Question

A solid cube of 4 inches has been painted red, green and black on the pair of opposite faces. It has been cut into one inch cubes. How many cubes have only red and green faces?

Answer 1

Answer:

8 cubes have both red and green faces without black.

Step-by-step explanation:

Given a solid cube of 4 inches

Cube is painted with red, green and black on the pair of opposite faces.

4 inch cut has been cut into one inch cubes.

So, totally there are $4\times 4\times 4=64$ one inch cubes.

Each color is painted on a pair of sides. And on each side there will be 16 cubes.

Assume that the top and bottom faces are of black. so, removing them, we remain with 32 cubes with either red or green or both.

And only the corner cubes will have a face painted with two colors.

Therefore, the two faces of four corners have only red and green faces i.e., $2\times 4=8$ faces                                    

So, only the center cubes of 16 cubes, that means only 4 cubes have a single colored face.

Therefore, 8 cubes have only red and green faces.

And on each side, the cubes that have only one color are $4\times 2=8$

Therefore, 8 cubes have only red and 8 cubes have only green faces.