Question

How many smaller cubes have only one of their faces painted black?

• A. 1
• B. 2
• C. 3
• D. 4
• E. 5

Answer 1

The correct option is D 4

This problem can be analysed by considering the three horizontal layers, separately.
In the top layer, the central cube has only one of its faces painted green; the four cubes at the corner have three of their faces painted-one face green and the other two faces black. The remaining four cubes have two of their faces painted-one green and one black.
In the middle layer, the central cube has none of the faces painted. Four cubes at the corners have two of their faces painted black. The remaining four cubes have only one of their faces painted black.
In the bottom layer, the central cube has one of its faces painted green, and four cubes at the corners have three of their faces painted-two black and one green. The remaining four cubes have two of their faces painted-one black and one green.
Thus, the middle cube from each of the four sides which are painted black will have only one face painted black.