Place the numbers 1-9 in the boxes so that the difference of each pair of numbers joined by a line is at least three. The number 8 has already been placed.

(In reply to Computer solution: not just for 8 by Charlie)

Extending Charlie's list, there is also a solution for 9 in the upper left corner, viz.  9-2-7   3-5-8   6-1-4  (again, the 5 and 8 can be interchanged).

The topological similarites of the 8-2-5 and 1-4-7 triangles of the original solution are intriguing but do not lead to generation of other solutions since the 1 has other connections. I just generated loops for the nine variables -- took less than 0.03 seconds execution time, for each corner start seed.

 

Posted by ed bottemiller on 2010-08-04 15:01:55