## Painting the faces of a cube

Considering the number of gray painted faces, we have:

Since 4 gray faces will have 2 white faces, it is equivalent to 2 gray faces. Similarly, 5 gray faces is equivalent to 1 gray face. And 6 gray faces are equivalent to no gray faces.

Number of different ways: | 1 | 1 | 2 | 2 | 2 | 1 | 1 |

Number of gray / white faces: | 0/6 | 1/5 | 2/4 | 3/3 | 4/2 | 5/1 | 6/0 |

So there are 1 + 1 + 2 + 2 + 2 + 1 + 1 = 10 ways to paint the cube with these two colors.

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