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+#+SETUPFILE: ~/.emacs.d/org-templates/level-3.org
+#+HTML_LINK_UP: ../../../writings/#aoc
+#+OPTIONS: toc:1
+#+EXPORT_FILE_NAME: index
+#+TITLE: Day 03 - Toboggan Trajectory
+
+* Puzzle
+- This puzzle is taken from: https://adventofcode.com/2020/day/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.
+
+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:
+#+BEGIN_SRC
+..##.......
+#...#...#..
+.#....#..#.
+..#.#...#.#
+.#...##..#.
+..#.##.....
+.#.#.#....#
+.#........#
+#.##...#...
+#...##....#
+.#..#...#.#
+#+END_SRC
+
+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:
+#+BEGIN_SRC
+..##.........##.........##.........##.........##.........##.......  --->
+#...#...#..#...#...#..#...#...#..#...#...#..#...#...#..#...#...#..
+.#....#..#..#....#..#..#....#..#..#....#..#..#....#..#..#....#..#.
+..#.#...#.#..#.#...#.#..#.#...#.#..#.#...#.#..#.#...#.#..#.#...#.#
+.#...##..#..#...##..#..#...##..#..#...##..#..#...##..#..#...##..#.
+..#.##.......#.##.......#.##.......#.##.......#.##.......#.##.....  --->
+.#.#.#....#.#.#.#....#.#.#.#....#.#.#.#....#.#.#.#....#.#.#.#....#
+.#........#.#........#.#........#.#........#.#........#.#........#
+#.##...#...#.##...#...#.##...#...#.##...#...#.##...#...#.##...#...
+#...##....##...##....##...##....##...##....##...##....##...##....#
+.#..#...#.#.#..#...#.#.#..#...#.#.#..#...#.#.#..#...#.#.#..#...#.#  --->
+#+END_SRC
+
+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:
+#+BEGIN_SRC
+..##.........##.........##.........##.........##.........##.......  --->
+#..O#...#..#...#...#..#...#...#..#...#...#..#...#...#..#...#...#..
+.#....X..#..#....#..#..#....#..#..#....#..#..#....#..#..#....#..#.
+..#.#...#O#..#.#...#.#..#.#...#.#..#.#...#.#..#.#...#.#..#.#...#.#
+.#...##..#..X...##..#..#...##..#..#...##..#..#...##..#..#...##..#.
+..#.##.......#.X#.......#.##.......#.##.......#.##.......#.##.....  --->
+.#.#.#....#.#.#.#.O..#.#.#.#....#.#.#.#....#.#.#.#....#.#.#.#....#
+.#........#.#........X.#........#.#........#.#........#.#........#
+#.##...#...#.##...#...#.X#...#...#.##...#...#.##...#...#.##...#...
+#...##....##...##....##...#X....##...##....##...##....##...##....#
+.#..#...#.#.#..#...#.#.#..#...X.#.#..#...#.#.#..#...#.#.#..#...#.#  --->
+#+END_SRC
+
+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?
+** Part 2
+Time to check the rest of the slopes - you need to minimize the
+probability of a sudden arboreal stop, after all.
+
+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:
+
+- Right 1, down 1.
+- Right 3, down 1. (This is the slope you already checked.)
+- Right 5, down 1.
+- Right 7, down 1.
+- Right 1, down 2.
+
+In the above example, these slopes would find 2, 7, 3, 4, and 2 tree(s)
+respectively; multiplied together, these produce the answer 336.
+
+What do you get if you multiply together the number of trees encountered
+on each of the listed slopes?
+* Solution
+=count-trees= is a subroutine that will count the number of trees we'll
+encounter, it needs =@input=, =$right=, =$down=.
+#+BEGIN_SRC raku
+sub count-trees (
+    @input,
+    Int $right,
+    Int $down
+) {
+    # Start at top left position.
+    my $x = 0;
+    my $y = 0;
+    my $trees = 0;
+
+    my $x-max = @input[0].elems - 1;
+    my $y-max = @input.elems - 1;
+
+    loop {
+        $trees++ if @input[$y][$x] eq '#';
+
+        $x += $right;
+        $y += $down;
+
+        # Cannot let $x become greater than $x-max because that'll produce
+        # error when we try to access @input with those positions. So, we
+        # wrap it around because the same map is repeated.
+        $x -= $x-max + 1 if $x > $x-max;
+
+        last if $y-max < $y;
+    }
+    return $trees;
+}
+#+END_SRC
+
+=$x-max= holds the last index of =@input= =x= coordinate & same for =$y-max=
+with =y= coordinate. The loop first checks if we've encountered a tree &
+increments =$trees= if true. Then =$x= & =$y= are incremented to new
+positions.
+
+Later we check if =$x= has become greater than =$-max=, if true then we just
+wrap =$x= around the map. The map is infinitely long in =x= axis, =$x-max + 1=
+is subtracted because that is the length of map in =x= axis after which it
+repeats infinitely. We stop when the we reach the bottom most corner of
+the map.
+
+For part 1 we simply pass (3, 1) for (=$right=, =$down=) values to
+subroutine =count-trees= & print the solution.
+#+BEGIN_SRC raku
+say "Part 1: ", count-trees(@input, 3, 1);
+#+END_SRC
+** Part 2
+For part 2 we calculate the number of trees for different sets of
+(=$right=, =$down=), multiply those numbers & print it.
+#+BEGIN_SRC raku
+my @trees = [{ right => 1, down => 1 },
+	     { right => 3, down => 1 },
+	     { right => 5, down => 1 },
+	     { right => 7, down => 1 },
+	     { right => 1, down => 2 },].map(
+    {count-trees(@input, $_<right>, $_<down>)}
+);
+say "Part 2: ", [*] @trees;
+#+END_SRC