A solid cube is painted yellow, blue and black such that opposite faces are of same colour. The cube is then cut into 36 cubes of two different sizes such that 32 cubes are small and the other four cubes are big. None of the faces of the bigger cubes is painted blue. How many cubes have only one face painted?

Correct Answer: (C) 8

The original cube has volume $64$ (formed by 32 cubes of $1$$\times$ 1 $\times$ 1 and 4 big cubes of $2$$\times$ 2 $\times$ 2). Since opposite faces share colors and the big cubes have no blue face, the blue faces are entirely composed of small cubes. Counting the inner face-centered cubes on each colored face that have no other painted sides yields exactly 8 cubes with only one face painted.