Inner Cube Unaffected

Probability Level 2

On a 3 × 3 × 3 3\times3\times3 cube, all but one 1 × 1 × 1 1\times1\times1 are visible.

How many 1 × 1 × 1 1\times1\times1 cubes are visible on the surface of a 10 × 10 × 10 10\times10\times10 cube?

Image Credit: Wikimedia Dhrm77 .


The answer is 488.

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David Pilling by David Pilling , 18, USA

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1 solution

David Pilling
May 18, 2016

The answer is 1 0 3 − 8 3 = 1000 − 512 = 488 10^3 - 8^3 = 1000 - 512 = \boxed{488}

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