My program is a bit faster, but as I have less machines at my disposal
and I started a bit later, my programs are still running.

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.

I also tried adding some extra tiles for the 10x10, and it began finding
solutions okay.

Question: did you add pieces at random, or did you add more duplicate
pieces?

I just gave it 5 of each piece, instead of 4 of most pieces and 5 of some.
It churned out positions pretty quick that way! But since this involved
giving it more than 100 tiles to draw from, it says nothing about Dik Winter's
claimed impossibility proof.

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!

-- Don.