PUMaC 2025 · 组合（A 组） · 第 6 题

PUMaC 2025 — Combinatorics (Division A) — Problem 6

Charles challenges David to a game of Fraction Fixer. In this game, David first picks two positive integers m ≤ n that sum to 2025. Next, Charles picks integers a and b at random, so a b that 0 ≤ a < m and 0 ≤ b < n , and computes + . If the sum is at least 1, David wins. m n Otherwise, Charles wins. If David chooses m and n optimally, what is the probability that David wins? 1

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