From cube-lovers-errors@curry.epilogue.com Wed May 29 15:25:56 1996 Return-Path: cube-lovers-errors@curry.epilogue.com Received: from curry.epilogue.com (localhost [127.0.0.1]) by curry.epilogue.com (8.6.12/8.6.12) with SMTP id PAA02702 for ; Wed, 29 May 1996 15:25:56 -0400 Precedence: bulk Errors-To: cube-lovers-errors@curry.epilogue.com Date: Wed, 29 May 1996 10:56:15 +0100 Message-Id: <9605290956.AA05172@mecmdb.me.ic.ac.uk> X-Sender: ars2@mecmdb.me.ic.ac.uk Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" To: CUBE-LOVERS@ai.mit.edu From: "We Love Stress Analysis." Subject: Ultimate Rubik's Cube. (how to make a 4x4x4) X-Mailer: I was thinking about something similar to this a while back. I asked (as did many others) about 4x4x4s, but soon after I sent that E-mail I realised that I was holding one with a few extra pieces. If we can consider a 3x3x3 Rubik's cube as a 2x2x2 with mid-edges and centres, in effect we can reverse this and ignore the centres and mid-edges of a 3x3x3 thus making it into a 2x2x2. Anyone who wanted a 2x2x2 could just pull the stickers from the central columns and rows of a 3x3x3. As this makes those pieces indistinguishable, they are no longer part of the puzzle. the relationship between 4x4x4 and 3x3x3 is slightly harder, but the above is true for 4x4x4 and 2x2x2 (but if ANYONE tries that with a 4x4x4, I'll hit them!!!!!!!). A more common cube than the 4x4x4 is the 5x5x5 (which is still in production, c/o Uwe Meffret). This can be transformed from a 5x5x5 into a 4x4x4 by removing the central lines of stickers. It can also be transformed into a 3x3x3 (why anyone would want to.................) by removing columns & rows 2&4 from each side, and 2x2x2 (I won't bother saying it.........) by removing columns and rows 2,3,&4 from each side. Higher orders of cubes aren't in production, but apparently do exist in cyberspace, These would display similar properties. The pattern is simple: smaller cubes with odd number of pieces per side can be incorporated with other pieces to form larger cubes with odd number of pieces per side. etc. etc. etc. 2x2x2 + (extras) = 3x3x3 2x2x2 + (extras) = 4x4x4 3x3x3 + 4x4x4 + (extras) = 5x5x5 I'm sure there is some mathematical proof to what I am trying to say, but I'm no mathematician. It might start off: Pieces Jump(from last) used before: 2x2x2 8 8 0 3x3x3 26 18 8 4x4x4 56 30 8 5x5x5 98 42 74 6x6x6 152 54 ??? I would say that the ultimate Rubik cube was in fact the 2x2x2 because it features in all the solutions. However, based on this logic, the 8086 is the ultimate P.C. as any P.C. can run 8086 software, but an 8086 can't run 80386 software................ I hope this E-mail hasn't been too scatter brained................... Andy. Fact: did you know that British Airways has more Super-Sonic flying time than any air force in the world??