CEMC Galois, 2007

Combinatorics Difficulty 3.0 AMC 10/12 Prove it Canada

Each face of a $5$ by $5$ by $5$ wooden cube is divided into $1$ by $1$ squares. Each square is painted black or white, as shown. Next, the cube is cut into $1$ by $1$ by $1$ cubes. How many of these cubes have at least two painted faces? Explain how you obtained your answer.

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