PUMaC 2024 · 组合（B 组） · 第 8 题

PUMaC 2024 — Combinatorics (Division B) — Problem 8

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 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. Name: Team: Write answers in table below: Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 2

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