pointing up and always rotates clockwise, vaporizing any asteroid it hits.
If multiple asteroids are exactly in line with the station, the laser only has enough power to vaporize one of them before continuing its rotation. In other words, the same asteroids that can be detected can be vaporized, but if vaporizing one asteroid makes another one detectable, the newly-detected asteroid won't be vaporized until the laser has returned to the same position by rotating a full 360 degrees.
For example, consider the following map, where the asteroid with the new monitoring station (and laser) is marked X:
.#....#####...#..
##...##.#####..##
##...#...#.#####.
..#.....X...###..
..#.#.....#....##
The first nine asteroids to get vaporized, in order, would be:
.#....###24...#..
##...##.13#67..9#
##...#...5.8####.
..#.....X...###..
..#.#.....#....##
Note that some asteroids (the ones behind the asteroids marked 1, 5, and 7) won't have a chance to be vaporized until the next full rotation. The laser continues rotating; the next nine to be vaporized are:
.#....###.....#..
##...##...#.....#
##...#......1234.
..#.....X...5##..
..#.9.....8....76
The next nine to be vaporized are then:
.8....###.....#..
56...9#...#.....#
34...7...........
..2.....X....##..
..1..............
Finally, the laser completes its first full rotation (1 through 3), a second rotation (4 through 8), and vaporizes the last asteroid (9) partway through its third rotation:
......234.....6..
......1...5.....7
.................
........X....89..
.................
In the large example above (the one with the best monitoring station location at 11,13):
The 1st asteroid to be vaporized is at 11,12.
The 2nd asteroid to be vaporized is at 12,1.
The 3rd asteroid to be vaporized is at 12,2.
The 10th asteroid to be vaporized is at 12,8.
The 20th asteroid to be vaporized is at 16,0.
The 50th asteroid to be vaporized is at 16,9.
The 100th asteroid to be vaporized is at 10,16.
The 199th asteroid to be vaporized is at 9,6.
The 200th asteroid to be vaporized is at 8,2.
The 201st asteroid to be vaporized is at 10,9.
The 299th and final asteroid to be vaporized is at 11,1.
The Elves are placing bets on which will be the 200th asteroid to be vaporized. Win the bet by determining which asteroid that will be; what do you get if you multiply its X coordinate by 100 and then add its Y coordinate? (For example, 8,2 becomes 802.)
| 383
|
--- Day 20: Infinite Elves and Infinite Houses ---
To keep the Elves busy, Santa has them deliver some presents by hand, door-to-door. He sends them down a street with infinite houses numbered sequentially: 1, 2, 3, 4, 5, and so on.
Each Elf is assigned a number, too, and delivers presents to houses based on that number:
The first Elf (number 1) delivers presents to every house: 1, 2, 3, 4, 5, ....
The second Elf (number 2) delivers presents to every second house: 2, 4, 6, 8, 10, ....
Elf number 3 delivers presents to every third house: 3, 6, 9, 12, 15, ....
There are infinitely many Elves, numbered starting with 1. Each Elf delivers presents equal to ten times his or her number at each house.
So, the first nine houses on the street end up like this:
House 1 got 10 presents.
House 2 got 30 presents.
House 3 got 40 presents.
House 4 got 70 presents.
House 5 got 60 presents.
House 6 got 120 presents.
House 7 got 80 presents.
House 8 got 150 presents.
House 9 got 130 presents.
The first house gets 10 presents: it is visited only by Elf 1, which delivers 1 * 10 = 10 presents. The fourth house gets 70 presents, because it is visited by Elves 1, 2, and 4, for a total of 10 + 20 + 40 = 70 presents.
What is the lowest house number of the house to get at least as many presents as the number in your puzzle input?
Your puzzle answer was 665280.
--- Part Two ---
The Elves decide they don't want to visit an infinite number of houses. Instead, each Elf will stop after delivering presents to 50 houses. To make up for it, they decide to deliver presents equal to eleven times their number at each house.
With these changes, what is the new lowest house number of the house to get at least as many presents as the number in your puzzle input?
| 384
|
--- Day 23: Category Six ---
The droids have finished repairing as much of the ship as they can. Their report indicates that this was a Category 6 disaster - not because it was that bad, but because it destroyed the stockpile of Category 6 network cables as well as most of the ship's network infrastructure.
You'll need to rebuild the network from scratch.
The computers on the network are standard Intcode computers that communicate by sending packets to each other. There are 50 of them in total, each running a copy of the same Network Interface Controller (NIC) software (your puzzle input). The computers have network addresses 0 through 49; when each computer boots up, it will request its network address via a single input instruction. Be sure to give each computer a unique network address.
Once a computer has received its network address, it will begin doing work and communicating over the network by sending and receiving packets. All packets contain two values named X and Y. Packets sent to a computer are queued by the recipient and read in the order they are received.
To send a packet to another computer, the NIC will use three output instructions that provide the destination address of the packet followed by its X and Y values. For example, three output instructions that provide the values 10, 20, 30 would send a packet with X=20 and Y=30 to the computer with address 10.
To receive a packet from another computer, the NIC will use an input instruction. If the incoming packet queue is empty, provide -1. Otherwise, provide the X value of the next packet; the computer will then use a second input instruction to receive the Y value for the same packet. Once both values of the packet are read in this way, the packet is removed from the queue.
Note that these input and output instructions never block. Specifically, output instructions do not wait for the sent packet to be received - the computer might send multiple packets before receiving any. Similarly, input instructions do not wait for a packet to arrive - if no packet is waiting, input instructions should receive -1.
Boot up all 50 computers and attach them to your network. What is the Y value of the first packet sent to address 255?
| 385
|
--- Day 4: High-Entropy Passphrases ---
A new system policy has been put in place that requires all accounts to use a passphrase instead of simply a password. A passphrase consists of a series of words (lowercase letters) separated by spaces.
To ensure security, a valid passphrase must contain no duplicate words.
For example:
aa bb cc dd ee is valid.
aa bb cc dd aa is not valid - the word aa appears more than once.
aa bb cc dd aaa is valid - aa and aaa count as different words.
The system's full passphrase list is available as your puzzle input. How many passphrases are valid?
Your puzzle answer was 451.
--- Part Two ---
For added security, yet another system policy has been put in place. Now, a valid passphrase must contain no two words that are anagrams of each other - that is, a passphrase is invalid if any word's letters can be rearranged to form any other word in the passphrase.
For example:
abcde fghij is a valid passphrase.
abcde xyz ecdab is not valid - the letters from the third word can be rearranged to form the first word.
a ab abc abd abf abj is a valid passphrase, because all letters need to be used when forming another word.
iiii oiii ooii oooi oooo is valid.
oiii ioii iioi iiio is not valid - any of these words can be rearranged to form any other word.
Under this new system policy, how many passphrases are valid?
| 386
|
--- Day 20: Grove Positioning System ---
It's finally time to meet back up with the Elves. When you try to contact them, however, you get no reply. Perhaps you're out of range?
You know they're headed to the grove where the star fruit grows, so if you can figure out where that is, you should be able to meet back up with them.
Fortunately, your handheld device has a file (your puzzle input) that contains the grove's coordinates! Unfortunately, the file is encrypted - just in case the device were to fall into the wrong hands.
Maybe you can decrypt it?
When you were still back at the camp, you overheard some Elves talking about coordinate file encryption. The main operation involved in decrypting the file is called mixing.
The encrypted file is a list of numbers. To mix the file, move each number forward or backward in the file a number of positions equal to the value of the number being moved. The list is circular, so moving a number off one end of the list wraps back around to the other end as if the ends were connected.
For example, to move the 1 in a sequence like 4, 5, 6, 1, 7, 8, 9, the 1 moves one position forward: 4, 5, 6, 7, 1, 8, 9. To move the -2 in a sequence like 4, -2, 5, 6, 7, 8, 9, the -2 moves two positions backward, wrapping around: 4, 5, 6, 7, 8, -2, 9.
The numbers should be moved in the order they originally appear in the encrypted file. Numbers moving around during the mixing process do not change the order in which the numbers are moved.
Consider this encrypted file:
1
2
-3
3
-2
0
4
Mixing this file proceeds as follows:
Initial arrangement:
1, 2, -3, 3, -2, 0, 4
1 moves between 2 and -3:
2, 1, -3, 3, -2, 0, 4
2 moves between -3 and 3:
1, -3, 2, 3, -2, 0, 4
-3 moves between -2 and 0:
1, 2, 3, -2, -3, 0, 4
3 moves between 0 and 4:
1, 2, -2, -3, 0, 3, 4
-2 moves between 4 and 1:
1, 2, -3, 0, 3, 4, -2
0 does not move:
1, 2, -3, 0, 3, 4, -2
4 moves between -3 and 0:
1, 2, -3, 4, 0, 3, -2
Then, the grove coordinates can be found by looking at the 1000th, 2000th, and 3000th numbers after the value 0, wrapping around the list as necessary. In the above example, the 1000th number after 0 is 4, the 2000th is -3, and the 3000th is 2; adding these together produces 3.
Mix your encrypted file exactly once. What is the sum of the three numbers that form the grove coordinates?
Your puzzle answer was 5904.
--- Part Two ---
The grove coordinate values seem nonsensical. While you ponder the mysteries of Elf encryption, you suddenly remember the rest of the decryption routine you overheard back at camp.
First, you need to apply the decryption key, 811589153. Multiply each number by the decryption key before you begin; this will produce the actual list of numbers to mix.
Second, you need to mix the list of numbers ten times. The order in which the numbers are mixed does not change during mixing; the numbers are still moved in the order they appeared in the original, pre-mixed list. (So, if -3 appears fourth in the original list of numbers to mix, -3 will be the fourth number to move during each round of mixing.)
Using the same example as above:
Initial arrangement:
811589153, 1623178306, -2434767459, 2434767459, -1623178306, 0, 3246356612
After 1 round of mixing:
0, -2434767459, 3246356612, -1623178306, 2434767459, 1623178306, 811589153
After 2 rounds of mixing:
0, 2434767459, 1623178306, 3246356612, -2434767459, -1623178306, 811589153
After 3 rounds of mixing:
0, 811589153, 2434767459, 3246356612, 1623178306, -1623178306, -2434767459
After 4 rounds of mixing:
0, 1623178306, -2434767459, 811589153, 2434767459, 3246356612, -1623178306
After 5 rounds of mixing:
0, 811589153, -1623178306, 1623178306, -2434767459, 3246356612, 2434767459
After 6 rounds of mixing:
0, 811589153, -1623178306, 3246356612, -2434767459, 1623178306, 2434767459
After 7 rounds of mixing:
0, -2434767459, 2434767459, 1623178306, -1623178306, 811589153, 3246356612
After 8 rounds of mixing:
0, 1623178306, 3246356612, 811589153, -2434767459, 2434767459, -1623178306
After 9 rounds of mixing:
0, 811589153, 1623178306, -2434767459, 3246356612, 2434767459, -1623178306
After 10 rounds of mixing:
0, -2434767459, 1623178306, 3246356612, -1623178306, 2434767459, 811589153
The grove coordinates can still be found in the same way. Here, the 1000th number after 0 is 811589153, the 2000th is 2434767459, and the 3000th is -1623178306; adding these together produces 1623178306.
Apply the decryption key and mix your encrypted file ten times. What is the sum of the three numbers that form the grove coordinates?
| 387
|
--- Day 23: A Long Walk ---
The Elves resume water filtering operations! Clean water starts flowing over the edge of Island Island.
They offer to help you go over the edge of Island Island, too! Just hold on tight to one end of this impossibly long rope and they'll lower you down a safe distance from the massive waterfall you just created.
As you finally reach Snow Island, you see that the water isn't really reaching the ground: it's being absorbed by the air itself. It looks like you'll finally have a little downtime while the moisture builds up to snow-producing levels. Snow Island is pretty scenic, even without any snow; why not take a walk?
There's a map of nearby hiking trails (your puzzle input) that indicates paths (.), forest (#), and steep slopes (^, >, v, and <).
For example:
#.#####################
#.......#########...###
#######.#########.#.###
###.....#.>.>.###.#.###
###v#####.#v#.###.#.###
###.>...#.#.#.....#...#
###v###.#.#.#########.#
###...#.#.#.......#...#
#####.#.#.#######.#.###
#.....#.#.#.......#...#
#.#####.#.#.#########v#
#.#...#...#...###...>.#
#.#.#v#######v###.###v#
#...#.>.#...>.>.#.###.#
#####v#.#.###v#.#.###.#
#.....#...#...#.#.#...#
#.#########.###.#.#.###
#...###...#...#...#.###
###.###.#.###v#####v###
#...#...#.#.>.>.#.>.###
#.###.###.#.###.#.#v###
#.....###...###...#...#
#####################.#
You're currently on the single path tile in the top row; your goal is to reach the single path tile in the bottom row. Because of all the mist from the waterfall, the slopes are probably quite icy; if you step onto a slope tile, your next step must be downhill (in the direction the arrow is pointing). To make sure you have the most scenic hike possible, never step onto the same tile twice. What is the longest hike you can take?
In the example above, the longest hike you can take is marked with O, and your starting position is marked S:
#S#####################
#OOOOOOO#########...###
#######O#########.#.###
###OOOOO#OOO>.###.#.###
###O#####O#O#.###.#.###
###OOOOO#O#O#.....#...#
###v###O#O#O#########.#
###...#O#O#OOOOOOO#...#
#####.#O#O#######O#.###
#.....#O#O#OOOOOOO#...#
#.#####O#O#O#########v#
#.#...#OOO#OOO###OOOOO#
#.#.#v#######O###O###O#
#...#.>.#...>OOO#O###O#
#####v#.#.###v#O#O###O#
#.....#...#...#O#O#OOO#
#.#########.###O#O#O###
#...###...#...#OOO#O###
###.###.#.###v#####O###
#...#...#.#.>.>.#.>O###
#.###.###.#.###.#.#O###
#.....###...###...#OOO#
#####################O#
This hike contains 94 steps. (The other possible hikes you could have taken were 90, 86, 82, 82, and 74 steps long.)
Find the longest hike you can take through the hiking trails listed on your map. How many steps long is the longest hike?
Your puzzle answer was 2110.
--- Part Two ---
As you reach the trailhead, you realize that the ground isn't as slippery as you expected; you'll have no problem climbing up the steep slopes.
Now, treat all slopes as if they were normal paths (.). You still want to make sure you have the most scenic hike possible, so continue to ensure that you never step onto the same tile twice. What is the longest hike you can take?
In the example above, this increases the longest hike to 154 steps:
#S#####################
#OOOOOOO#########OOO###
#######O#########O#O###
###OOOOO#.>OOO###O#O###
###O#####.#O#O###O#O###
###O>...#.#O#OOOOO#OOO#
###O###.#.#O#########O#
###OOO#.#.#OOOOOOO#OOO#
#####O#.#.#######O#O###
#OOOOO#.#.#OOOOOOO#OOO#
#O#####.#.#O#########O#
#O#OOO#...#OOO###...>O#
#O#O#O#######O###.###O#
#OOO#O>.#...>O>.#.###O#
#####O#.#.###O#.#.###O#
#OOOOO#...#OOO#.#.#OOO#
#O#########O###.#.#O###
#OOO###OOO#OOO#...#O###
###O###O#O###O#####O###
#OOO#OOO#O#OOO>.#.>O###
#O###O###O#O###.#.#O###
#OOOOO###OOO###...#OOO#
#####################O#
Find the longest hike you can take through the surprisingly dry hiking trails listed on your map. How many steps long is the longest hike?
| 388
|
--- Day 25: Sea Cucumber ---
This is it: the bottom of the ocean trench, the last place the sleigh keys could be. Your submarine's experimental antenna still isn't boosted enough to detect the keys, but they must be here. All you need to do is reach the seafloor and find them.
At least, you'd touch down on the seafloor if you could; unfortunately, it's completely covered by two large herds of sea cucumbers, and there isn't an open space large enough for your submarine.
You suspect that the Elves must have done this before, because just then you discover the phone number of a deep-sea marine biologist on a handwritten note taped to the wall of the submarine's cockpit.
"Sea cucumbers? Yeah, they're probably hunting for food. But don't worry, they're predictable critters: they move in perfectly straight lines, only moving forward when there's space to do so. They're actually quite polite!"
You explain that you'd like to predict when you could land your submarine.
"Oh that's easy, they'll eventually pile up and leave enough space for-- wait, did you say submarine? And the only place with that many sea cucumbers would be at the very bottom of the Mariana--" You hang up the phone.
There are two herds of sea cucumbers sharing the same region; one always moves east (>), while the other always moves south (v). Each location can contain at most one sea cucumber; the remaining locations are empty (.). The submarine helpfully generates a map of the situation (your puzzle input). For example:
v...>>.vv>
.vv>>.vv..
>>.>v>...v
>>v>>.>.v.
v>v.vv.v..
>.>>..v...
.vv..>.>v.
v.v..>>v.v
....v..v.>
Every step, the sea cucumbers in the east-facing herd attempt to move forward one location, then the sea cucumbers in the south-facing herd attempt to move forward one location. When a herd moves forward, every sea cucumber in the herd first simultaneously considers whether there is a sea cucumber in the adjacent location it's facing (even another sea cucumber facing the same direction), and then every sea cucumber facing an empty location simultaneously moves into that location.
So, in a situation like this:
...>>>>>...
After one step, only the rightmost sea cucumber would have moved:
...>>>>.>..
After the next step, two sea cucumbers move:
...>>>.>.>.
During a single step, the east-facing herd moves first, then the south-facing herd moves. So, given this situation:
..........
.>v....v..
.......>..
..........
After a single step, of the sea cucumbers on the left, only the south-facing sea cucumber has moved (as it wasn't out of the way in time for the east-facing cucumber on the left to move), but both sea cucumbers on the right have moved (as the east-facing sea cucumber moved out of the way of the south-facing sea cucumber):
..........
.>........
..v....v>.
..........
Due to strong water currents in the area, sea cucumbers that move off the right edge of the map appear on the left edge, and sea cucumbers that move off the bottom edge of the map appear on the top edge. Sea cucumbers always check whether their destination location is empty before moving, even if that destination is on the opposite side of the map:
Initial state:
...>...
.......
......>
v.....>
......>
.......
..vvv..
After 1 step:
..vv>..
.......
>......
v.....>
>......
.......
....v..
After 2 steps:
....v>.
..vv...
.>.....
......>
v>.....
.......
.......
After 3 steps:
......>
..v.v..
..>v...
>......
..>....
v......
.......
After 4 steps:
>......
..v....
..>.v..
.>.v...
...>...
.......
v......
To find a safe place to land your submarine, the sea cucumbers need to stop moving. Again consider the first example:
Initial state:
v...>>.vv>
.vv>>.vv..
>>.>v>...v
>>v>>.>.v.
v>v.vv.v..
>.>>..v...
.vv..>.>v.
v.v..>>v.v
....v..v.>
After 1 step:
....>.>v.>
v.v>.>v.v.
>v>>..>v..
>>v>v>.>.v
.>v.v...v.
v>>.>vvv..
..v...>>..
vv...>>vv.
>.v.v..v.v
After 2 steps:
>.v.v>>..v
v.v.>>vv..
>v>.>.>.v.
>>v>v.>v>.
.>..v....v
.>v>>.v.v.
v....v>v>.
.vv..>>v..
v>.....vv.
After 3 steps:
v>v.v>.>v.
v...>>.v.v
>vv>.>v>..
>>v>v.>.v>
..>....v..
.>.>v>v..v
..v..v>vv>
v.v..>>v..
.v>....v..
After 4 steps:
v>..v.>>..
v.v.>.>.v.
>vv.>>.v>v
>>.>..v>.>
..v>v...v.
..>>.>vv..
>.v.vv>v.v
.....>>vv.
vvv>...v..
After 5 steps:
vv>...>v>.
v.v.v>.>v.
>.v.>.>.>v
>v>.>..v>>
..v>v.v...
..>.>>vvv.
.>...v>v..
..v.v>>v.v
v.v.>...v.
...
After 10 steps:
..>..>>vv.
v.....>>.v
..v.v>>>v>
v>.>v.>>>.
..v>v.vv.v
.v.>>>.v..
v.v..>v>..
..v...>v.>
.vv..v>vv.
...
After 20 steps:
v>.....>>.
>vv>.....v
.>v>v.vv>>
v>>>v.>v.>
....vv>v..
.v.>>>vvv.
..v..>>vv.
v.v...>>.v
..v.....v>
...
After 30 steps:
.vv.v..>>>
v>...v...>
>.v>.>vv.>
>v>.>.>v.>
.>..v.vv..
..v>..>>v.
....v>..>v
v.v...>vv>
v.v...>vvv
...
After 40 steps:
>>v>v..v..
..>>v..vv.
..>>>v.>.v
..>>>>vvv>
v.....>...
v.v...>v>>
>vv.....v>
.>v...v.>v
vvv.v..v.>
...
After 50 steps:
..>>v>vv.v
..v.>>vv..
v.>>v>>v..
..>>>>>vv.
vvv....>vv
..v....>>>
v>.......>
.vv>....v>
.>v.vv.v..
...
After 55 steps:
..>>v>vv..
..v.>>vv..
..>>v>>vv.
..>>>>>vv.
v......>vv
v>v....>>v
vvv...>..>
>vv.....>.
.>v.vv.v..
After 56 steps:
..>>v>vv..
..v.>>vv..
..>>v>>vv.
..>>>>>vv.
v......>vv
v>v....>>v
vvv....>.>
>vv......>
.>v.vv.v..
After 57 steps:
..>>v>vv..
..v.>>vv..
..>>v>>vv.
..>>>>>vv.
v......>vv
v>v....>>v
vvv.....>>
>vv......>
.>v.vv.v..
After 58 steps:
..>>v>vv..
..v.>>vv..
..>>v>>vv.
..>>>>>vv.
v......>vv
v>v....>>v
vvv.....>>
>vv......>
.>v.vv.v..
In this example, the sea cucumbers stop moving after 58 steps.
Find somewhere safe to land your submarine. What is the first step on which no sea cucumbers move?
| 389
|
--- Day 13: Mine Cart Madness ---
A crop of this size requires significant logistics to transport produce, soil, fertilizer, and so on. The Elves are very busy pushing things around in carts on some kind of rudimentary system of tracks they've come up with.
Seeing as how cart-and-track systems don't appear in recorded history for another 1000 years, the Elves seem to be making this up as they go along. They haven't even figured out how to avoid collisions yet.
You map out the tracks (your puzzle input) and see where you can help.
Tracks consist of straight paths (| and -), curves (/ and ), and intersections (+). Curves connect exactly two perpendicular pieces of track; for example, this is a closed loop:
/----| |
| |
----/
Intersections occur when two perpendicular paths cross. At an intersection, a cart is capable of turning left, turning right, or continuing straight. Here are two loops connected by two intersections:
/-----| |
| /--+--| | | |
--+--/ |
| |
-----/
Several carts are also on the tracks. Carts always face either up (^), down (v), left (<), or right (>). (On your initial map, the track under each cart is a straight path matching the direction the cart is facing.)
Each time a cart has the option to turn (by arriving at any intersection), it turns left the first time, goes straight the second time, turns right the third time, and then repeats those directions starting again with left the fourth time, straight the fifth time, and so on. This process is independent of the particular intersection at which the cart has arrived - that is, the cart has no per-intersection memory.
Carts all move at the same speed; they take turns moving a single step at a time. They do this based on their current location: carts on the top row move first (acting from left to right), then carts on the second row move (again from left to right), then carts on the third row, and so on. Once each cart has moved one step, the process repeats; each of these loops is called a tick.
For example, suppose there are two carts on a straight track:
| | | | |
v | | | |
| v v | |
| | | v X
| | ^ ^ |
^ ^ | | |
| | | | |
First, the top cart moves. It is facing down (v), so it moves down one square. Second, the bottom cart moves. It is facing up (^), so it moves up one square. Because all carts have moved, the first tick ends. Then, the process repeats, starting with the first cart. The first cart moves down, then the second cart moves up - right into the first cart, colliding with it! (The location of the crash is marked with an X.) This ends the second and last tick.
Here is a longer example:
/->-
| | /----| /-+--+- |
| | | | v |
-+-/ -+--/
------/
/-->
| | /----| /-+--+- |
| | | | | |
-+-/ ->--/
------/
/---v
| | /----| /-+--+- |
| | | | | |
-+-/ -+>-/
------/
/---
| v /----| /-+--+- |
| | | | | |
-+-/ -+->/
------/
/---
| | /----| /->--+- |
| | | | | |
-+-/ -+--^
------/
/---
| | /----| /-+>-+- |
| | | | | ^
-+-/ -+--/
------/
/---
| | /----| /-+->+- ^
| | | | | |
-+-/ -+--/
------/
/---
| | /----<
| /-+-->- |
| | | | | |
-+-/ -+--/
------/
/---
| | /---<| /-+--+> |
| | | | | |
-+-/ -+--/
------/
/---
| | /--<-| /-+--+-v |
| | | | | |
-+-/ -+--/
------/
/---
| | /-<--| /-+--+- |
| | | | v |
-+-/ -+--/
------/
/---
| | /<---| /-+--+- |
| | | | | |
-+-/ -<--/
------/
/---
| | v----| /-+--+- |
| | | | | |
-+-/ <+--/
------/
/---
| | /----| /-+--v- |
| | | | | |
-+-/ ^-+--/
------/
/---
| | /----| /-+--+- |
| | | X | |
-+-/ -+--/
------/
After following their respective paths for a while, the carts eventually crash. To help prevent crashes, you'd like to know the location of the first crash. Locations are given in X,Y coordinates, where the furthest left column is X=0 and the furthest top row is Y=0:
111
0123456789012
0/---
1| | /----2| /-+--+- |
3| | | X | |
4-+-/ -+--/
5 ------/
In this example, the location of the first crash is 7,3.
Your puzzle answer was 130,104.
--- Part Two ---
There isn't much you can do to prevent crashes in this ridiculous system. However, by predicting the crashes, the Elves know where to be in advance and instantly remove the two crashing carts the moment any crash occurs.
They can proceed like this for a while, but eventually, they're going to run out of carts. It could be useful to figure out where the last cart that hasn't crashed will end up.
For example:
/>-<
| |
| /<+-| | | v
>+</ |
| ^
<->/
/---
| |
| v-+-| | | |
-+-/ |
| |
^---^
/---
| |
| /-+-| v | |
-+-/ |
^ ^
---/
/---
| |
| /-+-| | | |
-+-/ ^
| |
---/
After four very expensive crashes, a tick ends with only one cart remaining; its final location is 6,4.
What is the location of the last cart at the end of the first tick where it is the only cart left?
| 390
|
--- Day 20: Particle Swarm ---
Suddenly, the GPU contacts you, asking for help. Someone has asked it to simulate too many particles, and it won't be able to finish them all in time to render the next frame at this rate.
It transmits to you a buffer (your puzzle input) listing each particle in order (starting with particle 0, then particle 1, particle 2, and so on). For each particle, it provides the X, Y, and Z coordinates for the particle's position (p), velocity (v), and acceleration (a), each in the format <X,Y,Z>.
Each tick, all particles are updated simultaneously. A particle's properties are updated in the following order:
Increase the X velocity by the X acceleration.
Increase the Y velocity by the Y acceleration.
Increase the Z velocity by the Z acceleration.
Increase the X position by the X velocity.
Increase the Y position by the Y velocity.
Increase the Z position by the Z velocity.
Because of seemingly tenuous rationale involving z-buffering, the GPU would like to know which particle will stay closest to position <0,0,0> in the long term. Measure this using the Manhattan distance, which in this situation is simply the sum of the absolute values of a particle's X, Y, and Z position.
For example, suppose you are only given two particles, both of which stay entirely on the X-axis (for simplicity). Drawing the current states of particles 0 and 1 (in that order) with an adjacent a number line and diagram of current X positions (marked in parentheses), the following would take place:
p=< 3,0,0>, v=< 2,0,0>, a=<-1,0,0> -4 -3 -2 -1 0 1 2 3 4
p=< 4,0,0>, v=< 0,0,0>, a=<-2,0,0> (0)(1)
p=< 4,0,0>, v=< 1,0,0>, a=<-1,0,0> -4 -3 -2 -1 0 1 2 3 4
p=< 2,0,0>, v=<-2,0,0>, a=<-2,0,0> (1) (0)
p=< 4,0,0>, v=< 0,0,0>, a=<-1,0,0> -4 -3 -2 -1 0 1 2 3 4
p=<-2,0,0>, v=<-4,0,0>, a=<-2,0,0> (1) (0)
p=< 3,0,0>, v=<-1,0,0>, a=<-1,0,0> -4 -3 -2 -1 0 1 2 3 4
p=<-8,0,0>, v=<-6,0,0>, a=<-2,0,0> (0)
At this point, particle 1 will never be closer to <0,0,0> than particle 0, and so, in the long run, particle 0 will stay closest.
Which particle will stay closest to position <0,0,0> in the long term?
Your puzzle answer was 125.
--- Part Two ---
To simplify the problem further, the GPU would like to remove any particles that collide. Particles collide if their positions ever exactly match. Because particles are updated simultaneously, more than two particles can collide at the same time and place. Once particles collide, they are removed and cannot collide with anything else after that tick.
For example:
p=<-6,0,0>, v=< 3,0,0>, a=< 0,0,0>
p=<-4,0,0>, v=< 2,0,0>, a=< 0,0,0> -6 -5 -4 -3 -2 -1 0 1 2 3
p=<-2,0,0>, v=< 1,0,0>, a=< 0,0,0> (0) (1) (2) (3)
p=< 3,0,0>, v=<-1,0,0>, a=< 0,0,0>
p=<-3,0,0>, v=< 3,0,0>, a=< 0,0,0>
p=<-2,0,0>, v=< 2,0,0>, a=< 0,0,0> -6 -5 -4 -3 -2 -1 0 1 2 3
p=<-1,0,0>, v=< 1,0,0>, a=< 0,0,0> (0)(1)(2) (3)
p=< 2,0,0>, v=<-1,0,0>, a=< 0,0,0>
p=< 0,0,0>, v=< 3,0,0>, a=< 0,0,0>
p=< 0,0,0>, v=< 2,0,0>, a=< 0,0,0> -6 -5 -4 -3 -2 -1 0 1 2 3
p=< 0,0,0>, v=< 1,0,0>, a=< 0,0,0> X (3)
p=< 1,0,0>, v=<-1,0,0>, a=< 0,0,0>
------destroyed by collision------
------destroyed by collision------ -6 -5 -4 -3 -2 -1 0 1 2 3
------destroyed by collision------ (3)
p=< 0,0,0>, v=<-1,0,0>, a=< 0,0,0>
In this example, particles 0, 1, and 2 are simultaneously destroyed at the time and place marked X. On the next tick, particle 3 passes through unharmed.
How many particles are left after all collisions are resolved?
| 391
|
--- Day 23: Safe Cracking ---
This is one of the top floors of the nicest tower in EBHQ. The Easter Bunny's private office is here, complete with a safe hidden behind a painting, and who wouldn't hide a star in a safe behind a painting?
The safe has a digital screen and keypad for code entry. A sticky note attached to the safe has a password hint on it: "eggs". The painting is of a large rabbit coloring some eggs. You see 7.
When you go to type the code, though, nothing appears on the display; instead, the keypad comes apart in your hands, apparently having been smashed. Behind it is some kind of socket - one that matches a connector in your prototype computer! You pull apart the smashed keypad and extract the logic circuit, plug it into your computer, and plug your computer into the safe.
Now, you just need to figure out what output the keypad would have sent to the safe. You extract the assembunny code from the logic chip (your puzzle input).
The code looks like it uses almost the same architecture and instruction set that the monorail computer used! You should be able to use the same assembunny interpreter for this as you did there, but with one new instruction:
tgl x toggles the instruction x away (pointing at instructions like jnz does: positive means forward; negative means backward):
For one-argument instructions, inc becomes dec, and all other one-argument instructions become inc.
For two-argument instructions, jnz becomes cpy, and all other two-instructions become jnz.
The arguments of a toggled instruction are not affected.
If an attempt is made to toggle an instruction outside the program, nothing happens.
If toggling produces an invalid instruction (like cpy 1 2) and an attempt is later made to execute that instruction, skip it instead.
If tgl toggles itself (for example, if a is 0, tgl a would target itself and become inc a), the resulting instruction is not executed until the next time it is reached.
For example, given this program:
cpy 2 a
tgl a
tgl a
tgl a
cpy 1 a
dec a
dec a
cpy 2 a initializes register a to 2.
The first tgl a toggles an instruction a (2) away from it, which changes the third tgl a into inc a.
The second tgl a also modifies an instruction 2 away from it, which changes the cpy 1 a into jnz 1 a.
The fourth line, which is now inc a, increments a to 3.
Finally, the fifth line, which is now jnz 1 a, jumps a (3) instructions ahead, skipping the dec a instructions.
In this example, the final value in register a is 3.
The rest of the electronics seem to place the keypad entry (the number of eggs, 7) in register a, run the code, and then send the value left in register a to the safe.
What value should be sent to the safe?
| 392
|
--- Day 21: Fractal Art ---
You find a program trying to generate some art. It uses a strange process that involves repeatedly enhancing the detail of an image through a set of rules.
The image consists of a two-dimensional square grid of pixels that are either on (#) or off (.). The program always begins with this pattern:
.#.
..#
###
Because the pattern is both 3 pixels wide and 3 pixels tall, it is said to have a size of 3.
Then, the program repeats the following process:
If the size is evenly divisible by 2, break the pixels up into 2x2 squares, and convert each 2x2 square into a 3x3 square by following the corresponding enhancement rule.
Otherwise, the size is evenly divisible by 3; break the pixels up into 3x3 squares, and convert each 3x3 square into a 4x4 square by following the corresponding enhancement rule.
Because each square of pixels is replaced by a larger one, the image gains pixels and so its size increases.
The artist's book of enhancement rules is nearby (your puzzle input); however, it seems to be missing rules. The artist explains that sometimes, one must rotate or flip the input pattern to find a match. (Never rotate or flip the output pattern, though.) Each pattern is written concisely: rows are listed as single units, ordered top-down, and separated by slashes. For example, the following rules correspond to the adjacent patterns:
../.# = ..
.#
.#.
.#./..#/### = ..#
###
#..#
#..#/..../#..#/.##. = ....
#..#
.##.
When searching for a rule to use, rotate and flip the pattern as necessary. For example, all of the following patterns match the same rule:
.#. .#. #.. ###
..# #.. #.# ..#
### ### ##. .#.
Suppose the book contained the following two rules:
../.# => ##./#../...
.#./..#/### => #..#/..../..../#..#
As before, the program begins with this pattern:
.#.
..#
###
The size of the grid (3) is not divisible by 2, but it is divisible by 3. It divides evenly into a single square; the square matches the second rule, which produces:
#..#
....
....
#..#
The size of this enhanced grid (4) is evenly divisible by 2, so that rule is used. It divides evenly into four squares:
#.|.#
..|..
--+--
..|..
#.|.#
Each of these squares matches the same rule (../.# => ##./#../...), three of which require some flipping and rotation to line up with the rule. The output for the rule is the same in all four cases:
##.|##.
#..|#..
...|...
---+---
##.|##.
#..|#..
...|...
Finally, the squares are joined into a new grid:
##.##.
#..#..
......
##.##.
#..#..
......
Thus, after 2 iterations, the grid contains 12 pixels that are on.
How many pixels stay on after 5 iterations?
| 393
|
--- Day 10: Pipe Maze ---
You use the hang glider to ride the hot air from Desert Island all the way up to the floating metal island. This island is surprisingly cold and there definitely aren't any thermals to glide on, so you leave your hang glider behind.
You wander around for a while, but you don't find any people or animals. However, you do occasionally find signposts labeled "Hot Springs" pointing in a seemingly consistent direction; maybe you can find someone at the hot springs and ask them where the desert-machine parts are made.
The landscape here is alien; even the flowers and trees are made of metal. As you stop to admire some metal grass, you notice something metallic scurry away in your peripheral vision and jump into a big pipe! It didn't look like any animal you've ever seen; if you want a better look, you'll need to get ahead of it.
Scanning the area, you discover that the entire field you're standing on is densely packed with pipes; it was hard to tell at first because they're the same metallic silver color as the "ground". You make a quick sketch of all of the surface pipes you can see (your puzzle input).
The pipes are arranged in a two-dimensional grid of tiles:
| is a vertical pipe connecting north and south.
- is a horizontal pipe connecting east and west.
L is a 90-degree bend connecting north and east.
J is a 90-degree bend connecting north and west.
7 is a 90-degree bend connecting south and west.
F is a 90-degree bend connecting south and east.
. is ground; there is no pipe in this tile.
S is the starting position of the animal; there is a pipe on this tile, but your sketch doesn't show what shape the pipe has.
Based on the acoustics of the animal's scurrying, you're confident the pipe that contains the animal is one large, continuous loop.
For example, here is a square loop of pipe:
.....
.F-7.
.|.|.
.L-J.
.....
If the animal had entered this loop in the northwest corner, the sketch would instead look like this:
.....
.S-7.
.|.|.
.L-J.
.....
In the above diagram, the S tile is still a 90-degree F bend: you can tell because of how the adjacent pipes connect to it.
Unfortunately, there are also many pipes that aren't connected to the loop! This sketch shows the same loop as above:
-L|F7
7S-7|
L|7||
-L-J|
L|-JF
In the above diagram, you can still figure out which pipes form the main loop: they're the ones connected to S, pipes those pipes connect to, pipes those pipes connect to, and so on. Every pipe in the main loop connects to its two neighbors (including S, which will have exactly two pipes connecting to it, and which is assumed to connect back to those two pipes).
Here is a sketch that contains a slightly more complex main loop:
..F7.
.FJ|.
SJ.L7
|F--J
LJ...
Here's the same example sketch with the extra, non-main-loop pipe tiles also shown:
7-F7-
.FJ|7
SJLL7
|F--J
LJ.LJ
If you want to get out ahead of the animal, you should find the tile in the loop that is farthest from the starting position. Because the animal is in the pipe, it doesn't make sense to measure this by direct distance. Instead, you need to find the tile that would take the longest number of steps along the loop to reach from the starting point - regardless of which way around the loop the animal went.
In the first example with the square loop:
.....
.S-7.
.|.|.
.L-J.
.....
You can count the distance each tile in the loop is from the starting point like this:
.....
.012.
.1.3.
.234.
.....
In this example, the farthest point from the start is 4 steps away.
Here's the more complex loop again:
..F7.
.FJ|.
SJ.L7
|F--J
LJ...
Here are the distances for each tile on that loop:
..45.
.236.
01.78
14567
23...
Find the single giant loop starting at S. How many steps along the loop does it take to get from the starting position to the point farthest from the starting position?
| 394
|
--- Day 1: Chronal Calibration ---
"We've detected some temporal anomalies," one of Santa's Elves at the Temporal Anomaly Research and Detection Instrument Station tells you. She sounded pretty worried when she called you down here. "At 500-year intervals into the past, someone has been changing Santa's history!"
"The good news is that the changes won't propagate to our time stream for another 25 days, and we have a device" - she attaches something to your wrist - "that will let you fix the changes with no such propagation delay. It's configured to send you 500 years further into the past every few days; that was the best we could do on such short notice."
"The bad news is that we are detecting roughly fifty anomalies throughout time; the device will indicate fixed anomalies with stars. The other bad news is that we only have one device and you're the best person for the job! Good lu--" She taps a button on the device and you suddenly feel like you're falling. To save Christmas, you need to get all fifty stars by December 25th.
Collect stars by solving puzzles. Two puzzles will be made available on each day in the Advent calendar; the second puzzle is unlocked when you complete the first. Each puzzle grants one star. Good luck!
After feeling like you've been falling for a few minutes, you look at the device's tiny screen. "Error: Device must be calibrated before first use. Frequency drift detected. Cannot maintain destination lock." Below the message, the device shows a sequence of changes in frequency (your puzzle input). A value like +6 means the current frequency increases by 6; a value like -3 means the current frequency decreases by 3.
For example, if the device displays frequency changes of +1, -2, +3, +1, then starting from a frequency of zero, the following changes would occur:
Current frequency 0, change of +1; resulting frequency 1.
Current frequency 1, change of -2; resulting frequency -1.
Current frequency -1, change of +3; resulting frequency 2.
Current frequency 2, change of +1; resulting frequency 3.
In this example, the resulting frequency is 3.
Here are other example situations:
+1, +1, +1 results in 3
+1, +1, -2 results in 0
-1, -2, -3 results in -6
Starting with a frequency of zero, what is the resulting frequency after all of the changes in frequency have been applied?
| 395
|
--- Day 25: Cryostasis ---
As you approach Santa's ship, your sensors report two important details:
First, that you might be too late: the internal temperature is -40 degrees.
Second, that one faint life signature is somewhere on the ship.
The airlock door is locked with a code; your best option is to send in a small droid to investigate the situation. You attach your ship to Santa's, break a small hole in the hull, and let the droid run in before you seal it up again. Before your ship starts freezing, you detach your ship and set it to automatically stay within range of Santa's ship.
This droid can follow basic instructions and report on its surroundings; you can communicate with it through an Intcode program (your puzzle input) running on an ASCII-capable computer.
As the droid moves through its environment, it will describe what it encounters. When it says Command?, you can give it a single instruction terminated with a newline (ASCII code 10). Possible instructions are:
Movement via north, south, east, or west.
To take an item the droid sees in the environment, use the command take <name of item>. For example, if the droid reports seeing a red ball, you can pick it up with take red ball.
To drop an item the droid is carrying, use the command drop <name of item>. For example, if the droid is carrying a green ball, you can drop it with drop green ball.
To get a list of all of the items the droid is currently carrying, use the command inv (for "inventory").
Extra spaces or other characters aren't allowed - instructions must be provided precisely.
Santa's ship is a Reindeer-class starship; these ships use pressure-sensitive floors to determine the identity of droids and crew members. The standard configuration for these starships is for all droids to weigh exactly the same amount to make them easier to detect. If you need to get past such a sensor, you might be able to reach the correct weight by carrying items from the environment.
Look around the ship and see if you can find the password for the main airlock.
| 396
|
--- Day 16: Proboscidea Volcanium ---
The sensors have led you to the origin of the distress signal: yet another handheld device, just like the one the Elves gave you. However, you don't see any Elves around; instead, the device is surrounded by elephants! They must have gotten lost in these tunnels, and one of the elephants apparently figured out how to turn on the distress signal.
The ground rumbles again, much stronger this time. What kind of cave is this, exactly? You scan the cave with your handheld device; it reports mostly igneous rock, some ash, pockets of pressurized gas, magma... this isn't just a cave, it's a volcano!
You need to get the elephants out of here, quickly. Your device estimates that you have 30 minutes before the volcano erupts, so you don't have time to go back out the way you came in.
You scan the cave for other options and discover a network of pipes and pressure-release valves. You aren't sure how such a system got into a volcano, but you don't have time to complain; your device produces a report (your puzzle input) of each valve's flow rate if it were opened (in pressure per minute) and the tunnels you could use to move between the valves.
There's even a valve in the room you and the elephants are currently standing in labeled AA. You estimate it will take you one minute to open a single valve and one minute to follow any tunnel from one valve to another. What is the most pressure you could release?
For example, suppose you had the following scan output:
Valve AA has flow rate=0; tunnels lead to valves DD, II, BB
Valve BB has flow rate=13; tunnels lead to valves CC, AA
Valve CC has flow rate=2; tunnels lead to valves DD, BB
Valve DD has flow rate=20; tunnels lead to valves CC, AA, EE
Valve EE has flow rate=3; tunnels lead to valves FF, DD
Valve FF has flow rate=0; tunnels lead to valves EE, GG
Valve GG has flow rate=0; tunnels lead to valves FF, HH
Valve HH has flow rate=22; tunnel leads to valve GG
Valve II has flow rate=0; tunnels lead to valves AA, JJ
Valve JJ has flow rate=21; tunnel leads to valve II
All of the valves begin closed. You start at valve AA, but it must be damaged or jammed or something: its flow rate is 0, so there's no point in opening it. However, you could spend one minute moving to valve BB and another minute opening it; doing so would release pressure during the remaining 28 minutes at a flow rate of 13, a total eventual pressure release of 28 * 13 = 364. Then, you could spend your third minute moving to valve CC and your fourth minute opening it, providing an additional 26 minutes of eventual pressure release at a flow rate of 2, or 52 total pressure released by valve CC.
Making your way through the tunnels like this, you could probably open many or all of the valves by the time 30 minutes have elapsed. However, you need to release as much pressure as possible, so you'll need to be methodical. Instead, consider this approach:
== Minute 1 ==
No valves are open.
You move to valve DD.
== Minute 2 ==
No valves are open.
You open valve DD.
== Minute 3 ==
Valve DD is open, releasing 20 pressure.
You move to valve CC.
== Minute 4 ==
Valve DD is open, releasing 20 pressure.
You move to valve BB.
== Minute 5 ==
Valve DD is open, releasing 20 pressure.
You open valve BB.
== Minute 6 ==
Valves BB and DD are open, releasing 33 pressure.
You move to valve AA.
== Minute 7 ==
Valves BB and DD are open, releasing 33 pressure.
You move to valve II.
== Minute 8 ==
Valves BB and DD are open, releasing 33 pressure.
You move to valve JJ.
== Minute 9 ==
Valves BB and DD are open, releasing 33 pressure.
You open valve JJ.
== Minute 10 ==
Valves BB, DD, and JJ are open, releasing 54 pressure.
You move to valve II.
== Minute 11 ==
Valves BB, DD, and JJ are open, releasing 54 pressure.
You move to valve AA.
== Minute 12 ==
Valves BB, DD, and JJ are open, releasing 54 pressure.
You move to valve DD.
== Minute 13 ==
Valves BB, DD, and JJ are open, releasing 54 pressure.
You move to valve EE.
== Minute 14 ==
Valves BB, DD, and JJ are open, releasing 54 pressure.
You move to valve FF.
== Minute 15 ==
Valves BB, DD, and JJ are open, releasing 54 pressure.
You move to valve GG.
== Minute 16 ==
Valves BB, DD, and JJ are open, releasing 54 pressure.
You move to valve HH.
== Minute 17 ==
Valves BB, DD, and JJ are open, releasing 54 pressure.
You open valve HH.
== Minute 18 ==
Valves BB, DD, HH, and JJ are open, releasing 76 pressure.
You move to valve GG.
== Minute 19 ==
Valves BB, DD, HH, and JJ are open, releasing 76 pressure.
You move to valve FF.
== Minute 20 ==
Valves BB, DD, HH, and JJ are open, releasing 76 pressure.
You move to valve EE.
== Minute 21 ==
Valves BB, DD, HH, and JJ are open, releasing 76 pressure.
You open valve EE.
== Minute 22 ==
Valves BB, DD, EE, HH, and JJ are open, releasing 79 pressure.
You move to valve DD.
== Minute 23 ==
Valves BB, DD, EE, HH, and JJ are open, releasing 79 pressure.
You move to valve CC.
== Minute 24 ==
Valves BB, DD, EE, HH, and JJ are open, releasing 79 pressure.
You open valve CC.
== Minute 25 ==
Valves BB, CC, DD, EE, HH, and JJ are open, releasing 81 pressure.
== Minute 26 ==
Valves BB, CC, DD, EE, HH, and JJ are open, releasing 81 pressure.
== Minute 27 ==
Valves BB, CC, DD, EE, HH, and JJ are open, releasing 81 pressure.
== Minute 28 ==
Valves BB, CC, DD, EE, HH, and JJ are open, releasing 81 pressure.
== Minute 29 ==
Valves BB, CC, DD, EE, HH, and JJ are open, releasing 81 pressure.
== Minute 30 ==
Valves BB, CC, DD, EE, HH, and JJ are open, releasing 81 pressure.
This approach lets you release the most pressure possible in 30 minutes with this valve layout, 1651.
Work out the steps to release the most pressure in 30 minutes. What is the most pressure you can release?
Your puzzle answer was 2250.
--- Part Two ---
You're worried that even with an optimal approach, the pressure released won't be enough. What if you got one of the elephants to help you?
It would take you 4 minutes to teach an elephant how to open the right valves in the right order, leaving you with only 26 minutes to actually execute your plan. Would having two of you working together be better, even if it means having less time? (Assume that you teach the elephant before opening any valves yourself, giving you both the same full 26 minutes.)
In the example above, you could teach the elephant to help you as follows:
== Minute 1 ==
No valves are open.
You move to valve II.
The elephant moves to valve DD.
== Minute 2 ==
No valves are open.
You move to valve JJ.
The elephant opens valve DD.
== Minute 3 ==
Valve DD is open, releasing 20 pressure.
You open valve JJ.
The elephant moves to valve EE.
== Minute 4 ==
Valves DD and JJ are open, releasing 41 pressure.
You move to valve II.
The elephant moves to valve FF.
== Minute 5 ==
Valves DD and JJ are open, releasing 41 pressure.
You move to valve AA.
The elephant moves to valve GG.
== Minute 6 ==
Valves DD and JJ are open, releasing 41 pressure.
You move to valve BB.
The elephant moves to valve HH.
== Minute 7 ==
Valves DD and JJ are open, releasing 41 pressure.
You open valve BB.
The elephant opens valve HH.
== Minute 8 ==
Valves BB, DD, HH, and JJ are open, releasing 76 pressure.
You move to valve CC.
The elephant moves to valve GG.
== Minute 9 ==
Valves BB, DD, HH, and JJ are open, releasing 76 pressure.
You open valve CC.
The elephant moves to valve FF.
== Minute 10 ==
Valves BB, CC, DD, HH, and JJ are open, releasing 78 pressure.
The elephant moves to valve EE.
== Minute 11 ==
Valves BB, CC, DD, HH, and JJ are open, releasing 78 pressure.
The elephant opens valve EE.
(At this point, all valves are open.)
== Minute 12 ==
Valves BB, CC, DD, EE, HH, and JJ are open, releasing 81 pressure.
...
== Minute 20 ==
Valves BB, CC, DD, EE, HH, and JJ are open, releasing 81 pressure.
...
== Minute 26 ==
Valves BB, CC, DD, EE, HH, and JJ are open, releasing 81 pressure.
With the elephant helping, after 26 minutes, the best you could do would release a total of 1707 pressure.
With you and an elephant working together for 26 minutes, what is the most pressure you could release?
| 397
|
--- Day 8: Handheld Halting ---
Your flight to the major airline hub reaches cruising altitude without incident. While you consider checking the in-flight menu for one of those drinks that come with a little umbrella, you are interrupted by the kid sitting next to you.
Their handheld game console won't turn on! They ask if you can take a look.
You narrow the problem down to a strange infinite loop in the boot code (your puzzle input) of the device. You should be able to fix it, but first you need to be able to run the code in isolation.
The boot code is represented as a text file with one instruction per line of text. Each instruction consists of an operation (acc, jmp, or nop) and an argument (a signed number like +4 or -20).
acc increases or decreases a single global value called the accumulator by the value given in the argument. For example, acc +7 would increase the accumulator by 7. The accumulator starts at 0. After an acc instruction, the instruction immediately below it is executed next.
jmp jumps to a new instruction relative to itself. The next instruction to execute is found using the argument as an offset from the jmp instruction; for example, jmp +2 would skip the next instruction, jmp +1 would continue to the instruction immediately below it, and jmp -20 would cause the instruction 20 lines above to be executed next.
nop stands for No OPeration - it does nothing. The instruction immediately below it is executed next.
For example, consider the following program:
nop +0
acc +1
jmp +4
acc +3
jmp -3
acc -99
acc +1
jmp -4
acc +6
These instructions are visited in this order:
nop +0 | 1
acc +1 | 2, 8(!)
jmp +4 | 3
acc +3 | 6
jmp -3 | 7
acc -99 |
acc +1 | 4
jmp -4 | 5
acc +6 |
First, the nop +0 does nothing. Then, the accumulator is increased from 0 to 1 (acc +1) and jmp +4 sets the next instruction to the other acc +1 near the bottom. After it increases the accumulator from 1 to 2, jmp -4 executes, setting the next instruction to the only acc +3. It sets the accumulator to 5, and jmp -3 causes the program to continue back at the first acc +1.
This is an infinite loop: with this sequence of jumps, the program will run forever. The moment the program tries to run any instruction a second time, you know it will never terminate.
Immediately before the program would run an instruction a second time, the value in the accumulator is 5.
Run your copy of the boot code. Immediately before any instruction is executed a second time, what value is in the accumulator?
| 398
|
--- Day 20: Firewall Rules ---
You'd like to set up a small hidden computer here so you can use it to get back into the network later. However, the corporate firewall only allows communication with certain external IP addresses.
You've retrieved the list of blocked IPs from the firewall, but the list seems to be messy and poorly maintained, and it's not clear which IPs are allowed. Also, rather than being written in dot-decimal notation, they are written as plain 32-bit integers, which can have any value from 0 through 4294967295, inclusive.
For example, suppose only the values 0 through 9 were valid, and that you retrieved the following blacklist:
5-8
0-2
4-7
The blacklist specifies ranges of IPs (inclusive of both the start and end value) that are not allowed. Then, the only IPs that this firewall allows are 3 and 9, since those are the only numbers not in any range.
Given the list of blocked IPs you retrieved from the firewall (your puzzle input), what is the lowest-valued IP that is not blocked?
| 399
|
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