|
1 | | -# days/day-03 |
2 | | -## --- Part 1 --- |
3 | | -## --- Part 2 --- |
| 1 | +# --- Day 3: Toboggan Trajectory --- |
| 2 | + |
| 3 | +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. |
| 4 | + |
| 5 | +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: |
| 6 | + |
| 7 | +``` |
| 8 | +..##....... |
| 9 | +#...#...#.. |
| 10 | +.#....#..#. |
| 11 | +..#.#...#.# |
| 12 | +.#...##..#. |
| 13 | +..#.##..... |
| 14 | +.#.#.#....# |
| 15 | +.#........# |
| 16 | +#.##...#... |
| 17 | +#...##....# |
| 18 | +.#..#...#.# |
| 19 | +``` |
| 20 | + |
| 21 | +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: |
| 22 | + |
| 23 | +``` |
| 24 | +..##.........##.........##.........##.........##.........##....... ---> |
| 25 | +#...#...#..#...#...#..#...#...#..#...#...#..#...#...#..#...#...#.. |
| 26 | +.#....#..#..#....#..#..#....#..#..#....#..#..#....#..#..#....#..#. |
| 27 | +..#.#...#.#..#.#...#.#..#.#...#.#..#.#...#.#..#.#...#.#..#.#...#.# |
| 28 | +.#...##..#..#...##..#..#...##..#..#...##..#..#...##..#..#...##..#. |
| 29 | +..#.##.......#.##.......#.##.......#.##.......#.##.......#.##..... ---> |
| 30 | +.#.#.#....#.#.#.#....#.#.#.#....#.#.#.#....#.#.#.#....#.#.#.#....# |
| 31 | +.#........#.#........#.#........#.#........#.#........#.#........# |
| 32 | +#.##...#...#.##...#...#.##...#...#.##...#...#.##...#...#.##...#... |
| 33 | +#...##....##...##....##...##....##...##....##...##....##...##....# |
| 34 | +.#..#...#.#.#..#...#.#.#..#...#.#.#..#...#.#.#..#...#.#.#..#...#.# ---> |
| 35 | +``` |
| 36 | + |
| 37 | +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). |
| 38 | + |
| 39 | +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: |
| 40 | + |
| 41 | +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. |
| 42 | + |
| 43 | +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: |
| 44 | + |
| 45 | +``` |
| 46 | +..##.........##.........##.........##.........##.........##....... ---> |
| 47 | +#..O#...#..#...#...#..#...#...#..#...#...#..#...#...#..#...#...#.. |
| 48 | +.#....X..#..#....#..#..#....#..#..#....#..#..#....#..#..#....#..#. |
| 49 | +..#.#...#O#..#.#...#.#..#.#...#.#..#.#...#.#..#.#...#.#..#.#...#.# |
| 50 | +.#...##..#..X...##..#..#...##..#..#...##..#..#...##..#..#...##..#. |
| 51 | +..#.##.......#.X#.......#.##.......#.##.......#.##.......#.##..... ---> |
| 52 | +.#.#.#....#.#.#.#.O..#.#.#.#....#.#.#.#....#.#.#.#....#.#.#.#....# |
| 53 | +.#........#.#........X.#........#.#........#.#........#.#........# |
| 54 | +#.##...#...#.##...#...#.X#...#...#.##...#...#.##...#...#.##...#... |
| 55 | +#...##....##...##....##...#X....##...##....##...##....##...##....# |
| 56 | +.#..#...#.#.#..#...#.#.#..#...X.#.#..#...#.#.#..#...#.#.#..#...#.# ---> |
| 57 | +``` |
| 58 | + |
| 59 | +In this example, traversing the map using this slope would cause you to encounter 7 trees. |
| 60 | + |
| 61 | +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? |
| 62 | + |
| 63 | +## --- Part Two --- |
| 64 | + |
| 65 | +Time to check the rest of the slopes - you need to minimize the probability of a sudden arboreal stop, after all. |
| 66 | + |
| 67 | +Determine the number of trees you would encounter if, for each of the following slopes, you start at the top-left corner and traverse the map all the way to the bottom: |
| 68 | + |
| 69 | +``` |
| 70 | + Right 1, down 1. |
| 71 | + Right 3, down 1. (This is the slope you already checked.) |
| 72 | + Right 5, down 1. |
| 73 | + Right 7, down 1. |
| 74 | + Right 1, down 2. |
| 75 | +``` |
| 76 | + |
| 77 | +In the above example, these slopes would find 2, 7, 3, 4, and 2 tree(s) respectively; multiplied together, these produce the answer 336. |
| 78 | + |
| 79 | +What do you get if you multiply together the number of trees encountered on each of the listed slopes? |
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