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MathNet 2026 — Part 10 Question 129

Math Olympiad Vault · MathNet 2026 — Part 10

Question 129

Art and Ben play a game while sharing an $m \times n$ chocolate bar. They take turns breaking the bar into two rectangular pieces along one of the lines and eating the smaller piece. (If the two pieces are equal, they can choose which piece to eat.) Whoever is left with the last $1 \times 1$ square of chocolate loses. If Art moves first, describe all pairs $(m, n)$ for which Ben has a winning strategy.