PUMaC 2025 · 组合（A 组） · 第 5 题

PUMaC 2025 — Combinatorics (Division A) — Problem 5

Alice wants to send Bob the integer 120, represented as a binary string of length 7. However, her computer is being bombarded by cosmic rays, which can flip 00 to 11 and vice versa an arbitrary amount of times! Bob receives a possibly altered binary string, and writes down the integer in decimal. Find the sum of the possible numbers Bob could have written down (including 120 itself).

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