From Don.Woods@eng.sun.com Mon Jan 3 05:45:40 1994 Return-Path: Received: from Sun.COM by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA23952; Mon, 3 Jan 94 05:45:40 EST Received: from Eng.Sun.COM (zigzag.Eng.Sun.COM) by Sun.COM (4.1/SMI-4.1) id AA10025; Mon, 3 Jan 94 02:45:24 PST Received: from colossal.Eng.Sun.COM by Eng.Sun.COM (4.1/SMI-4.1) id AA09005; Mon, 3 Jan 94 02:43:43 PST Received: by colossal.Eng.Sun.COM (5.0/SMI-SVR4) id AA14295; Mon, 3 Jan 94 02:45:35 PST Date: Mon, 3 Jan 94 02:45:35 PST From: Don.Woods@eng.sun.com (Don Woods) Message-Id: <9401031045.AA14295@colossal.Eng.Sun.COM> To: cube-lovers@ai.mit.edu, jandr@xirion.nl Subject: Re: 10x10 Tangle Content-Length: 1209 > 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.