new puzzle challenge

[Claudio L.]

(04-04-2015 11:43 PM)Paul Dale Wrote:  Getting rid of reflections is easy by forcing the order of two adjacent edge middles. E.g. B>D. This would give an early pruning of the search space.

I think it eliminates some reflections but may not work all the time, because depending on your choice of variables you are using a different axis of symmetry.
For example, the 2 solutions with initial variable A=3 are:

Code:


A  B  C  D ...
3 19 16 12 10 13 15 14 9 11 18 17 | 2 4 8 6 1 7 5
3 17 18 11 9 14 15 13 10 12 16 19 | 1 6 8 4 2 7 5

These two solutions are clearly reflections, but B>D is true in both cases.
In this case, B>L would be perhaps a better choice since it is mirroring about the axis that passes through the initial value and the center of the hexagon.
But this would only eliminate a solution after we computed L, which means we already have the outer ring completely solved, so not much of a speedup in this algorithm. Also, it wouldn't eliminate the reflections of the rotated solutions, since the axis of symmetry is different. Perhaps if the algorithm tried to advance in both directions at once it would be much quicker to eliminate the reflections (but what a mess trying to find values with PICK for the equations!).

In any case, I'm inclined to leave those optimizations "as an exercise for the reader".