PUMaC 2024 · 组合（A 组） · 第 6 题

PUMaC 2024 — Combinatorics (Division A) — Problem 6

Ezzie is walking around the perimeter of a regular hexagon. Each vertex of the hexagon has an instruction telling him to move clockwise or counterclockwise around the hexagon. However, when he leaves a vertex the instruction switches from clockwise to counterclockwise on that vertex, or vice versa. We say that a configuration C of Ezzie’s position and the instructions 1 on the vertices is irrepeatable if, when starting from configuration C , configuration C only appears finitely many more times. Find the number of irrepeatable configurations. 2 πi/ 20 19

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