From dn1l+@andrew.cmu.edu Tue Dec 14 11:29:57 1993 Return-Path: Received: from po4.andrew.cmu.edu by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA24359; Tue, 14 Dec 93 11:29:57 EST Received: from localhost (postman@localhost) by po4.andrew.cmu.edu (8.6.4/8.6.4) id LAA04307 for Cube-Lovers@ai.mit.edu; Tue, 14 Dec 1993 11:29:35 -0500 Received: via switchmail; Tue, 14 Dec 1993 11:29:21 -0500 (EST) Received: from loiosh.andrew.cmu.edu via qmail ID ; Tue, 14 Dec 1993 11:28:51 -0500 (EST) Received: from loiosh.andrew.cmu.edu via qmail ID ; Tue, 14 Dec 1993 11:28:42 -0500 (EST) Received: from mms.4.60.Nov..4.1993.10.47.44.sun4c.411.EzMail.2.0.CUILIB.3.45.SNAP.NOT.LINKED.loiosh.andrew.cmu.edu.sun4c.411 via MS.5.6.loiosh.andrew.cmu.edu.sun4c_411; Tue, 14 Dec 1993 11:28:41 -0500 (EST) Message-Id: Date: Tue, 14 Dec 1993 11:28:41 -0500 (EST) From: "Dale I. Newfield" To: Cube Lovers Subject: Re: Tangle Cc: In-Reply-To: Could you explain what your algorithm was? I have one of the puzzles, number 4, I believe, and spent a large amount of time trying to find a solution that was not trial and error. I could not. The algorithm that I used to have the computer solve it for me was to fill the 5x5 in the following manner, recursively, returning when no possible pieces fit. 1 2 4 7 11 / / / / / / / / 3 5 8 12 16 / / / / / / / / 6 9 13 17 20 / / / / / / / / 10 14 18 21 23 / / / / / / / / 15 19 22 24 25 (wrapping at the edges to keep incrementing properly) I did that because given any pieces diagonal from one another, there are at most two pieces that can fill the gap (line up with both correctly). (When the four colors are different, there are two tiles When there is a single repeated color, there is one tile When there are 2 pairs of colors there is no tile And in all these cases, if the tile(s) was already used, or didn't exist, that is the bottom of that branch of the search tree) Is this better or worse than the algorithm you used? Has anyone found a non-brute-force solution scheme? -Dale