PUMaC 2025 · 组合（A 组） · 第 2 题

PUMaC 2025 — Combinatorics (Division A) — Problem 2

You find yourself standing at vertex A in the triangle grid shown below. Two monsters are standing at vertices B and C , respectively. Each minute, you move along an edge that takes you closer to BC , choosing an edge randomly out of the two possible edges. In the same way, the monster starting at B moves towards AC , and the monster starting at C moves towards AB . If you ever encounter a monster on a vertex not on BC , you die. Otherwise, if you reach BC without dying, you survive (even if you encounter a monster at some vertex on BC ). Compute the probability that you survive. A B C

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