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Platonic Colors (Posted on 2011-11-21) Difficulty: 3 of 5
I have a set of N identical Platonic (regular) solids, each painted with a different color on each face--the same set of colors for each of them. If I choose at random one face of each of the solids, the probability that all the chosen faces are of different colors is 2/3 the probability that there are three of one color and the rest all different colors.

How many of these solids do I have, and how many faces are on each?

See The Solution Submitted by Charlie    
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  Subject Author Date
SolutionFormula and solution. No derivation.Jer2011-11-21 16:13:44
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