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Unformatted text preview: 8V = 2S , since summing the vertex numbers for each of the eight corners sums each of the edges twice. Similarly, 6F = 2S . The equations 4V = S = 3F give that S must be divisible by 12. Since S is at least 1 + 2 + . .. + 12 = 78 , the smallest possible value for S is 84, which is the sum of the integers given above. The rest involves a small amount of trial and error. Labeled Cube...
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 Spring '10
 AlbertoDelgado
 Combinatorics, Permutations, Addition, Summation, Prime number, Ray Kremer, unique smallest solution

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