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Paint the cube!

For first side we can choose colors in 6 ways. For second, 5, and so on. So we can paint the cube in 6! ways.

However, it has 8 corners. Any three colors, painted on three faces meeting in a corner, can be reproduced on any of these.

Also, around a corner, we can rotate the a color combo three times and rotate the cube back, to get the same view of the cube.

Hence the number of distinct cubes will be
6!/(8*3)

Ali Hasnain Baqri
Monday, April 15, 2002

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