HOW MANY UNIT CUBES ARE PAINTED WITH ONLY 1 COLOR?

Question

the cube shown is composed of 27 unit cubes. the top and bottom faces of the cube are painted red, and the other faces are painted blue. how many unit cubes are painted with only 1 color.

Answer 1

Only one of the 27 cubes is unpainted. Of the 18 cubes on the top and bottom painted red, only 2 are in the middle and only painted red. Then, 27 - 1 - 18 = 8 faces are painted only blue; we can actually find them, the four in the middle of each vertical face and the four with middle height where two of the vertical faces meet.

Then, 8 + 2 = 10.