From dn1l+@andrew.cmu.edu Sun Aug 8 00:21:54 1993 Return-Path: Received: from andrew.cmu.edu by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA16550; Sun, 8 Aug 93 00:21:54 EDT Received: from localhost (postman@localhost) by andrew.cmu.edu (8.5/8.5) id AAA06744; Sun, 8 Aug 1993 00:21:45 -0400 Received: via switchmail; Sun, 8 Aug 1993 00:21:37 -0400 (EDT) Received: from dollar.mg.andrew.cmu.edu via qmail ID ; Sat, 7 Aug 1993 19:36:59 -0400 (EDT) Received: from dollar.mg.andrew.cmu.edu via qmail ID ; Sat, 7 Aug 1993 19:36:48 -0400 (EDT) Received: from mms.0.1.23.EzMail.2.0.CUILIB.3.45.SNAP.NOT.LINKED.dollar.mg.andrew.cmu.edu.pmax.ul4 via MS.5.6.dollar.mg.andrew.cmu.edu.pmax_ul4; Sat, 7 Aug 1993 19:36:39 -0400 (EDT) Message-Id: Date: Sat, 7 Aug 1993 19:36:39 -0400 (EDT) From: "Dale I. Newfield" To: cube-lovers@life.ai.mit.edu Subject: Re: Tangle (Was: Re: Square-1 Puzzle Party) Cc: In-Reply-To: <9308072132.AA01481@chaucer> Excerpts from mail: 7-Aug-93 Tangle (Was: Re: Square-1 P.. by weber@src.dec.com > I was thinking about the Rubik's Tangle, and what was puzzling me was > WHY there should be only one solution (apart from the obvious symmetries). > After all, all pieces are identical except for coloring, and a set consists > of all 24 possible coloring, and 1 duplicate, and this doesn't sound like > an artificial construction. Is there any mathematical reason for the > uniqueness of the solution? What possible "Tangle-like" puzzles have > unique solutions? The section I had (4) had 2 distinct solutions (apart from the exchange of the 2 identical pieces, and the 4 orientations). In fact, the box that the puzzle came in said it should have 2 solutions. -Dale