Given Data

1. A cube is painted on all six outer faces and divided into 5 x 5 x 5 equal cubes.

Question

How many small cubes have exactly two faces painted?

Answer

36.

Solution

1. Cubes with exactly two painted faces lie on edges, excluding corners.
2. Each of 12 edges contributes 5 - 2 = 3 such cubes.
3. 12 x 3 = 36.