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The Painted Cube Riddle: Which Cubes Stay Unpainted?
A 4×4×4 cube is painted on all faces then cut into 64 equal unit cubes. How many unit cubes have no paint whatsoever?
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What is the answer to the painted cube riddle?
The answer is 8. Only the inner 2x2x2 core is hidden from every painted face, and 2 x 2 x 2 = 8 unit cubes with no paint.
Why do exactly 8 cubes have no paint?
Strip away the outer painted shell of the 4x4x4 cube and you are left with a 2x2x2 block in the center. None of its faces touch the outside, so all 8 of those cubes stay unpainted.
How many of the 64 cubes have paint on them?
56 cubes have at least one painted face (8 corners with 3 sides, 24 edges with 2 sides, 24 faces with 1 side), leaving 8 completely unpainted.