Twelve faces of different colors
Public  02/08/16  15xp  Math  27.3% 
Let there be N distinct colors. Let a_{n} = (a_{n1} + a_{n2}) % 9 with a_{1} = a_{2} = 1 Consider the ways to paint all the faces of dodecahedron using these N distinct colors. If selected, you can use up to a_{i}+2 but no less than 2 of i_{th} color where i = 1 to N. What is the total number of ways to paint a dodecahedron if N = 1000? Answer format: number Example: 652706 if N = 5 or 130992447 if N = 10 [My timing: 2s]
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