Computational Analysis of 3×N Chomp

Chomp is an impartial game on a grid. The 2×n case is solved, but 3×n has no closed form. For my senior capstone I looked for structure directly in the set of P-positions (losing positions).

Highlights

• Memoized recursive solver in Python over Young-diagram states, mapping boards up to n = 500.
• Proved by induction two infinite linear families of P-positions: (a+4, a+2, 2) and (a+11, a+7, 5).
• Gap Principle conjecture: if third-row length k admits an infinite linear family, k+1 cannot.
• Opening moves: data suggests the unique winning move from (n, n, n) is always to the second or third row, never both.