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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