PUMaC 2008 · 组合（A 组） · 第 7 题

PUMaC 2008 — Combinatorics (Division A) — Problem 7

(5 points) Joe makes two cubes of sidelengths 9 and 10 from 1729 randomly oriented and randomly arranged unit cubes, which are initially unpainted. These cubes are dipped into white paint. Then two cubes of sidelengths 1 and 12 are formed from the same unit cubes, again randomly oriented and randomly arranged, and these cubes are dipped into paint remover. Joe continues to alternately dip cubes of sides 9 and 10 into paint and cubes of sides 1 and 12 into paint remover ad nauseam. What is the limit of the expected number of painted unit cube faces immediately after dipping in paint remover? 1 Combinatorics A

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