Day 13

There's no way I was going to end up solving this myself, so I found "Cramer's Rule" that solves a system of equations.

src/13.cs

@@ -0,0 +1,60 @@
+using aoc2024.Util;
+
+namespace aoc2024;
+
+internal class Day13 : Day
+{
+    private record machine(ivec2 ButtonA, ivec2 ButtonB, ivec2 Prize);
+
+    private readonly List<machine> machines = [];
+
+    internal override void Parse()
+    {
+        var lines = Util.Parsing.ReadAllLines($"{GetDay()}").ToList();
+        for (int i = 0; i < lines.Count; i += 4)
+        {
+            var btnA = lines[i + 0].Split('+');
+            var btnAX = int.Parse(btnA[1].Split(',')[0]);
+            var btnAY = int.Parse(btnA[2]);
+
+            var btnB = lines[i + 1].Split('+');
+            var btnBX = int.Parse(btnB[1].Split(',')[0]);
+            var btnBY = int.Parse(btnB[2]);
+
+            var prize = lines[i + 2].Split('=');
+            var prizeX = int.Parse(prize[1].Split(',')[0]);
+            var prizeY = int.Parse(prize[2]);
+
+            machines.Add(new machine(new ivec2(btnAX, btnAY), new ivec2(btnBX, btnBY), new ivec2(prizeX, prizeY)));
+        }
+    }
+
+    // "Cramer's Rule" implementation for solving a system of equations
+    private static long SolveMachine(machine m, long offset)
+    {
+        var prize = new ivec2(m.Prize.x + offset, m.Prize.y + offset);
+
+        var determinant = (m.ButtonA.x * m.ButtonB.y) - (m.ButtonA.y * m.ButtonB.x);
+        var a = ((prize.x * m.ButtonB.y) - (prize.y * m.ButtonB.x)) / determinant;
+        var b = ((m.ButtonA.x * prize.y) - (m.ButtonA.y * prize.x)) / determinant;
+
+        if (new ivec2((m.ButtonA.x * a) + (m.ButtonB.x * b), (m.ButtonA.y * a) + (m.ButtonB.y * b)) == prize)
+        {
+            return a * 3 + b;
+        }
+
+        return 0;
+    }
+
+    internal override string Part1()
+    {
+        long totalTokens = machines.Sum(m => SolveMachine(m, 0));
+        return $"Tokens necessary to win possible prizes: <+white>{totalTokens}";
+    }
+
+    internal override string Part2()
+    {
+        long totalTokens = machines.Sum(m => SolveMachine(m, 10000000000000));
+        return $"Tokens necessary to win inflated prizes: <+white>{totalTokens}";
+    }
+}