A wooden cube has each of its six faces painted either white or grey.
How many different cubes can be made?
Let us consider the number of grey faces painted.
4 grey faces will have 2 white faces and so is equivalent to 2 grey faces, similarly 5 grey faces is equivalent to 1 grey face and 6 grey faces is equivalent to no grey faces.
So there are 1 + 1 + 2 + 2 + 2 + 1 + 1 = 10 ways to paint a cube with two colours.
How many ways can you paint a cube with three colours?