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Edge Numbered Cube (Posted on 2008-03-19) Difficulty: 3 of 5
Can you assign twelve distinct positive integers, one to each edge of a cube, so that the sum of the three numbers assigned to the edges forming a vertex is always the same, and the total sum of the assigned numbers is minimized?

For referencing purposes, let the cube have vertices with coordinates: A(0,0,0), B(1,0,0), C(1,1,0), D(0,1,0), E(0,0,1), F(1,0,1), G(1,1,1), and H(0,1,1), so that the edges are: AB, BC, CD, DA, EF, FG, GH, HE, AE, BF, CG, and DH.

See The Solution Submitted by Dennis    
Rating: 4.5000 (2 votes)

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  Subject Author Date
Solutioncomputer solution (spoiler)Charlie2008-03-19 18:41:48
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