PUMaC 2025 · 组合（A 组） · 第 3 题

PUMaC 2025 — Combinatorics (Division A) — Problem 3

A stone is placed on a square of a 5 × 5 grid. Alice and Bob take turns moving the stone to an orthogonally adjacent square (i.e. up/down/left/right). Alice moves first. Once a square has been visited, it cannot be visited again (and they cannot visit the starting square again). A player loses if they cannot make a legal move. For how many starting squares does Alice have a winning strategy?

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