PUMaC 2024 · 组合（A 组） · 第 4 题

PUMaC 2024 — Combinatorics (Division A) — Problem 4

Michael and Steven are playing the card game War with a deck of 4 cards numbered 1 through
The deck is shuffled randomly and Michael gets a stack of 1 card and Steven gets a stack of 3 cards. In each round, the players reveal the top card from their stack, and the player whose card was higher collects both cards to the bottom of their stack in random order. A player wins when they get all four cards in their hand. The probability that Michael wins after m exactly 5 rounds is for coprime positive integers m and n . Find m + n . n

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