Visible small cubes in a 4x4x4 puzzle cube

Question

A $4\times4\times4$ puzzle cube is assembled from $64$ unit cubes, and coloured stickers cover the entire outside surface. How many of the unit cubes carry at least one sticker?

Short answer

56. A unit cube is hidden exactly when it is in the interior $2\times2\times2$ block, which contains $8$ cubes. All the others touch the surface, giving $64-8=56$ .

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Lessons behind this question

Counting and Combinatorics

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