Question

3 x 3 x 3 cube is painted and it is cut into 27 cubes how many small cubes will have paint on exactly two faces

Answer 1

12

Explanation:

See attached picture. We have a 3x3x3 cube. If we cut it into 27 cubes, we will end up with a rubik's cube like cube. Each of the small cubes will measure 1x1x1. So if we pay close attention to the cube, we will see that only the cubes on the edges will have two of its faces painted in two colors. We can think of the cube as having three layers. Each of the layers will have 4 edge cubes, so we will have in total:

3x4=12 cubes that will have only two of its faces with paint on them.