Question

A solid cube is painted red on two adjacent faces and black on the faces opposite to those painted red. The remaining faces are painted green and the cube is then cut into 64 smaller cubes of equal size.

How many smaller cubes are painted red on one face and black on the other?

• A. 24
• B. 10
• C. 8
• D. 0
• E. None of these

Answer 1

Answer: (C)

8

The larger cube is cut into 64 smaller cubes. This implies that the edge of a smaller cube is one-fourth that of the larger cube. We know that the two adjacent faces are painted red and the two faces opposite to these faces are painted black. This implies that the top and the bottom faces are painted green. Thus, there are two edges where the faces painted red and black meet, and each edge has four cubes. Thus, there are totally 88 smaller cubes on each face. So, there are 32 smaller cubes which have at least one of their faces green. The remaining 64 - 32 = 32 smaller cubes have none of their faces green.