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 Octo Vertices (Posted on 2008-12-30)
In the following octahedral net the vertices A, B, C, D, E and F, and are to be assigned distinctive values from 1 through 9.

M, N, O, P, Q, R, S and T are the values of the respective sums of the three vertices which form the respective surfaces to which each is assigned.

M + N = O + P = Q + R = S + T

Find unique sets of values1 for A, B, C, D, E and F such that the values of M through T (but not necessarily in that order) form series which increment by 2 of which there are 7.
```Background statistics:
Unique        Actual
M+N=   Interval     Sets2       Solutions
21       1           1            96
23       1           2            96
25       1           2            96
26       2           2            96
27       1           5           480
29       1           4           288
30       2           3           144
31       1           8           288
33       1           6           480
34       2           2            96
35       1           2            96
37       1           2            96
39       1           1            96
40          2448

Note:
1. For M+N=21,
1, 2, 3, 6, 4, 5
1, 2, 3, 6, 5, 4
and 1, 2, 5, 3, 4, 6
are the first 3 of 96 solutions.  The 96 values do not
discriminate amongst vertex rotation or reflections.
2. Each unique set configures the octahedron in more ways than one.
```

 See The Solution Submitted by brianjn No Rating

 Subject Author Date re: computer solution brianjn 2008-12-31 22:23:10 computer solution Charlie 2008-12-30 17:45:22 A wee start analytically rod hines 2008-12-30 17:41:36

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