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Challenge Response 184


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:1122211
Number of gray / white faces:0/61/52/43/34/25/16/0

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

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