Subject: Re: 10x10 Tangle
Incidentally, I would be interested in seeing your program. (And am
willing to send you mine.) I'm always willing to learn something about
how to make combinatorial searches more efficient.
Will be sent separately (and yes, I would like to see yours too!)
It's a shame, really. I'll bet that it would be possible to come up with
four Tangles that (a) really are different instead of being simple color
permutations of each other, (b) each have a unique solution (not counting
rotations) instead of two, and (c) can be combined to form a 10x10 that has
a unique solution. Well, strike the "unique" from (c) and I'd make the bet;
but with the "unique" I certainly wouldn't bet against it!
When you limit yourself to 4 ropes with 4 colours, you always get 24 pieces,
and when you want to build a puzzle of 25 pieces, you will have to duplicate
one, which causes (a).
Using 5 colours instead, creates a set of 120 pieces, from which you could
probably pick 25 pieces (without duplication) which would satisfy both (a)
and (b), and probably 4 such sets could be found to satisfy (c) as well,
but such a puzzle would be less attractive, because the choice of 25 from
120 is somewhat arbitrary, and a puzzler would probably be more inclined
to use all 120 pieces... Of course it is all a matter of taste.