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Problem 3 - Olympiad

A cube of side 3 cm is cut into smaller cubes of side 1 cm. How many such small cubes will have exactly two faces painted if the original cube is painted on all faces?

Correct: A

On each face of the cube, the cubes with exactly two faces painted lie on edges but not at corners. Since the original cube is 3 cm, each edge has 1 such cube. A cube has 12 edges. Total = 12 × 1 = 12.