Create day13problem1.md

adventofcode2023/day13/day13problem1.md

@@ -0,0 +1,98 @@
+### --- Day 13: Point of Incidence ---
+
+With your help, the hot springs team locates an appropriate spring which
+launches you neatly and precisely up to the edge of **Lava Island**.
+
+There's just one problem: you don't see any **lava**.
+
+You **do** see a lot of ash and igneous rock; there are even what look like
+gray mountains scattered around. After a while, you make your way to a
+nearby cluster of mountains only to discover that the valley between them
+is completely full of large **mirrors**. Most of the mirrors seem to be aligned
+in a consistent way; perhaps you should head in that direction?
+
+As you move through the valley of mirrors, you find that several of them
+have fallen from the large metal frames keeping them in place. The mirrors
+are extremely flat and shiny, and many of the fallen mirrors have lodged
+into the ash at strange angles. Because the terrain is all one color, it's
+hard to tell where it's safe to walk or where you're about to run into a
+mirror.
+
+You note down the patterns of ash (`.`) and rocks (`#`) that you see as you
+walk (your puzzle input); perhaps by carefully analyzing these patterns,
+you can figure out where the mirrors are!
+
+For example:
+
+<pre>
+#.##..##.
+..#.##.#.
+##......#
+##......#
+..#.##.#.
+..##..##.
+#.#.##.#.
+
+#...##..#
+#....#..#
+..##..###
+#####.##.
+#####.##.
+..##..###
+#....#..#
+</pre>
+
+To find the reflection in each pattern, you need to find a perfect
+reflection across either a horizontal line between two rows or across a
+vertical line between two columns.
+
+In the first pattern, the reflection is across a vertical line between two
+columns; arrows on each of the two columns point at the line between the
+columns:
+
+<pre>
+123456789
+    ><   
+#.##..##.
+..#.##.#.
+##......#
+##......#
+..#.##.#.
+..##..##.
+#.#.##.#.
+    ><   
+123456789
+</pre>
+
+In this pattern, the line of reflection is the vertical line between
+columns 5 and 6. Because the vertical line is not perfectly in the middle
+of the pattern, part of the pattern (column 1) has nowhere to reflect onto
+and can be ignored; every other column has a reflected column within the
+pattern and must match exactly: column 2 matches column 9, column 3 matches
+8, 4 matches 7, and 5 matches 6.
+
+The second pattern reflects across a horizontal line instead:
+
+<pre>
+1 #...##..# 1
+2 #....#..# 2
+3 ..##..### 3
+4v#####.##.v4
+5^#####.##.^5
+6 ..##..### 6
+7 #....#..# 7
+</pre>
+
+This pattern reflects across the horizontal line between rows 4 and 5. Row
+1 would reflect with a hypothetical row 8, but since that's not in the
+pattern, row 1 doesn't need to match anything. The remaining rows match:
+row 2 matches row 7, row 3 matches row 6, and row 4 matches row 5.
+
+To **summarize** your pattern notes, add up **the number of columns** to the left
+of each vertical line of reflection; to that, also add **100 multiplied by
+the number of rows** above each horizontal line of reflection. In the above
+example, the first pattern's vertical line has `5` columns to its left and
+the second pattern's horizontal line has `4` rows above it, a total of **`405`**.
+
+Find the line of reflection in each of the patterns in your notes. **What
+number do you get after summarizing all of your notes?**