PUMaC 2024 · 组合（B 组） · 第 3 题

PUMaC 2024 — Combinatorics (Division B) — Problem 3

Consider the Sierpinski triangle iterations drawn below. S is a single triangle, and S 0 n +1 consists of three copies of S . Let a maximal line segment be line segment in the drawing of n S which cannot be extended any further while remaining in S . For example, S has three k k 0 maximal line segments and S has 6 maximal line segments. How many maximal line segments 1 are there in S ? 5 S S S S 0 1 2 3

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