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You are cordially invited to match wits with some of the best minds in IBM Research.
Seems some of us can't see a problem without wanting to take a crack at solving it. Does that sound like you? Good. Forge ahead and ponder this month's problem. We'll post a new one every month, and allow two to three weeks for you to submit solutions (we may even publish submitted answers, especially if they're correct). We won't reply individually to submitted solutions but every few days we will update a list of people who answered correctly. Towards the end of the month, we'll post the answer.
October 2007 Challenge:
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There are 5 platonic solids, the tetrahedron (4 vertices, 4 triangular faces, 6 edges), the cube (8 vertices, 6 square faces, 12 edges), the octahedron (6 vertices, 8 triangular faces, 12 edges), the dodecahedron (20 vertices, 12 pentagonal faces, 30 edges) and the icosahedron (12 vertices, 20 triangular faces, 30 edges). Consider open models of these solids with wire edges connecting the vertices. Suppose each wire has unit resistance. For each case find the total resistance between a pair of adjacent vertices. Express each answer as a rational number.
Hint: The answers can be found by brute force but there is a way to use symmetry.
I can't even begin to understand the problems, nevermind solve them.
