From dn1l+@andrew.cmu.edu Wed Dec 15 13:17:11 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 AA26346; Wed, 15 Dec 93 13:17:11 EST Received: from localhost (postman@localhost) by po4.andrew.cmu.edu (8.6.4/8.6.4) id NAA04816; Wed, 15 Dec 1993 13:16:56 -0500 Received: via switchmail; Wed, 15 Dec 1993 13:16:53 -0500 (EST) Received: from loiosh.andrew.cmu.edu via qmail ID ; Wed, 15 Dec 1993 13:15:58 -0500 (EST) Received: from loiosh.andrew.cmu.edu via qmail ID ; Wed, 15 Dec 1993 13:15:46 -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; Wed, 15 Dec 1993 13:15:45 -0500 (EST) Message-Id: Date: Wed, 15 Dec 1993 13:15:45 -0500 (EST) From: "Dale I. Newfield" To: cube-lovers@ai.mit.edu Subject: Re: Description of Tangle, Part 2 Cc: don.woods@eng.sun.com, acw@riverside.scrc.symbolics.com In-Reply-To: <920425084746.2bc000e4@EQL.Caltech.Edu> Just to make sure everyone knows what we are talking about, here is a message from the archives: Excerpts from mail: 25-Apr-92 Description of Tangle, Part 2 by Chris Worrell@eql.caltec > Annotating Don.Woods diagram (which is in the correct orientation) > 2 3 > --------------------- > | @ # | > | @ # | > 1 |$$ @ # %%%%| 4 > | $ @ %#% | > | $ @ %% # | > | $ %@ # | > | $ %% @@# | > | %%% #@@ | > 4 |%%%% $ # @@@| 2 > | $ # | > | $ # | > --------------------- > 1 3 > > The duplicate piece in each tangle is: > 1 2 3 4 > Tangle 1 Blue Red Yellow Green > Tangle 2 Yellow Blue Green Red > Tangle 3 Green Yellow Blue Red > Tangle 4 Red Green Yellow Blue > > All 4 Tangles are the same puzzle, just colored differently. > Each has all 24 color permutations, plus a duplicate. I had kind of hoped that the connectivity on the different puzzles was different, instead of just the colors. (Actually, the sequence I sent before was slightly wrong--here is the one I actually used. Using Don's format) >Don used the sequence: Dale used: > > 1 3 5 7 9 1 2 6 10 15 > 2 4 6 8 10 3 4 7 11 16 > 11 12 13 14 15 5 8 12 17 20 > 16 17 18 19 20 9 13 18 21 23 > 21 22 23 24 25 14 19 22 24 25 But yes, Don's fillpattern still gets more constraints in earlier--here is the number of constraints at each step Don's: 0 1 1 2 1 2 1 2 1 2 1 2 2 2 2 1 2 2 2 2 1 2 2 2 2 Mine: 0 1 1 2 1 1 2 2 1 1 2 2 2 1 1 2 2 2 2 2 2 2 2 2 2 As you can see, I had my 1's clustered more toward the beginning, which is non-optimal. Assuming that there is only a change in color(and not in connectivity), as was posted by Chris in april of 92, I would think modifying code to attempt the 10x10 would be fairly simple...(seeing as my code went poof sometime last year, when a disk crashed(not that it was complicated))...wanna try? (Thanks for the pointers to the Apr 92 discussion) I agree with the concensus expressed in the archives that this puzzle is inherently "not that great" because no non-brute-force method has been found/seems to exist. -Dale