To: Don.Woods@eng.sun.com, cube-lovers@ai.mit.edu
Subject: RE: 10x10 Tangle

Hm. Well, I split up the 10x10 Tangle exhaustive search and ran it on
several machines over Christmas break, getting the 90 days of compute
time done in about 10.

And turned up no solutions.

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.
Up until now they did not produce a solution either. I am starting
to get worried.

There could of course be a bug in my program, but the same code with
minor changes finds the same solutions as others have found for the 5x5.

The same goes for me.

I did doublecheck that the 100 tiles matched the info
posted to Cube-Lovers re which tiles are duplicated in the four 5x5s;
I have no way of checking whether that info was correct.

I have the puzzles myself, and checked the info in the message from
Dale I Newfield (15 Dec 1993), which quotes the archives.
I can assure you: those are indeed the duplicate pieces.

Has anyone out there ever heard definitely that someone has found a
solution to the 10x10? 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? (Seems pretty sleazy if so,
but then, having Tangles 2-4 be merely color permutations of #1 is
pretty weak in the first place.)

I thought about that too, but considered that the choice for precisely
those four duplicate pieces could be dictated by the desire to have
a solution for the 10x10.

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?
In the latter case you may have found the duplications that should have
been made to get a solvable 10x10.
That in turn would show there could not exist an argument disallowing
10x10 (as claimed by Dik Winter), unless that argument is based on the
particular colouring of the four duplicated pieces...

-- Jan