Question

A cube is painted yellow on two adjacent faces, blue on the two faces opposite to the yellow faces, and black on the remaining faces. It is then cut into 216 smaller cubes of equal size. How many cubes are painted on all faces?

• A. 36
• B. 25
• C. 20
• D. 0

Hint:

When dealing with cubes cut into smaller cubes, corner cubes and edge cubes will have painted faces, but only corner cubes will have multiple painted faces. However, no cube will have all faces painted.

Answer 1

The Correct Option is D

The cube is cut into \( 216 \) smaller cubes, which means it is divided into \( 6 \times 6 \times 6 \) smaller cubes. Since the cube is painted on 3 faces and is cut into smaller cubes, no smaller cube will have all its faces painted. A smaller cube at the center or any other position in the interior of the large cube will have only one or two faces painted, and corner cubes will have at most 3 faces painted. But none will have all 6 faces painted. Thus, the number of cubes painted on all faces is \( 0 \).