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.

(In reply to computer solution by Charlie)

I had forgotten until posting that I had included a computer listing with my solution.

It stores all data to a text file (as well as displaying on screen). From there one needs a word processor.

One thing I noted from Charlie's listing is the relative ease in which he admitted only unique values per event against my awkward boolean IF statement.

Posted by brianjn on 2008-12-31 22:23:10