Paint it blue

Geometry Level 2

Each face of a $6 \times 6 \times 6$ cube is painted blue. This cube is then cut into $216$ unit cubes. How many of the unit cubes have no faces that are painted blue?

The answer is 64.

1 solution

A Former Brilliant Member
Jun 13, 2017

Removing the outer layer of faces of the $6 \times 6 \times 6$ cube leaves a $4 \times 4 \times 4$ inner cube. Each of the unit cubes in this inner $4 \times 4 \times 4$ cube has no sides painted. Thus, there are $4 \times 4 \times 4=$ $\boxed{64}$ cubes with no blue faces.

Paint it blue

The answer is 64.

1 solution

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