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    OlympiadHardGeometry5–6

    A cube built from 2727 small identical cubes is painted on all its outer faces. How many of the small cubes end up with exactly two painted faces?

    Um cubo construído com 2727 cubinhos iguais é pintado em todas as faces exteriores. Quantos cubinhos ficam com exatamente duas faces pintadas?

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    Solution

    Step 1 of 3

    1. 1.The big cube is 33 by 33 by 33. Corner cubes have three painted faces, face-centre cubes have one, and the very middle cube has none.