PUMaC 2007 · 组合（A 组） · 第 6 题

PUMaC 2007 — Combinatorics (Division A) — Problem 6

Joe has 1729 randomly oriented and randomly arranged unit cubes, which are initially unpainted. He makes two cubes of sidelengths 9 and 10 or of sidelengths 1 and 12 (randomly chosen). These cubes are dipped into white paint. Then two more cubes of sidelengths 1 and 12 or 9 and 10 are formed from the same unit cubes, again randomly oriented and randomly arranged, and dipped into paint. Joe continues this process until every side of every unit cube is painted. After how many times of doing this is the expected number of painted faces closest to half of the total?

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