Painting A Cube

 

Solution

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Let the six faces be a, b, c, d, e and f. With face a opposite face b, there are six arrangements for the other four colors around the cube: cdef, cdfe, cedf, cefd, cfde and cfed. Likewise for face a opposite face c; face a opposite face d; face a opposite face e; face a opposite face f; all have six arrangements for the remaining four colors. Hence the total is 5 x 6 = 30 arrangements.

Posted: July 1, 2009
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