PUMaC 2025 · 个人决赛（B 组） · 第 1 题

PUMaC 2025 — Individual Finals (Division B) — Problem 1

In an atom of PUMaCium, there are 2 N energy levels that an electron can occupy, indexed { 1 , 2 , . . . , 2 N } . A given electron can only travel from a lower-indexed energy level to a higher- indexed one. Whenever it travels from i to j , it emits light of energy E . Supposing that ij all the E are distinct, show that the minimum number of electrons you need to use to get ij 2 every possible energy of light to be emitted is N . You are allowed to reuse an electron to get multiple light emissions, as long as it does not go from a higher-indexed energy level to a lower one. x y 2

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