Distinct Colorings of a Cube: How Many Are There?

Thread starter kingtaf
Start date Dec 1, 2010
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Cube

AI Thread Summary

The discussion centers on determining the number of distinct colorings of a cube when each face is painted a different color from a set of six fixed colors. Initially, one participant suggests that the answer is simply 6!, but another points out that this does not account for the rotational symmetries of the cube. The challenge lies in recognizing that many of the colorings will appear identical after the cube is rotated. This indicates that the actual number of distinct colorings is less than 720 (6!). The conversation encourages participants to think critically about the problem and find the solution considering these symmetries.

Dec 1, 2010

kingtaf

Check it out: 'Each of the faces of the cube are colored by a different of six fixed colors. How many of the colorings are distinct?'
I figured it would be 6!,very simple.
But no,there's a trick, can u figure it out!

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Dec 2, 2010

tiny-tim

Science Advisor

Homework Helper

hi kingtaf!

some of your 6! are the same after a rotation

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