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# Advent of Code
--- 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?
Your puzzle answer was 765.
--- Part Two ---
Finish folding the transparent paper according to the instructions. The manual says the code is always eight capital letters.
What code do you use to activate the infrared thermal imaging camera system?
Your puzzle answer was RZKZLPGH.
Both parts of this puzzle are complete! They provide two gold stars: **
At this point, all that is left is for you to admire your Advent calendar.
If you still want to see it, you can get your puzzle input.
References
Visible links
. https://adventofcode.com/
. https://adventofcode.com/2021/about
. https://adventofcode.com/2021/events
. https://adventofcode.com/2021/settings
. https://adventofcode.com/2021/auth/logout
. Advent of Code Supporter
https://adventofcode.com/2021/support
. https://adventofcode.com/2021
. https://adventofcode.com/2021
. https://adventofcode.com/2021/support
. https://adventofcode.com/2021/sponsors
. https://adventofcode.com/2021/leaderboard
. https://adventofcode.com/2021/stats
. https://adventofcode.com/2021/sponsors
. https://en.wikipedia.org/wiki/Transparency_(projection)
. https://adventofcode.com/2021
. https://adventofcode.com/2021/day/13/input

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# Advent of Code
--- Day 15: Chiton ---
You've almost reached the exit of the cave, but the walls are getting closer together. Your submarine can barely still fit, though; the main problem is that the walls of the cave are covered in chitons, and it would be best not to
bump any of them.
The cavern is large, but has a very low ceiling, restricting your motion to two dimensions. The shape of the cavern resembles a square; a quick scan of chiton density produces a map of risk level throughout the cave (your puzzle
input). For example:
1163751742
1381373672
2136511328
3694931569
7463417111
1319128137
1359912421
3125421639
1293138521
2311944581
You start in the top left position, your destination is the bottom right position, and you cannot move diagonally. The number at each position is its risk level; to determine the total risk of an entire path, add up the risk levels
of each position you enter (that is, don't count the risk level of your starting position unless you enter it; leaving it adds no risk to your total).
Your goal is to find a path with the lowest total risk. In this example, a path with the lowest total risk is highlighted here:
1163751742
1381373672
2136511328
3694931569
7463417111
1319128137
1359912421
3125421639
1293138521
2311944581
The total risk of this path is 40 (the starting position is never entered, so its risk is not counted).
What is the lowest total risk of any path from the top left to the bottom right?
Your puzzle answer was 366.
--- Part Two ---
Now that you know how to find low-risk paths in the cave, you can try to find your way out.
The entire cave is actually five times larger in both dimensions than you thought; the area you originally scanned is just one tile in a 5x5 tile area that forms the full map. Your original map tile repeats to the right and
downward; each time the tile repeats to the right or downward, all of its risk levels are 1 higher than the tile immediately up or left of it. However, risk levels above 9 wrap back around to 1. So, if your original map had some
position with a risk level of 8, then that same position on each of the 25 total tiles would be as follows:
8 9 1 2 3
9 1 2 3 4
1 2 3 4 5
2 3 4 5 6
3 4 5 6 7
Each single digit above corresponds to the example position with a value of 8 on the top-left tile. Because the full map is actually five times larger in both dimensions, that position appears a total of 25 times, once in each
duplicated tile, with the values shown above.
Here is the full five-times-as-large version of the first example above, with the original map in the top left corner highlighted:
11637517422274862853338597396444961841755517295286
13813736722492484783351359589446246169155735727126
21365113283247622439435873354154698446526571955763
36949315694715142671582625378269373648937148475914
74634171118574528222968563933317967414442817852555
13191281372421239248353234135946434524615754563572
13599124212461123532357223464346833457545794456865
31254216394236532741534764385264587549637569865174
12931385212314249632342535174345364628545647573965
23119445813422155692453326671356443778246755488935
22748628533385973964449618417555172952866628316397
24924847833513595894462461691557357271266846838237
32476224394358733541546984465265719557637682166874
47151426715826253782693736489371484759148259586125
85745282229685639333179674144428178525553928963666
24212392483532341359464345246157545635726865674683
24611235323572234643468334575457944568656815567976
42365327415347643852645875496375698651748671976285
23142496323425351743453646285456475739656758684176
34221556924533266713564437782467554889357866599146
33859739644496184175551729528666283163977739427418
35135958944624616915573572712668468382377957949348
43587335415469844652657195576376821668748793277985
58262537826937364893714847591482595861259361697236
96856393331796741444281785255539289636664139174777
35323413594643452461575456357268656746837976785794
35722346434683345754579445686568155679767926678187
53476438526458754963756986517486719762859782187396
34253517434536462854564757396567586841767869795287
45332667135644377824675548893578665991468977611257
44961841755517295286662831639777394274188841538529
46246169155735727126684683823779579493488168151459
54698446526571955763768216687487932779859814388196
69373648937148475914825958612593616972361472718347
17967414442817852555392896366641391747775241285888
46434524615754563572686567468379767857948187896815
46833457545794456865681556797679266781878137789298
64587549637569865174867197628597821873961893298417
45364628545647573965675868417678697952878971816398
56443778246755488935786659914689776112579188722368
55172952866628316397773942741888415385299952649631
57357271266846838237795794934881681514599279262561
65719557637682166874879327798598143881961925499217
71484759148259586125936169723614727183472583829458
28178525553928963666413917477752412858886352396999
57545635726865674683797678579481878968159298917926
57944568656815567976792667818781377892989248891319
75698651748671976285978218739618932984172914319528
56475739656758684176786979528789718163989182927419
67554889357866599146897761125791887223681299833479
Equipped with the full map, you can now find a path from the top left corner to the bottom right corner with the lowest total risk:
11637517422274862853338597396444961841755517295286
13813736722492484783351359589446246169155735727126
21365113283247622439435873354154698446526571955763
36949315694715142671582625378269373648937148475914
74634171118574528222968563933317967414442817852555
13191281372421239248353234135946434524615754563572
13599124212461123532357223464346833457545794456865
31254216394236532741534764385264587549637569865174
12931385212314249632342535174345364628545647573965
23119445813422155692453326671356443778246755488935
22748628533385973964449618417555172952866628316397
24924847833513595894462461691557357271266846838237
32476224394358733541546984465265719557637682166874
47151426715826253782693736489371484759148259586125
85745282229685639333179674144428178525553928963666
24212392483532341359464345246157545635726865674683
24611235323572234643468334575457944568656815567976
42365327415347643852645875496375698651748671976285
23142496323425351743453646285456475739656758684176
34221556924533266713564437782467554889357866599146
33859739644496184175551729528666283163977739427418
35135958944624616915573572712668468382377957949348
43587335415469844652657195576376821668748793277985
58262537826937364893714847591482595861259361697236
96856393331796741444281785255539289636664139174777
35323413594643452461575456357268656746837976785794
35722346434683345754579445686568155679767926678187
53476438526458754963756986517486719762859782187396
34253517434536462854564757396567586841767869795287
45332667135644377824675548893578665991468977611257
44961841755517295286662831639777394274188841538529
46246169155735727126684683823779579493488168151459
54698446526571955763768216687487932779859814388196
69373648937148475914825958612593616972361472718347
17967414442817852555392896366641391747775241285888
46434524615754563572686567468379767857948187896815
46833457545794456865681556797679266781878137789298
64587549637569865174867197628597821873961893298417
45364628545647573965675868417678697952878971816398
56443778246755488935786659914689776112579188722368
55172952866628316397773942741888415385299952649631
57357271266846838237795794934881681514599279262561
65719557637682166874879327798598143881961925499217
71484759148259586125936169723614727183472583829458
28178525553928963666413917477752412858886352396999
57545635726865674683797678579481878968159298917926
57944568656815567976792667818781377892989248891319
75698651748671976285978218739618932984172914319528
56475739656758684176786979528789718163989182927419
67554889357866599146897761125791887223681299833479
The total risk of this path is 315 (the starting position is still never entered, so its risk is not counted).
Using the full map, what is the lowest total risk of any path from the top left to the bottom right?
Your puzzle answer was 2829.
Both parts of this puzzle are complete! They provide two gold stars: **
At this point, all that is left is for you to admire your Advent calendar.
If you still want to see it, you can get your puzzle input.
References
Visible links
. https://adventofcode.com/
. https://adventofcode.com/2021/about
. https://adventofcode.com/2021/events
. https://adventofcode.com/2021/settings
. https://adventofcode.com/2021/auth/logout
. Advent of Code Supporter
https://adventofcode.com/2021/support
. https://adventofcode.com/2021
. https://adventofcode.com/2021
. https://adventofcode.com/2021/support
. https://adventofcode.com/2021/sponsors
. https://adventofcode.com/2021/leaderboard
. https://adventofcode.com/2021/stats
. https://adventofcode.com/2021/sponsors
. https://en.wikipedia.org/wiki/Chiton
. https://adventofcode.com/2021
. https://adventofcode.com/2021/day/15/input

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# Advent of Code
--- Day 16: Packet Decoder ---
As you leave the cave and reach open waters, you receive a transmission from the Elves back on the ship.
The transmission was sent using the Buoyancy Interchange Transmission System (BITS), a method of packing numeric expressions into a binary sequence. Your submarine's computer has saved the transmission in hexadecimal (your puzzle
input).
The first step of decoding the message is to convert the hexadecimal representation into binary. Each character of hexadecimal corresponds to four bits of binary data:
0 = 0000
1 = 0001
2 = 0010
3 = 0011
4 = 0100
5 = 0101
6 = 0110
7 = 0111
8 = 1000
9 = 1001
A = 1010
B = 1011
C = 1100
D = 1101
E = 1110
F = 1111
The BITS transmission contains a single packet at its outermost layer which itself contains many other packets. The hexadecimal representation of this packet might encode a few extra 0 bits at the end; these are not part of the
transmission and should be ignored.
Every packet begins with a standard header: the first three bits encode the packet version, and the next three bits encode the packet type ID. These two values are numbers; all numbers encoded in any packet are represented as
binary with the most significant bit first. For example, a version encoded as the binary sequence 100 represents the number 4.
Packets with type ID 4 represent a literal value. Literal value packets encode a single binary number. To do this, the binary number is padded with leading zeroes until its length is a multiple of four bits, and then it is broken
into groups of four bits. Each group is prefixed by a 1 bit except the last group, which is prefixed by a 0 bit. These groups of five bits immediately follow the packet header. For example, the hexadecimal string D2FE28 becomes:
110100101111111000101000
VVVTTTAAAAABBBBBCCCCC
Below each bit is a label indicating its purpose:
• The three bits labeled V (110) are the packet version, 6.
• The three bits labeled T (100) are the packet type ID, 4, which means the packet is a literal value.
• The five bits labeled A (10111) start with a 1 (not the last group, keep reading) and contain the first four bits of the number, 0111.
• The five bits labeled B (11110) start with a 1 (not the last group, keep reading) and contain four more bits of the number, 1110.
• The five bits labeled C (00101) start with a 0 (last group, end of packet) and contain the last four bits of the number, 0101.
• The three unlabeled 0 bits at the end are extra due to the hexadecimal representation and should be ignored.
So, this packet represents a literal value with binary representation 011111100101, which is 2021 in decimal.
Every other type of packet (any packet with a type ID other than 4) represent an operator that performs some calculation on one or more sub-packets contained within. Right now, the specific operations aren't important; focus on
parsing the hierarchy of sub-packets.
An operator packet contains one or more packets. To indicate which subsequent binary data represents its sub-packets, an operator packet can use one of two modes indicated by the bit immediately after the packet header; this is
called the length type ID:
• If the length type ID is 0, then the next 15 bits are a number that represents the total length in bits of the sub-packets contained by this packet.
• If the length type ID is 1, then the next 11 bits are a number that represents the number of sub-packets immediately contained by this packet.
Finally, after the length type ID bit and the 15-bit or 11-bit field, the sub-packets appear.
For example, here is an operator packet (hexadecimal string 38006F45291200) with length type ID 0 that contains two sub-packets:
00111000000000000110111101000101001010010001001000000000
VVVTTTILLLLLLLLLLLLLLLAAAAAAAAAAABBBBBBBBBBBBBBBB
• The three bits labeled V (001) are the packet version, 1.
• The three bits labeled T (110) are the packet type ID, 6, which means the packet is an operator.
• The bit labeled I (0) is the length type ID, which indicates that the length is a 15-bit number representing the number of bits in the sub-packets.
• The 15 bits labeled L (000000000011011) contain the length of the sub-packets in bits, 27.
• The 11 bits labeled A contain the first sub-packet, a literal value representing the number 10.
• The 16 bits labeled B contain the second sub-packet, a literal value representing the number 20.
After reading 11 and 16 bits of sub-packet data, the total length indicated in L (27) is reached, and so parsing of this packet stops.
As another example, here is an operator packet (hexadecimal string EE00D40C823060) with length type ID 1 that contains three sub-packets:
11101110000000001101010000001100100000100011000001100000
VVVTTTILLLLLLLLLLLAAAAAAAAAAABBBBBBBBBBBCCCCCCCCCCC
• The three bits labeled V (111) are the packet version, 7.
• The three bits labeled T (011) are the packet type ID, 3, which means the packet is an operator.
• The bit labeled I (1) is the length type ID, which indicates that the length is a 11-bit number representing the number of sub-packets.
• The 11 bits labeled L (00000000011) contain the number of sub-packets, 3.
• The 11 bits labeled A contain the first sub-packet, a literal value representing the number 1.
• The 11 bits labeled B contain the second sub-packet, a literal value representing the number 2.
• The 11 bits labeled C contain the third sub-packet, a literal value representing the number 3.
After reading 3 complete sub-packets, the number of sub-packets indicated in L (3) is reached, and so parsing of this packet stops.
For now, parse the hierarchy of the packets throughout the transmission and add up all of the version numbers.
Here are a few more examples of hexadecimal-encoded transmissions:
• 8A004A801A8002F478 represents an operator packet (version 4) which contains an operator packet (version 1) which contains an operator packet (version 5) which contains a literal value (version 6); this packet has a version sum
of 16.
• 620080001611562C8802118E34 represents an operator packet (version 3) which contains two sub-packets; each sub-packet is an operator packet that contains two literal values. This packet has a version sum of 12.
• C0015000016115A2E0802F182340 has the same structure as the previous example, but the outermost packet uses a different length type ID. This packet has a version sum of 23.
• A0016C880162017C3686B18A3D4780 is an operator packet that contains an operator packet that contains an operator packet that contains five literal values; it has a version sum of 31.
Decode the structure of your hexadecimal-encoded BITS transmission; what do you get if you add up the version numbers in all packets?
Your puzzle answer was 999.
--- Part Two ---
Now that you have the structure of your transmission decoded, you can calculate the value of the expression it represents.
Literal values (type ID 4) represent a single number as described above. The remaining type IDs are more interesting:
• Packets with type ID 0 are sum packets - their value is the sum of the values of their sub-packets. If they only have a single sub-packet, their value is the value of the sub-packet.
• Packets with type ID 1 are product packets - their value is the result of multiplying together the values of their sub-packets. If they only have a single sub-packet, their value is the value of the sub-packet.
• Packets with type ID 2 are minimum packets - their value is the minimum of the values of their sub-packets.
• Packets with type ID 3 are maximum packets - their value is the maximum of the values of their sub-packets.
• Packets with type ID 5 are greater than packets - their value is 1 if the value of the first sub-packet is greater than the value of the second sub-packet; otherwise, their value is 0. These packets always have exactly two
sub-packets.
• Packets with type ID 6 are less than packets - their value is 1 if the value of the first sub-packet is less than the value of the second sub-packet; otherwise, their value is 0. These packets always have exactly two
sub-packets.
• Packets with type ID 7 are equal to packets - their value is 1 if the value of the first sub-packet is equal to the value of the second sub-packet; otherwise, their value is 0. These packets always have exactly two sub-packets.
Using these rules, you can now work out the value of the outermost packet in your BITS transmission.
For example:
• C200B40A82 finds the sum of 1 and 2, resulting in the value 3.
• 04005AC33890 finds the product of 6 and 9, resulting in the value 54.
• 880086C3E88112 finds the minimum of 7, 8, and 9, resulting in the value 7.
• CE00C43D881120 finds the maximum of 7, 8, and 9, resulting in the value 9.
• D8005AC2A8F0 produces 1, because 5 is less than 15.
• F600BC2D8F produces 0, because 5 is not greater than 15.
• 9C005AC2F8F0 produces 0, because 5 is not equal to 15.
• 9C0141080250320F1802104A08 produces 1, because 1 + 3 = 2 * 2.
What do you get if you evaluate the expression represented by your hexadecimal-encoded BITS transmission?
Your puzzle answer was 3408662834145.
Both parts of this puzzle are complete! They provide two gold stars: **
At this point, all that is left is for you to admire your Advent calendar.
If you still want to see it, you can get your puzzle input.
References
Visible links
. https://adventofcode.com/
. https://adventofcode.com/2021/about
. https://adventofcode.com/2021/events
. https://adventofcode.com/2021/settings
. https://adventofcode.com/2021/auth/logout
. Advent of Code Supporter
https://adventofcode.com/2021/support
. https://adventofcode.com/2021
. https://adventofcode.com/2021
. https://adventofcode.com/2021/support
. https://adventofcode.com/2021/sponsors
. https://adventofcode.com/2021/leaderboard
. https://adventofcode.com/2021/stats
. https://adventofcode.com/2021/sponsors
. https://en.wikipedia.org/wiki/Hexadecimal
. https://adventofcode.com/2021
. https://adventofcode.com/2021/day/16/input

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# Advent of Code
--- 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?
Your puzzle answer was 4186.
--- Part Two ---
Maybe a fancy trick shot isn't the best idea; after all, you only have one probe, so you had better not miss.
To get the best idea of what your options are for launching the probe, you need to find every initial velocity that causes the probe to eventually be within the target area after any step.
In the above example, there are 112 different initial velocity values that meet these criteria:
23,-10 25,-9 27,-5 29,-6 22,-6 21,-7 9,0 27,-7 24,-5
25,-7 26,-6 25,-5 6,8 11,-2 20,-5 29,-10 6,3 28,-7
8,0 30,-6 29,-8 20,-10 6,7 6,4 6,1 14,-4 21,-6
26,-10 7,-1 7,7 8,-1 21,-9 6,2 20,-7 30,-10 14,-3
20,-8 13,-2 7,3 28,-8 29,-9 15,-3 22,-5 26,-8 25,-8
25,-6 15,-4 9,-2 15,-2 12,-2 28,-9 12,-3 24,-6 23,-7
25,-10 7,8 11,-3 26,-7 7,1 23,-9 6,0 22,-10 27,-6
8,1 22,-8 13,-4 7,6 28,-6 11,-4 12,-4 26,-9 7,4
24,-10 23,-8 30,-8 7,0 9,-1 10,-1 26,-5 22,-9 6,5
7,5 23,-6 28,-10 10,-2 11,-1 20,-9 14,-2 29,-7 13,-3
23,-5 24,-8 27,-9 30,-7 28,-5 21,-10 7,9 6,6 21,-5
27,-10 7,2 30,-9 21,-8 22,-7 24,-9 20,-6 6,9 29,-5
8,-2 27,-8 30,-5 24,-7
How many distinct initial velocity values cause the probe to be within the target area after any step?
Your puzzle answer was 2709.
Both parts of this puzzle are complete! They provide two gold stars: **
At this point, all that is left is for you to admire your Advent calendar.
If you still want to see it, you can get your puzzle input.
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# Advent of Code
--- Day 18: Snailfish ---
You descend into the ocean trench and encounter some snailfish. They say they saw the sleigh keys! They'll even tell you which direction the keys went if you help one of the smaller snailfish with his math homework.
Snailfish numbers aren't like regular numbers. Instead, every snailfish number is a pair - an ordered list of two elements. Each element of the pair can be either a regular number or another pair.
Pairs are written as [x,y], where x and y are the elements within the pair. Here are some example snailfish numbers, one snailfish number per line:
[1,2]
[[1,2],3]
[9,[8,7]]
[[1,9],[8,5]]
[[[[1,2],[3,4]],[[5,6],[7,8]]],9]
[[[9,[3,8]],[[0,9],6]],[[[3,7],[4,9]],3]]
[[[[1,3],[5,3]],[[1,3],[8,7]]],[[[4,9],[6,9]],[[8,2],[7,3]]]]
This snailfish homework is about addition. To add two snailfish numbers, form a pair from the left and right parameters of the addition operator. For example, [1,2] + [[3,4],5] becomes [[1,2],[[3,4],5]].
There's only one problem: snailfish numbers must always be reduced, and the process of adding two snailfish numbers can result in snailfish numbers that need to be reduced.
To reduce a snailfish number, you must repeatedly do the first action in this list that applies to the snailfish number:
• If any pair is nested inside four pairs, the leftmost such pair explodes.
• If any regular number is 10 or greater, the leftmost such regular number splits.
Once no action in the above list applies, the snailfish number is reduced.
During reduction, at most one action applies, after which the process returns to the top of the list of actions. For example, if split produces a pair that meets the explode criteria, that pair explodes before other splits occur.
To explode a pair, the pair's left value is added to the first regular number to the left of the exploding pair (if any), and the pair's right value is added to the first regular number to the right of the exploding pair (if any).
Exploding pairs will always consist of two regular numbers. Then, the entire exploding pair is replaced with the regular number 0.
Here are some examples of a single explode action:
• [[[[[9,8],1],2],3],4] becomes [[[[0,9],2],3],4] (the 9 has no regular number to its left, so it is not added to any regular number).
• [7,[6,[5,[4,[3,2]]]]] becomes [7,[6,[5,[7,0]]]] (the 2 has no regular number to its right, and so it is not added to any regular number).
• [[6,[5,[4,[3,2]]]],1] becomes [[6,[5,[7,0]]],3].
• [[3,[2,[1,[7,3]]]],[6,[5,[4,[3,2]]]]] becomes [[3,[2,[8,0]]],[9,[5,[4,[3,2]]]]] (the pair [3,2] is unaffected because the pair [7,3] is further to the left; [3,2] would explode on the next action).
• [[3,[2,[8,0]]],[9,[5,[4,[3,2]]]]] becomes [[3,[2,[8,0]]],[9,[5,[7,0]]]].
To split a regular number, replace it with a pair; the left element of the pair should be the regular number divided by two and rounded down, while the right element of the pair should be the regular number divided by two and
rounded up. For example, 10 becomes [5,5], 11 becomes [5,6], 12 becomes [6,6], and so on.
Here is the process of finding the reduced result of [[[[4,3],4],4],[7,[[8,4],9]]] + [1,1]:
after addition: [[[[[4,3],4],4],[7,[[8,4],9]]],[1,1]]
after explode: [[[[0,7],4],[7,[[8,4],9]]],[1,1]]
after explode: [[[[0,7],4],[15,[0,13]]],[1,1]]
after split: [[[[0,7],4],[[7,8],[0,13]]],[1,1]]
after split: [[[[0,7],4],[[7,8],[0,[6,7]]]],[1,1]]
after explode: [[[[0,7],4],[[7,8],[6,0]]],[8,1]]
Once no reduce actions apply, the snailfish number that remains is the actual result of the addition operation: [[[[0,7],4],[[7,8],[6,0]]],[8,1]].
The homework assignment involves adding up a list of snailfish numbers (your puzzle input). The snailfish numbers are each listed on a separate line. Add the first snailfish number and the second, then add that result and the
third, then add that result and the fourth, and so on until all numbers in the list have been used once.
For example, the final sum of this list is [[[[1,1],[2,2]],[3,3]],[4,4]]:
[1,1]
[2,2]
[3,3]
[4,4]
The final sum of this list is [[[[3,0],[5,3]],[4,4]],[5,5]]:
[1,1]
[2,2]
[3,3]
[4,4]
[5,5]
The final sum of this list is [[[[5,0],[7,4]],[5,5]],[6,6]]:
[1,1]
[2,2]
[3,3]
[4,4]
[5,5]
[6,6]
Here's a slightly larger example:
[[[0,[4,5]],[0,0]],[[[4,5],[2,6]],[9,5]]]
[7,[[[3,7],[4,3]],[[6,3],[8,8]]]]
[[2,[[0,8],[3,4]]],[[[6,7],1],[7,[1,6]]]]
[[[[2,4],7],[6,[0,5]]],[[[6,8],[2,8]],[[2,1],[4,5]]]]
[7,[5,[[3,8],[1,4]]]]
[[2,[2,2]],[8,[8,1]]]
[2,9]
[1,[[[9,3],9],[[9,0],[0,7]]]]
[[[5,[7,4]],7],1]
[[[[4,2],2],6],[8,7]]
The final sum [[[[8,7],[7,7]],[[8,6],[7,7]]],[[[0,7],[6,6]],[8,7]]] is found after adding up the above snailfish numbers:
[[[0,[4,5]],[0,0]],[[[4,5],[2,6]],[9,5]]]
+ [7,[[[3,7],[4,3]],[[6,3],[8,8]]]]
= [[[[4,0],[5,4]],[[7,7],[6,0]]],[[8,[7,7]],[[7,9],[5,0]]]]
[[[[4,0],[5,4]],[[7,7],[6,0]]],[[8,[7,7]],[[7,9],[5,0]]]]
+ [[2,[[0,8],[3,4]]],[[[6,7],1],[7,[1,6]]]]
= [[[[6,7],[6,7]],[[7,7],[0,7]]],[[[8,7],[7,7]],[[8,8],[8,0]]]]
[[[[6,7],[6,7]],[[7,7],[0,7]]],[[[8,7],[7,7]],[[8,8],[8,0]]]]
+ [[[[2,4],7],[6,[0,5]]],[[[6,8],[2,8]],[[2,1],[4,5]]]]
= [[[[7,0],[7,7]],[[7,7],[7,8]]],[[[7,7],[8,8]],[[7,7],[8,7]]]]
[[[[7,0],[7,7]],[[7,7],[7,8]]],[[[7,7],[8,8]],[[7,7],[8,7]]]]
+ [7,[5,[[3,8],[1,4]]]]
= [[[[7,7],[7,8]],[[9,5],[8,7]]],[[[6,8],[0,8]],[[9,9],[9,0]]]]
[[[[7,7],[7,8]],[[9,5],[8,7]]],[[[6,8],[0,8]],[[9,9],[9,0]]]]
+ [[2,[2,2]],[8,[8,1]]]
= [[[[6,6],[6,6]],[[6,0],[6,7]]],[[[7,7],[8,9]],[8,[8,1]]]]
[[[[6,6],[6,6]],[[6,0],[6,7]]],[[[7,7],[8,9]],[8,[8,1]]]]
+ [2,9]
= [[[[6,6],[7,7]],[[0,7],[7,7]]],[[[5,5],[5,6]],9]]
[[[[6,6],[7,7]],[[0,7],[7,7]]],[[[5,5],[5,6]],9]]
+ [1,[[[9,3],9],[[9,0],[0,7]]]]
= [[[[7,8],[6,7]],[[6,8],[0,8]]],[[[7,7],[5,0]],[[5,5],[5,6]]]]
[[[[7,8],[6,7]],[[6,8],[0,8]]],[[[7,7],[5,0]],[[5,5],[5,6]]]]
+ [[[5,[7,4]],7],1]
= [[[[7,7],[7,7]],[[8,7],[8,7]]],[[[7,0],[7,7]],9]]
[[[[7,7],[7,7]],[[8,7],[8,7]]],[[[7,0],[7,7]],9]]
+ [[[[4,2],2],6],[8,7]]
= [[[[8,7],[7,7]],[[8,6],[7,7]]],[[[0,7],[6,6]],[8,7]]]
To check whether it's the right answer, the snailfish teacher only checks the magnitude of the final sum. The magnitude of a pair is 3 times the magnitude of its left element plus 2 times the magnitude of its right element. The
magnitude of a regular number is just that number.
For example, the magnitude of [9,1] is 3*9 + 2*1 = 29; the magnitude of [1,9] is 3*1 + 2*9 = 21. Magnitude calculations are recursive: the magnitude of [[9,1],[1,9]] is 3*29 + 2*21 = 129.
Here are a few more magnitude examples:
• [[1,2],[[3,4],5]] becomes 143.
• [[[[0,7],4],[[7,8],[6,0]]],[8,1]] becomes 1384.
• [[[[1,1],[2,2]],[3,3]],[4,4]] becomes 445.
• [[[[3,0],[5,3]],[4,4]],[5,5]] becomes 791.
• [[[[5,0],[7,4]],[5,5]],[6,6]] becomes 1137.
• [[[[8,7],[7,7]],[[8,6],[7,7]]],[[[0,7],[6,6]],[8,7]]] becomes 3488.
So, given this example homework assignment:
[[[0,[5,8]],[[1,7],[9,6]]],[[4,[1,2]],[[1,4],2]]]
[[[5,[2,8]],4],[5,[[9,9],0]]]
[6,[[[6,2],[5,6]],[[7,6],[4,7]]]]
[[[6,[0,7]],[0,9]],[4,[9,[9,0]]]]
[[[7,[6,4]],[3,[1,3]]],[[[5,5],1],9]]
[[6,[[7,3],[3,2]]],[[[3,8],[5,7]],4]]
[[[[5,4],[7,7]],8],[[8,3],8]]
[[9,3],[[9,9],[6,[4,9]]]]
[[2,[[7,7],7]],[[5,8],[[9,3],[0,2]]]]
[[[[5,2],5],[8,[3,7]]],[[5,[7,5]],[4,4]]]
The final sum is:
[[[[6,6],[7,6]],[[7,7],[7,0]]],[[[7,7],[7,7]],[[7,8],[9,9]]]]
The magnitude of this final sum is 4140.
Add up all of the snailfish numbers from the homework assignment in the order they appear. What is the magnitude of the final sum?
Your puzzle answer was 4116.
--- Part Two ---
You notice a second question on the back of the homework assignment:
What is the largest magnitude you can get from adding only two of the snailfish numbers?
Note that snailfish addition is not commutative - that is, x + y and y + x can produce different results.
Again considering the last example homework assignment above:
[[[0,[5,8]],[[1,7],[9,6]]],[[4,[1,2]],[[1,4],2]]]
[[[5,[2,8]],4],[5,[[9,9],0]]]
[6,[[[6,2],[5,6]],[[7,6],[4,7]]]]
[[[6,[0,7]],[0,9]],[4,[9,[9,0]]]]
[[[7,[6,4]],[3,[1,3]]],[[[5,5],1],9]]
[[6,[[7,3],[3,2]]],[[[3,8],[5,7]],4]]
[[[[5,4],[7,7]],8],[[8,3],8]]
[[9,3],[[9,9],[6,[4,9]]]]
[[2,[[7,7],7]],[[5,8],[[9,3],[0,2]]]]
[[[[5,2],5],[8,[3,7]]],[[5,[7,5]],[4,4]]]
The largest magnitude of the sum of any two snailfish numbers in this list is 3993. This is the magnitude of [[2,[[7,7],7]],[[5,8],[[9,3],[0,2]]]] + [[[0,[5,8]],[[1,7],[9,6]]],[[4,[1,2]],[[1,4],2]]], which reduces to
[[[[7,8],[6,6]],[[6,0],[7,7]]],[[[7,8],[8,8]],[[7,9],[0,6]]]].
What is the largest magnitude of any sum of two different snailfish numbers from the homework assignment?
Your puzzle answer was 4638.
Both parts of this puzzle are complete! They provide two gold stars: **
At this point, all that is left is for you to admire your Advent calendar.
If you still want to see it, you can get your puzzle input.
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. https://en.wikipedia.org/wiki/Snailfish
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. https://adventofcode.com/2021/day/18/input

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# Advent of Code
--- Day 19: Beacon Scanner ---
As your probe drifted down through this area, it released an assortment of beacons and scanners into the water. It's difficult to navigate in the pitch black open waters of the ocean trench, but if you can build a map of the trench
using data from the scanners, you should be able to safely reach the bottom.
The beacons and scanners float motionless in the water; they're designed to maintain the same position for long periods of time. Each scanner is capable of detecting all beacons in a large cube centered on the scanner; beacons that
are at most 1000 units away from the scanner in each of the three axes (x, y, and z) have their precise position determined relative to the scanner. However, scanners cannot detect other scanners. The submarine has automatically
summarized the relative positions of beacons detected by each scanner (your puzzle input).
For example, if a scanner is at x,y,z coordinates 500,0,-500 and there are beacons at -500,1000,-1500 and 1501,0,-500, the scanner could report that the first beacon is at -1000,1000,-1000 (relative to the scanner) but would not
detect the second beacon at all.
Unfortunately, while each scanner can report the positions of all detected beacons relative to itself, the scanners do not know their own position. You'll need to determine the positions of the beacons and scanners yourself.
The scanners and beacons map a single contiguous 3d region. This region can be reconstructed by finding pairs of scanners that have overlapping detection regions such that there are at least 12 beacons that both scanners detect
within the overlap. By establishing 12 common beacons, you can precisely determine where the scanners are relative to each other, allowing you to reconstruct the beacon map one scanner at a time.
For a moment, consider only two dimensions. Suppose you have the following scanner reports:
--- scanner 0 ---
0,2
4,1
3,3
--- scanner 1 ---
-1,-1
-5,0
-2,1
Drawing x increasing rightward, y increasing upward, scanners as S, and beacons as B, scanner 0 detects this:
...B.
B....
....B
S....
Scanner 1 detects this:
...B..
B....S
....B.
For this example, assume scanners only need 3 overlapping beacons. Then, the beacons visible to both scanners overlap to produce the following complete map:
...B..
B....S
....B.
S.....
Unfortunately, there's a second problem: the scanners also don't know their rotation or facing direction. Due to magnetic alignment, each scanner is rotated some integer number of 90-degree turns around all of the x, y, and z axes.
That is, one scanner might call a direction positive x, while another scanner might call that direction negative y. Or, two scanners might agree on which direction is positive x, but one scanner might be upside-down from the
perspective of the other scanner. In total, each scanner could be in any of 24 different orientations: facing positive or negative x, y, or z, and considering any of four directions "up" from that facing.
For example, here is an arrangement of beacons as seen from a scanner in the same position but in different orientations:
--- scanner 0 ---
-1,-1,1
-2,-2,2
-3,-3,3
-2,-3,1
5,6,-4
8,0,7
--- scanner 0 ---
1,-1,1
2,-2,2
3,-3,3
2,-1,3
-5,4,-6
-8,-7,0
--- scanner 0 ---
-1,-1,-1
-2,-2,-2
-3,-3,-3
-1,-3,-2
4,6,5
-7,0,8
--- scanner 0 ---
1,1,-1
2,2,-2
3,3,-3
1,3,-2
-4,-6,5
7,0,8
--- scanner 0 ---
1,1,1
2,2,2
3,3,3
3,1,2
-6,-4,-5
0,7,-8
By finding pairs of scanners that both see at least 12 of the same beacons, you can assemble the entire map. For example, consider the following report:
--- scanner 0 ---
404,-588,-901
528,-643,409
-838,591,734
390,-675,-793
-537,-823,-458
-485,-357,347
-345,-311,381
-661,-816,-575
-876,649,763
-618,-824,-621
553,345,-567
474,580,667
-447,-329,318
-584,868,-557
544,-627,-890
564,392,-477
455,729,728
-892,524,684
-689,845,-530
423,-701,434
7,-33,-71
630,319,-379
443,580,662
-789,900,-551
459,-707,401
--- scanner 1 ---
686,422,578
605,423,415
515,917,-361
-336,658,858
95,138,22
-476,619,847
-340,-569,-846
567,-361,727
-460,603,-452
669,-402,600
729,430,532
-500,-761,534
-322,571,750
-466,-666,-811
-429,-592,574
-355,545,-477
703,-491,-529
-328,-685,520
413,935,-424
-391,539,-444
586,-435,557
-364,-763,-893
807,-499,-711
755,-354,-619
553,889,-390
--- scanner 2 ---
649,640,665
682,-795,504
-784,533,-524
-644,584,-595
-588,-843,648
-30,6,44
-674,560,763
500,723,-460
609,671,-379
-555,-800,653
-675,-892,-343
697,-426,-610
578,704,681
493,664,-388
-671,-858,530
-667,343,800
571,-461,-707
-138,-166,112
-889,563,-600
646,-828,498
640,759,510
-630,509,768
-681,-892,-333
673,-379,-804
-742,-814,-386
577,-820,562
--- scanner 3 ---
-589,542,597
605,-692,669
-500,565,-823
-660,373,557
-458,-679,-417
-488,449,543
-626,468,-788
338,-750,-386
528,-832,-391
562,-778,733
-938,-730,414
543,643,-506
-524,371,-870
407,773,750
-104,29,83
378,-903,-323
-778,-728,485
426,699,580
-438,-605,-362
-469,-447,-387
509,732,623
647,635,-688
-868,-804,481
614,-800,639
595,780,-596
--- scanner 4 ---
727,592,562
-293,-554,779
441,611,-461
-714,465,-776
-743,427,-804
-660,-479,-426
832,-632,460
927,-485,-438
408,393,-506
466,436,-512
110,16,151
-258,-428,682
-393,719,612
-211,-452,876
808,-476,-593
-575,615,604
-485,667,467
-680,325,-822
-627,-443,-432
872,-547,-609
833,512,582
807,604,487
839,-516,451
891,-625,532
-652,-548,-490
30,-46,-14
Because all coordinates are relative, in this example, all "absolute" positions will be expressed relative to scanner 0 (using the orientation of scanner 0 and as if scanner 0 is at coordinates 0,0,0).
Scanners 0 and 1 have overlapping detection cubes; the 12 beacons they both detect (relative to scanner 0) are at the following coordinates:
-618,-824,-621
-537,-823,-458
-447,-329,318
404,-588,-901
544,-627,-890
528,-643,409
-661,-816,-575
390,-675,-793
423,-701,434
-345,-311,381
459,-707,401
-485,-357,347
These same 12 beacons (in the same order) but from the perspective of scanner 1 are:
686,422,578
605,423,415
515,917,-361
-336,658,858
-476,619,847
-460,603,-452
729,430,532
-322,571,750
-355,545,-477
413,935,-424
-391,539,-444
553,889,-390
Because of this, scanner 1 must be at 68,-1246,-43 (relative to scanner 0).
Scanner 4 overlaps with scanner 1; the 12 beacons they both detect (relative to scanner 0) are:
459,-707,401
-739,-1745,668
-485,-357,347
432,-2009,850
528,-643,409
423,-701,434
-345,-311,381
408,-1815,803
534,-1912,768
-687,-1600,576
-447,-329,318
-635,-1737,486
So, scanner 4 is at -20,-1133,1061 (relative to scanner 0).
Following this process, scanner 2 must be at 1105,-1205,1229 (relative to scanner 0) and scanner 3 must be at -92,-2380,-20 (relative to scanner 0).
The full list of beacons (relative to scanner 0) is:
-892,524,684
-876,649,763
-838,591,734
-789,900,-551
-739,-1745,668
-706,-3180,-659
-697,-3072,-689
-689,845,-530
-687,-1600,576
-661,-816,-575
-654,-3158,-753
-635,-1737,486
-631,-672,1502
-624,-1620,1868
-620,-3212,371
-618,-824,-621
-612,-1695,1788
-601,-1648,-643
-584,868,-557
-537,-823,-458
-532,-1715,1894
-518,-1681,-600
-499,-1607,-770
-485,-357,347
-470,-3283,303
-456,-621,1527
-447,-329,318
-430,-3130,366
-413,-627,1469
-345,-311,381
-36,-1284,1171
-27,-1108,-65
7,-33,-71
12,-2351,-103
26,-1119,1091
346,-2985,342
366,-3059,397
377,-2827,367
390,-675,-793
396,-1931,-563
404,-588,-901
408,-1815,803
423,-701,434
432,-2009,850
443,580,662
455,729,728
456,-540,1869
459,-707,401
465,-695,1988
474,580,667
496,-1584,1900
497,-1838,-617
527,-524,1933
528,-643,409
534,-1912,768
544,-627,-890
553,345,-567
564,392,-477
568,-2007,-577
605,-1665,1952
612,-1593,1893
630,319,-379
686,-3108,-505
776,-3184,-501
846,-3110,-434
1135,-1161,1235
1243,-1093,1063
1660,-552,429
1693,-557,386
1735,-437,1738
1749,-1800,1813
1772,-405,1572
1776,-675,371
1779,-442,1789
1780,-1548,337
1786,-1538,337
1847,-1591,415
1889,-1729,1762
1994,-1805,1792
In total, there are 79 beacons.
Assemble the full map of beacons. How many beacons are there?
Your puzzle answer was 414.
--- Part Two ---
Sometimes, it's a good idea to appreciate just how big the ocean is. Using the Manhattan distance, how far apart do the scanners get?
In the above example, scanners 2 (1105,-1205,1229) and 3 (-92,-2380,-20) are the largest Manhattan distance apart. In total, they are 1197 + 1175 + 1249 = 3621 units apart.
What is the largest Manhattan distance between any two scanners?
Your puzzle answer was 13000.
Both parts of this puzzle are complete! They provide two gold stars: **
At this point, all that is left is for you to admire your Advent calendar.
If you still want to see it, you can get your puzzle input.
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# Advent of Code
--- 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 5218.
--- 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?
Your puzzle answer was 15527.
Both parts of this puzzle are complete! They provide two gold stars: **
At this point, all that is left is for you to admire your Advent calendar.
If you still want to see it, you can get your puzzle input.
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# Advent of Code
--- Day 21: Dirac Dice ---
There's not much to do as you slowly descend to the bottom of the ocean. The submarine computer challenges you to a nice game of Dirac Dice.
This game consists of a single die, two pawns, and a game board with a circular track containing ten spaces marked 1 through 10 clockwise. Each player's starting space is chosen randomly (your puzzle input). Player 1 goes first.
Players take turns moving. On each player's turn, the player rolls the die three times and adds up the results. Then, the player moves their pawn that many times forward around the track (that is, moving clockwise on spaces in
order of increasing value, wrapping back around to 1 after 10). So, if a player is on space 7 and they roll 2, 2, and 1, they would move forward 5 times, to spaces 8, 9, 10, 1, and finally stopping on 2.
After each player moves, they increase their score by the value of the space their pawn stopped on. Players' scores start at 0. So, if the first player starts on space 7 and rolls a total of 5, they would stop on space 2 and add 2
to their score (for a total score of 2). The game immediately ends as a win for any player whose score reaches at least 1000.
Since the first game is a practice game, the submarine opens a compartment labeled deterministic dice and a 100-sided die falls out. This die always rolls 1 first, then 2, then 3, and so on up to 100, after which it starts over at
1 again. Play using this die.
For example, given these starting positions:
Player 1 starting position: 4
Player 2 starting position: 8
This is how the game would go:
• Player 1 rolls 1+2+3 and moves to space 10 for a total score of 10.
• Player 2 rolls 4+5+6 and moves to space 3 for a total score of 3.
• Player 1 rolls 7+8+9 and moves to space 4 for a total score of 14.
• Player 2 rolls 10+11+12 and moves to space 6 for a total score of 9.
• Player 1 rolls 13+14+15 and moves to space 6 for a total score of 20.
• Player 2 rolls 16+17+18 and moves to space 7 for a total score of 16.
• Player 1 rolls 19+20+21 and moves to space 6 for a total score of 26.
• Player 2 rolls 22+23+24 and moves to space 6 for a total score of 22.
...after many turns...
• Player 2 rolls 82+83+84 and moves to space 6 for a total score of 742.
• Player 1 rolls 85+86+87 and moves to space 4 for a total score of 990.
• Player 2 rolls 88+89+90 and moves to space 3 for a total score of 745.
• Player 1 rolls 91+92+93 and moves to space 10 for a final score, 1000.
Since player 1 has at least 1000 points, player 1 wins and the game ends. At this point, the losing player had 745 points and the die had been rolled a total of 993 times; 745 * 993 = 739785.
Play a practice game using the deterministic 100-sided die. The moment either player wins, what do you get if you multiply the score of the losing player by the number of times the die was rolled during the game?
Your puzzle answer was 908595.
--- Part Two ---
Now that you're warmed up, it's time to play the real game.
A second compartment opens, this time labeled Dirac dice. Out of it falls a single three-sided die.
As you experiment with the die, you feel a little strange. An informational brochure in the compartment explains that this is a quantum die: when you roll it, the universe splits into multiple copies, one copy for each possible
outcome of the die. In this case, rolling the die always splits the universe into three copies: one where the outcome of the roll was 1, one where it was 2, and one where it was 3.
The game is played the same as before, although to prevent things from getting too far out of hand, the game now ends when either player's score reaches at least 21.
Using the same starting positions as in the example above, player 1 wins in 444356092776315 universes, while player 2 merely wins in 341960390180808 universes.
Using your given starting positions, determine every possible outcome. Find the player that wins in more universes; in how many universes does that player win?
Your puzzle answer was 91559198282731.
Both parts of this puzzle are complete! They provide two gold stars: **
At this point, all that is left is for you to admire your Advent calendar.
If you still want to see it, you can get your puzzle input.
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# Advent of Code
--- 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?
Your puzzle answer was 547648.
--- Part Two ---
Now that the initialization procedure is complete, you can reboot the reactor.
Starting with all cubes off, run all of the reboot steps for all cubes in the reactor.
Consider the following reboot steps:
on x=-5..47,y=-31..22,z=-19..33
on x=-44..5,y=-27..21,z=-14..35
on x=-49..-1,y=-11..42,z=-10..38
on x=-20..34,y=-40..6,z=-44..1
off x=26..39,y=40..50,z=-2..11
on x=-41..5,y=-41..6,z=-36..8
off x=-43..-33,y=-45..-28,z=7..25
on x=-33..15,y=-32..19,z=-34..11
off x=35..47,y=-46..-34,z=-11..5
on x=-14..36,y=-6..44,z=-16..29
on x=-57795..-6158,y=29564..72030,z=20435..90618
on x=36731..105352,y=-21140..28532,z=16094..90401
on x=30999..107136,y=-53464..15513,z=8553..71215
on x=13528..83982,y=-99403..-27377,z=-24141..23996
on x=-72682..-12347,y=18159..111354,z=7391..80950
on x=-1060..80757,y=-65301..-20884,z=-103788..-16709
on x=-83015..-9461,y=-72160..-8347,z=-81239..-26856
on x=-52752..22273,y=-49450..9096,z=54442..119054
on x=-29982..40483,y=-108474..-28371,z=-24328..38471
on x=-4958..62750,y=40422..118853,z=-7672..65583
on x=55694..108686,y=-43367..46958,z=-26781..48729
on x=-98497..-18186,y=-63569..3412,z=1232..88485
on x=-726..56291,y=-62629..13224,z=18033..85226
on x=-110886..-34664,y=-81338..-8658,z=8914..63723
on x=-55829..24974,y=-16897..54165,z=-121762..-28058
on x=-65152..-11147,y=22489..91432,z=-58782..1780
on x=-120100..-32970,y=-46592..27473,z=-11695..61039
on x=-18631..37533,y=-124565..-50804,z=-35667..28308
on x=-57817..18248,y=49321..117703,z=5745..55881
on x=14781..98692,y=-1341..70827,z=15753..70151
on x=-34419..55919,y=-19626..40991,z=39015..114138
on x=-60785..11593,y=-56135..2999,z=-95368..-26915
on x=-32178..58085,y=17647..101866,z=-91405..-8878
on x=-53655..12091,y=50097..105568,z=-75335..-4862
on x=-111166..-40997,y=-71714..2688,z=5609..50954
on x=-16602..70118,y=-98693..-44401,z=5197..76897
on x=16383..101554,y=4615..83635,z=-44907..18747
off x=-95822..-15171,y=-19987..48940,z=10804..104439
on x=-89813..-14614,y=16069..88491,z=-3297..45228
on x=41075..99376,y=-20427..49978,z=-52012..13762
on x=-21330..50085,y=-17944..62733,z=-112280..-30197
on x=-16478..35915,y=36008..118594,z=-7885..47086
off x=-98156..-27851,y=-49952..43171,z=-99005..-8456
off x=2032..69770,y=-71013..4824,z=7471..94418
on x=43670..120875,y=-42068..12382,z=-24787..38892
off x=37514..111226,y=-45862..25743,z=-16714..54663
off x=25699..97951,y=-30668..59918,z=-15349..69697
off x=-44271..17935,y=-9516..60759,z=49131..112598
on x=-61695..-5813,y=40978..94975,z=8655..80240
off x=-101086..-9439,y=-7088..67543,z=33935..83858
off x=18020..114017,y=-48931..32606,z=21474..89843
off x=-77139..10506,y=-89994..-18797,z=-80..59318
off x=8476..79288,y=-75520..11602,z=-96624..-24783
on x=-47488..-1262,y=24338..100707,z=16292..72967
off x=-84341..13987,y=2429..92914,z=-90671..-1318
off x=-37810..49457,y=-71013..-7894,z=-105357..-13188
off x=-27365..46395,y=31009..98017,z=15428..76570
off x=-70369..-16548,y=22648..78696,z=-1892..86821
on x=-53470..21291,y=-120233..-33476,z=-44150..38147
off x=-93533..-4276,y=-16170..68771,z=-104985..-24507
After running the above reboot steps, 2758514936282235 cubes are on. (Just for fun, 474140 of those are also in the initialization procedure region.)
Starting again with all cubes off, execute all reboot steps. Afterward, considering all cubes, how many cubes are on?
Your puzzle answer was 1206644425246111.
Both parts of this puzzle are complete! They provide two gold stars: **
At this point, all that is left is for you to admire your Advent calendar.
If you still want to see it, you can get your puzzle input.
References
Visible links
. https://adventofcode.com/
. https://adventofcode.com/2021/about
. https://adventofcode.com/2021/events
. https://adventofcode.com/2021/settings
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. Advent of Code Supporter
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. https://adventofcode.com/2021
. https://adventofcode.com/2021
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. https://adventofcode.com/2021/leaderboard
. https://adventofcode.com/2021/stats
. https://adventofcode.com/2021/sponsors
. https://adventofcode.com/2020/day/17
. https://en.wikipedia.org/wiki/Cuboid
. https://adventofcode.com/2021
. https://adventofcode.com/2021/day/22/input

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# Advent of Code
--- Day 23: Amphipod ---
A group of amphipods notice your fancy submarine and flag you down. "With such an impressive shell," one amphipod says, "surely you can help us with a question that has stumped our best scientists."
They go on to explain that a group of timid, stubborn amphipods live in a nearby burrow. Four types of amphipods live there: Amber (A), Bronze (B), Copper (C), and Desert (D). They live in a burrow that consists of a hallway and
four side rooms. The side rooms are initially full of amphipods, and the hallway is initially empty.
They give you a diagram of the situation (your puzzle input), including locations of each amphipod (A, B, C, or D, each of which is occupying an otherwise open space), walls (#), and open space (.).
For example:
#############
#...........#
###B#C#B#D###
#A#D#C#A#
#########
The amphipods would like a method to organize every amphipod into side rooms so that each side room contains one type of amphipod and the types are sorted A-D going left to right, like this:
#############
#...........#
###A#B#C#D###
#A#B#C#D#
#########
Amphipods can move up, down, left, or right so long as they are moving into an unoccupied open space. Each type of amphipod requires a different amount of energy to move one step: Amber amphipods require 1 energy per step, Bronze
amphipods require 10 energy, Copper amphipods require 100, and Desert ones require 1000. The amphipods would like you to find a way to organize the amphipods that requires the least total energy.
However, because they are timid and stubborn, the amphipods have some extra rules:
• Amphipods will never stop on the space immediately outside any room. They can move into that space so long as they immediately continue moving. (Specifically, this refers to the four open spaces in the hallway that are directly
above an amphipod starting position.)
• Amphipods will never move from the hallway into a room unless that room is their destination room and that room contains no amphipods which do not also have that room as their own destination. If an amphipod's starting room is
not its destination room, it can stay in that room until it leaves the room. (For example, an Amber amphipod will not move from the hallway into the right three rooms, and will only move into the leftmost room if that room is
empty or if it only contains other Amber amphipods.)
• Once an amphipod stops moving in the hallway, it will stay in that spot until it can move into a room. (That is, once any amphipod starts moving, any other amphipods currently in the hallway are locked in place and will not
move again until they can move fully into a room.)
In the above example, the amphipods can be organized using a minimum of 12521 energy. One way to do this is shown below.
Starting configuration:
#############
#...........#
###B#C#B#D###
#A#D#C#A#
#########
One Bronze amphipod moves into the hallway, taking 4 steps and using 40 energy:
#############
#...B.......#
###B#C#.#D###
#A#D#C#A#
#########
The only Copper amphipod not in its side room moves there, taking 4 steps and using 400 energy:
#############
#...B.......#
###B#.#C#D###
#A#D#C#A#
#########
A Desert amphipod moves out of the way, taking 3 steps and using 3000 energy, and then the Bronze amphipod takes its place, taking 3 steps and using 30 energy:
#############
#.....D.....#
###B#.#C#D###
#A#B#C#A#
#########
The leftmost Bronze amphipod moves to its room using 40 energy:
#############
#.....D.....#
###.#B#C#D###
#A#B#C#A#
#########
Both amphipods in the rightmost room move into the hallway, using 2003 energy in total:
#############
#.....D.D.A.#
###.#B#C#.###
#A#B#C#.#
#########
Both Desert amphipods move into the rightmost room using 7000 energy:
#############
#.........A.#
###.#B#C#D###
#A#B#C#D#
#########
Finally, the last Amber amphipod moves into its room, using 8 energy:
#############
#...........#
###A#B#C#D###
#A#B#C#D#
#########
What is the least energy required to organize the amphipods?
Your puzzle answer was 16300.
--- Part Two ---
As you prepare to give the amphipods your solution, you notice that the diagram they handed you was actually folded up. As you unfold it, you discover an extra part of the diagram.
Between the first and second lines of text that contain amphipod starting positions, insert the following lines:
#D#C#B#A#
#D#B#A#C#
So, the above example now becomes:
#############
#...........#
###B#C#B#D###
#D#C#B#A#
#D#B#A#C#
#A#D#C#A#
#########
The amphipods still want to be organized into rooms similar to before:
#############
#...........#
###A#B#C#D###
#A#B#C#D#
#A#B#C#D#
#A#B#C#D#
#########
In this updated example, the least energy required to organize these amphipods is 44169:
#############
#...........#
###B#C#B#D###
#D#C#B#A#
#D#B#A#C#
#A#D#C#A#
#########
#############
#..........D#
###B#C#B#.###
#D#C#B#A#
#D#B#A#C#
#A#D#C#A#
#########
#############
#A.........D#
###B#C#B#.###
#D#C#B#.#
#D#B#A#C#
#A#D#C#A#
#########
#############
#A........BD#
###B#C#.#.###
#D#C#B#.#
#D#B#A#C#
#A#D#C#A#
#########
#############
#A......B.BD#
###B#C#.#.###
#D#C#.#.#
#D#B#A#C#
#A#D#C#A#
#########
#############
#AA.....B.BD#
###B#C#.#.###
#D#C#.#.#
#D#B#.#C#
#A#D#C#A#
#########
#############
#AA.....B.BD#
###B#.#.#.###
#D#C#.#.#
#D#B#C#C#
#A#D#C#A#
#########
#############
#AA.....B.BD#
###B#.#.#.###
#D#.#C#.#
#D#B#C#C#
#A#D#C#A#
#########
#############
#AA...B.B.BD#
###B#.#.#.###
#D#.#C#.#
#D#.#C#C#
#A#D#C#A#
#########
#############
#AA.D.B.B.BD#
###B#.#.#.###
#D#.#C#.#
#D#.#C#C#
#A#.#C#A#
#########
#############
#AA.D...B.BD#
###B#.#.#.###
#D#.#C#.#
#D#.#C#C#
#A#B#C#A#
#########
#############
#AA.D.....BD#
###B#.#.#.###
#D#.#C#.#
#D#B#C#C#
#A#B#C#A#
#########
#############
#AA.D......D#
###B#.#.#.###
#D#B#C#.#
#D#B#C#C#
#A#B#C#A#
#########
#############
#AA.D......D#
###B#.#C#.###
#D#B#C#.#
#D#B#C#.#
#A#B#C#A#
#########
#############
#AA.D.....AD#
###B#.#C#.###
#D#B#C#.#
#D#B#C#.#
#A#B#C#.#
#########
#############
#AA.......AD#
###B#.#C#.###
#D#B#C#.#
#D#B#C#.#
#A#B#C#D#
#########
#############
#AA.......AD#
###.#B#C#.###
#D#B#C#.#
#D#B#C#.#
#A#B#C#D#
#########
#############
#AA.......AD#
###.#B#C#.###
#.#B#C#.#
#D#B#C#D#
#A#B#C#D#
#########
#############
#AA.D.....AD#
###.#B#C#.###
#.#B#C#.#
#.#B#C#D#
#A#B#C#D#
#########
#############
#A..D.....AD#
###.#B#C#.###
#.#B#C#.#
#A#B#C#D#
#A#B#C#D#
#########
#############
#...D.....AD#
###.#B#C#.###
#A#B#C#.#
#A#B#C#D#
#A#B#C#D#
#########
#############
#.........AD#
###.#B#C#.###
#A#B#C#D#
#A#B#C#D#
#A#B#C#D#
#########
#############
#..........D#
###A#B#C#.###
#A#B#C#D#
#A#B#C#D#
#A#B#C#D#
#########
#############
#...........#
###A#B#C#D###
#A#B#C#D#
#A#B#C#D#
#A#B#C#D#
#########
Using the initial configuration from the full diagram, what is the least energy required to organize the amphipods?
Your puzzle answer was 48676.
Both parts of this puzzle are complete! They provide two gold stars: **
At this point, all that is left is for you to admire your Advent calendar.
If you still want to see it, you can get your puzzle input.
References
Visible links
. https://adventofcode.com/
. https://adventofcode.com/2021/about
. https://adventofcode.com/2021/events
. https://adventofcode.com/2021/settings
. https://adventofcode.com/2021/auth/logout
. Advent of Code Supporter
https://adventofcode.com/2021/support
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. https://adventofcode.com/2021/leaderboard
. https://adventofcode.com/2021/stats
. https://adventofcode.com/2021/sponsors
. https://en.wikipedia.org/wiki/Amphipoda
. https://adventofcode.com/2021
. https://adventofcode.com/2021/day/23/input

109
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# Advent of Code
--- 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 69914999975369.
--- 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?
Your puzzle answer was 14911675311114.
Both parts of this puzzle are complete! They provide two gold stars: **
At this point, all that is left is for you to admire your Advent calendar.
If you still want to see it, you can get your puzzle input.
References
Visible links
. https://adventofcode.com/
. https://adventofcode.com/2021/about
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. https://adventofcode.com/2021/settings
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. Advent of Code Supporter
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. https://adventofcode.com/2021/leaderboard
. https://adventofcode.com/2021/stats
. https://adventofcode.com/2021/sponsors
. https://en.wikipedia.org/wiki/Magic_smoke
. https://en.wikipedia.org/wiki/Arithmetic_logic_unit
. https://en.wikipedia.org/wiki/Modulo_operation
. https://en.wikipedia.org/wiki/Japanese_raccoon_dog
. https://www.youtube.com/watch?v=RXJKdh1KZ0w
. https://adventofcode.com/2021
. https://adventofcode.com/2021/day/24/input

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# Advent of Code
--- 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?
Your puzzle answer was 458.
--- Part Two ---
Suddenly, the experimental antenna control console lights up:
Sleigh keys detected!
According to the console, the keys are directly under the submarine. You landed right on them! Using a robotic arm on the submarine, you move the sleigh keys into the airlock.
Now, you just need to get them to Santa in time to save Christmas! You check your clock - it is Christmas. There's no way you can get them back to the surface in time.
Just as you start to lose hope, you notice a button on the sleigh keys: remote start. You can start the sleigh from the bottom of the ocean! You just need some way to boost the signal from the keys so it actually reaches the
sleigh. Good thing the submarine has that experimental antenna! You'll definitely need 50 stars to boost it that far, though.
The experimental antenna control console lights up again:
Energy source detected.
Integrating energy source from device "sleigh keys"...done.
Installing device drivers...done.
Recalibrating experimental antenna...done.
Boost strength due to matching signal phase: 1 star
Only 49 stars to go.
If you like, you can [ [Remotely Start The Sleigh Again] ] .
Both parts of this puzzle are complete! They provide two gold stars: **
At this point, all that is left is for you to admire your Advent calendar.
If you still want to see it, you can get your puzzle input.
References
Visible links
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