alleryAfter painting a 4x4x4 cube, it is sliced into 64 unit cubes. How many have no paint?
A24
B4
C16
D8
Answer & Solution
Correct answer: D. 8
1. Only cubes touching an outer face carry paint.
2. Removing the outer layer leaves a 2 x 2 x 2 block inside, since 4 - 2 = 2 along each direction.
3. So 2 x 2 x 2 = 8 cubes are unpainted.
4. The other 56 cubes touch at least one painted face.
_Source: Wikipedia, Cube (CC BY-SA 4.0), Cube_
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