Has anyone out there ever heard definitely that someone has found a
solution to the 10x10?

As I wrote before, I have embedded in my memory that there is an easy
argument that the 10x10 is *not* solvable. I do not know whether I
found it myself (and ever did mail it to other people) or whether I
found it somewhere on the net; it is a long time ago. When I find the
time I will do a check. (I know very sure that I have had a program
running at that time but that I abandoned the search because it would
be fruitless.)

Is it possible that the makers of Tangle (Matchbox,
using Rubik's name under license) merely claimed that such a solution
exists, without actually verifying it?

Yes, very probable. You should never trust the number of solutions the
manufacturers give. Sometimes it is much more, in this case it is less.
An actual example is a puzzle that consists of of nine rings (eh, this
is from memory, I do not have access to the puzzle at this time). Five
rings contain digits; three rings contain operators; one ring contains
equal signs. All in four positions around the rings. The idea is to
create correct sums (like 5 + 1 - 4 + 1 = 3) on all four positions of the
rings. The claim was that there was only a single solution. Actually
there are many. If there is interest I can hunt down the rings and
describe them in more detail. (An interesting detail is that my father
was the first to find the puzzle; he had correct solutions like:
1 + 3 : 2 + 1 = 3. He was a physicist. The accomanying leaflet did not
give details about operator priorities. Hence it actually makes two
puzzles; one with regards to priorities, the other just going left to
right.)

                                        (Seems pretty sleazy if so,
but then, having Tangles 2-4 be merely color permutations of #1 is
pretty weak in the first place.)

Indeed, the mass manufacturers are sleazy.

Cheers.

I will mail when I find back the argument disallowing 10x10.
--
dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924098
home: bovenover 215, 1025 jn amsterdam, nederland; e-mail: dik@cwi.nl