PUMaC 2024 · 组合（A 组） · 第 8 题

PUMaC 2024 — Combinatorics (Division A) — Problem 8

Let the Sierpinski triangle graph S be defined as follows. S consists of three vertices and n 0 three edges in a triangle. S consists of 6 vertices and 9 edges. To make S , we take three 1 n +1 copies of S and merge vertices at the corners, where the bottom-left corner of the top copy n merges with the top corner of the bottom-left copy, etc. Then the number of cycles on S , 4 which visit each vertex exactly once and traverse each edge at most once, can be expressed as e e 1 2 p p for some primes p , p and positive integers e , e . Find p + p + e + e . 1 2 1 2 1 2 1 2 1 2 S S S S 0 1 2 3 Name: Team: Write answers in table below: Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 2

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