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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

Ali Hasnain Baqri
Monday, April 15, 2002

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