From cube-lovers-errors@mc.lcs.mit.edu Thu Mar 25 14:32:49 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id OAA08105 for ; Thu, 25 Mar 1999 14:32:49 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Sun, 21 Mar 1999 11:59:19 -0500 (EST) From: der Mouse Message-Id: <199903211659.LAA04577@Twig.Rodents.Montreal.QC.CA> To: cube-lovers@ai.mit.edu Subject: Re: Taking apart the 5^3 >>>> I found it more effective to turn a "thick slice" (ie, the outer >>>> two slices turned together) about 45 degrees, then pry with my >>>> thumb between the corner and wing of the turned slice.... > That procedure is not recommended as it voids the implied warranty (a) doesn't this depend on the manufacturer? (b) doesn't taking it apart at all do that anyway? > and has the danger of permanently stripping the thread inside the > center of the cube. I can't see how. Based on how I saw my cube move as I did this, I don't believe it's putting significant stress on any of the face-center cubies. Remember, what I said to do was to push the wing cubie away from the corner cubie, not vice versa; the only face cubie anywhere near the operation is the one you're prying towards, and the wing cubie is pivoting around that, not prying past it. > If you must take the cube apart do so by prying off one of the center > small squares and then loosening one of the screws, After disassembling my cube, I remembered this advice, and tried to get one of the face centers off. Even with the cube disassembled, I desisted for fear of breaking the plastic rather than the glue join. Perhaps there are multiple production runs in existence and some of them come apart more easily this way than others? der Mouse mouse@rodents.montreal.qc.ca 7D C8 61 52 5D E7 2D 39 4E F1 31 3E E8 B3 27 4B From cube-lovers-errors@mc.lcs.mit.edu Thu Mar 25 14:42:29 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id OAA08119 for ; Thu, 25 Mar 1999 14:42:29 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu From: "Dallas Foster" Reply-To: "Dallas Foster" To: Subject: Instructions needed Date: Thu, 25 Mar 1999 13:01:23 -0500 Message-Id: <01be76e9$7e7e0c40$03c3d4d1@dallasfo> I have a Rubik's Magic Strategy Game that consists of the playing board, 16 playpieces and instructions. Unfortunately we have lost the instructions and our son, who's game it is no longer lives at home and can't remember how it was played. Would you have or know where I might obtain a copy of these instructions. The game is of no use to us with out them. The game was distributed by Matchbox toys in 1987. Any help you can lend would be greatly appreciated. Thank You, Mrs. D.D. Foster 2734 W. Maple Street Anderson, IN 46013 USA fostindi@ecicnet.com From cube-lovers-errors@mc.lcs.mit.edu Thu Mar 25 19:29:58 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id TAA08877 for ; Thu, 25 Mar 1999 19:29:58 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Thu, 25 Mar 1999 21:59:53 +0000 From: David Singmaster To: jbryan@pstcc.cc.tn.us Cc: cube-lovers@ai.mit.edu Message-Id: <009D5A93.46B93D17.11@ice.sbu.ac.uk> Subject: RE: Re : RE: parity pairs If one really wants trouble with cube colors being indistinguishable try solving under a sodium vapor street lamp. I found this gave two colors: grey and greyer! DAVID SINGMASTER, Professor of Mathematics and Metagrobologist School of Computing, Information Systems and Mathematics Southbank University, London, SE1 0AA, UK. Tel: 0171-815 7411; fax: 0171-815 7499; email: zingmast or David.Singmaster @sbu.ac.uk From cube-lovers-errors@mc.lcs.mit.edu Fri Mar 26 15:39:42 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id PAA12037 for ; Fri, 26 Mar 1999 15:39:42 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Thu, 25 Mar 1999 23:58:38 -0500 (Eastern Standard Time) From: Dale Newfield Reply-To: DNewfield@cs.virginia.edu To: cube-lovers@ai.mit.edu Subject: RE: Re : RE: parity pairs In-Reply-To: <009D5A93.46B93D17.11@ice.sbu.ac.uk> Message-Id: On Thu, 25 Mar 1999, David Singmaster wrote: > If one really wants trouble with cube colors being indistinguishable > try solving under a sodium vapor street lamp. I found this gave two colors: > grey and greyer! Or corner Andrew Plotkin and get him to let you try out "The Liquid Crystal Cube" (http://www.eblong.com/~zarf/custom-cubes.html) -- Apparently quite a challenge. -Dale [Moderator's note: I was going to say "Mood cube", but of course zarf has already heard that one. Tastefully, he resists the nomenclature. --Dan ] From cube-lovers-errors@mc.lcs.mit.edu Fri Mar 26 18:20:51 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id SAA12501 for ; Fri, 26 Mar 1999 18:20:51 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <19990326231259.15935.qmail@hotmail.com> From: "Don Harper" To: Cube-Lovers@ai.mit.edu Subject: Subject: RE: Re : RE: parity pairs Date: Fri, 26 Mar 1999 15:12:58 PST I always had problems solving the cube in bars. I would always have a "friend" that would want to drag me into a bar and make money off of my cube solving skills, but the lighting was always low and I couldn't tell the colors apart. Along those lines, I have a brass cube. Easy to solve, or nearly impossible? It is heavy, even though I believe it is only "plated". I have a picture of it on my web site at: http://www.geocities.com/Colosseum/Sideline/2953/ I also have a "cubo 15" cube you all may find interesting. Thanks! Don Harper From cube-lovers-errors@mc.lcs.mit.edu Fri Mar 26 18:37:05 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id SAA12529 for ; Fri, 26 Mar 1999 18:37:05 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Fri, 26 Mar 1999 03:46:13 -0500 (EST) From: Nicholas Bodley To: David Singmaster Cc: jbryan@pstcc.cc.tn.us, cube-lovers@ai.mit.edu Subject: Colors under Na vapor lamps (Was: RE: Re : RE: parity pairs) In-Reply-To: <009D5A93.46B93D17.11@ice.sbu.ac.uk> Message-Id: On Thu, 25 Mar 1999, David Singmaster wrote: } If one really wants trouble with cube colors being indistinguishable }try solving under a sodium vapor street lamp. I found this gave two colors: }grey and greyer! Here in the northeastern US, high-pressure sodium (Na) vapor lamps are common; they have a much broader spectrum that the essentially monochromatic low-pressure lamps. The latter are rather strange! They're also more efficient, I'm fairly sure. I haven't looked at a cube under the h.p. lamps, though. |* Nicholas Bodley *|* Autodidact & Polymath * Electronic Tech. (ret.) |* Waltham, Mass. *|* ----------------------------------------------- |* nbodley@tiac.net *|* |* Amateur musician *|* From cube-lovers-errors@mc.lcs.mit.edu Mon Mar 29 12:46:44 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id MAA20106 for ; Mon, 29 Mar 1999 12:46:44 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu To: cube-lovers@ai.mit.edu From: whuang@ugcs.caltech.edu (Wei-Hwa Huang) Subject: Re: Instructions needed Date: 26 Mar 1999 23:51:28 GMT Organization: California Institute of Technology, Pasadena Message-Id: <7dh6i0$ekh@gap.cco.caltech.edu> References: "Dallas Foster" writes: >I have a Rubik's Magic Strategy Game that consists of the playing board, >16 playpieces and instructions. Unfortunately we have lost the >instructions and our son, who's game it is no longer lives at home and >can't remember how it was played. >Would you have or know where I might obtain a copy of these >instructions. The game is of no use to us with out them. The game was >distributed by Matchbox toys in 1987. The simplest thing you can do is to go to your local store and buy a copy of "Rubik's Eclipse". The rules are identical. I may have a copy of the original game lying around if this is unsucessful. -- Wei-Hwa Huang, whuang@ugcs.caltech.edu, http://www.ugcs.caltech.edu/~whuang/ --------------------------------------------------------------------------- This new video game can challenge feet (8,7) From cube-lovers-errors@mc.lcs.mit.edu Mon Mar 29 13:47:07 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id NAA20317 for ; Mon, 29 Mar 1999 13:47:06 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu From: WaVeReBeL@webtv.net Date: Fri, 26 Mar 1999 23:57:49 -0800 (PST) To: Cube-Lovers@ai.mit.edu Subject: Wrist pains Message-Id: <10861-36FC8F7D-5994@mailtod-121.bryant.webtv.net> Hi all, I've been having some marathon cubing sessions lately, and sometimes my wrists, fingers, or forearms would hurt. It's really hard to stop because I'm so addicted, but I have to because I'm scared I might get carpal tunnel syndrome or some sort of repetitive stress problem. I love computers, and since I'm studying computer science, and because I'll have many many hours on a keyboard ahead of me, this scares me even more. Does anyone else have have this problem? Any advice? Thanks. -Alex Montilla- [ Moderator's note: Dame Kathleen Ollerenshaw is mentioned in Singmaster's notes as being one of the first to develop cubist's thumb; Roger Frye also got a wrist sprain as he mentioned on this list in 1981. Repetitive stress injury is nothing to play with, and continuing only makes recovery take longer, so stop now! Switch to a simulator. Simulators I've seen are somewhat less convenient to use than a real cube (though I haven't seen the recent ones), but if that's the case I hope this motivates you to change that sorry state. -- Dan ] From cube-lovers-errors@mc.lcs.mit.edu Mon Mar 29 14:18:29 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id OAA20419 for ; Mon, 29 Mar 1999 14:18:29 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <36FEEE8F.CE5E8EBE@binghamton.edu> Date: Sun, 28 Mar 1999 22:07:59 -0500 From: Mirek Goljan Organization: SUNY Binghamton To: sausage@zeta.org.au Cc: cube-lovers@ai.mit.edu Subject: Speed cubing Hello, Wayne and other speed cubists, if you see about 15 year backwards you would realize that a few speed cubists have their average time below 20 sec and quite a lot of others below 25 sec. But you are interested in CURRENT Best Time and Average Time, I see. After a few weeks of practicing my times are: 18 sec, 24 sec, (not bad after some years of 'abstinence' :-)) My method is Jiri's. Beside that, I practice in solving the cube in minimum moves (face moves) for which I use slightly different method for first two layers: 2x2 subcube first, 2x2x3 next, 2x3x3 - two layers and for the last layer I may or may not use some more moves than Jiri's method uses. My average number of moves is about 48 within 2 min restriction. Mirek ******************************** Miroslav Goljan Watson School of Engineering and Applied Science, Dept. of EE State University of New York PO BOX 00238 Binghamton, NY 13902-6000 e-mail: bg22976@binghamton.edu ******************************** From cube-lovers-errors@mc.lcs.mit.edu Mon Mar 29 15:19:18 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id PAA20818 for ; Mon, 29 Mar 1999 15:19:18 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu To: cube-lovers@ai.mit.edu From: whuang@ugcs.caltech.edu (Wei-Hwa Huang) Subject: Re: Taking apart the 5^3 Date: 26 Mar 1999 23:43:35 GMT Organization: California Institute of Technology, Pasadena Message-Id: <7dh637$ea1@gap.cco.caltech.edu> References: der Mouse writes: >Perhaps there are multiple production runs in existence and some of >them come apart more easily this way than others? This is definitely true. Mine fell off after a few days -- I eventually glued them back on. -- Wei-Hwa Huang, whuang@ugcs.caltech.edu, http://www.ugcs.caltech.edu/~whuang/ --------------------------------------------------------------------------- This new video game can challenge feet (8,7) From cube-lovers-errors@mc.lcs.mit.edu Mon Mar 29 18:40:48 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id SAA21466 for ; Mon, 29 Mar 1999 18:40:47 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu From: wheeler@cipr.rpi.edu (Frederick W. Wheeler) Message-Id: <14080.1711.289304.134028@cipr.no_spam.rpi.edu> Date: Mon, 29 Mar 1999 18:03:11 -0500 (EST) To: Cube-Lovers@ai.mit.edu Subject: Inventing your own techniques I've been reading Cube-Lovers e-mail for a few months now and am enjoying it very much. It is one of the great benefits of the Internet that people with a common interest, but spread so far apart, can so easily communicate like this. For me, the most fun, and the ultimate challenge, in cubing comes from figuring out how to solve the puzzle in the first place. I avoid published and posted techniques. I'd really like to hear from people on this list on how you go about inventing new moves and techniques or how you feel about learning to solve a puzzle on your own. I vaguely remember how I learned to solve the 3x3x3 back in the early 80's. I was in 8th grade at the time; now I'm in 25th grade. According to my family I quite thoroughly infatuated by the puzzle at the time. Solving one side was faily easy and then I was able to get 2 and 3 sides, but with a disorganized and perhaps even random method. I heard from a friend (who had a solution book) that the key to solving the top and bottom was a set of special moves that allowed you to manipulate the bottom corner pieces without affecting the top side. I set out to find these moves on my own and did. I would carefully record the position and orientation of each corner piece, then move a top corner out of position and then back into position in a different way and check how the bottom side changed. This led to a few sequences which I could repeatedly apply to solve the bottom corners. The rest was fairly easy, except for the situation in which two edges were flipped. I had to have someone show me a move to get past this point. I couldn't figure it out. Otherwise, I had a 50% chance of solving on any given attempt. Now I have a 4x4x4 and a 5x5x5 cube as well. I've been able to solve these primarily using extensions of the techniques I learned for the 3x3x3 and a few new extras, but only to a point. I'm now stuck if one pair of "wing" pieces are switched. If two pairs are switched, I can solve it, but not if only one are switched. Again, I solve it 50% of the times I set out. Of course, there was at least on posted solution for this very problem to this list a couple of weeks ago. I saved it to a folder just in case I decide to resort to it, but in the mean time want to figure this out on my own. Regards, Fred Wheeler -- Fred Wheeler wheeler@cipr.rpi.edu www.cipr.rpi.edu/wheeler From cube-lovers-errors@mc.lcs.mit.edu Tue Mar 30 14:02:52 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id OAA24505 for ; Tue, 30 Mar 1999 14:02:51 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Reply-To: From: "Noel Dillabough" To: "Cube Lovers (E-mail)" Cc: Subject: RE: Wrist pains Date: Mon, 29 Mar 1999 23:42:38 -0500 Message-Id: <000001be7a68$23427d20$040a0a0a@laptop> In-Reply-To: <10861-36FC8F7D-5994@mailtod-121.bryant.webtv.net> [ Moderator's note: Dame Kathleen Ollerenshaw is mentioned in Singmaster's notes as being one of the first to develop cubist's thumb; Roger Frye also got a wrist sprain as he mentioned on this list in 1981. Repetitive stress injury is nothing to play with, and continuing only makes recovery take longer, so stop now! Switch to a simulator. Simulators I've seen are somewhat less convenient to use than a real cube (though I haven't seen the recent ones), but if that's the case I hope this motivates you to change that sorry state. -- Dan ] As a programmer, I am no stranger to repetitive stress related aches and pains. I even had cubist's thumb way back :) My simulator, puzzler, has mainly a mouse interface and this given enough time can cause you to be rather sore as well. I was wondering if anyone had an idea for a "hands on keyboard" approach that would allow you to naturally move the puzzles' slices. There is a macro interface for the cubes to enter moves in UDFBLR notation, but I am thinking of something that you could, with practice, manipulate a cube in realtime using a keyboard. Any ideas would be appreciated and I'll try my best to implement the best one. If simulators "felt" like a cube when you used them they would be more fun (and move without jamming etc) -Noel From cube-lovers-errors@mc.lcs.mit.edu Tue Mar 30 15:11:03 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id PAA24788 for ; Tue, 30 Mar 1999 15:11:03 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Tue, 30 Mar 1999 12:53:02 +0100 From: David Singmaster To: WaVeReBeL@webtv.net Cc: cube-lovers@ai.mit.edu Message-Id: <009D5E34.B59FB7EA.32@ice.sbu.ac.uk> Subject: RE: Wrist pains Beryl Fletcher, who organized my first cube at the International Congress of Mathematicians in Helsinki in 1978, also developed Cubist's Thumb. The early cubes were stiff and one held them with a corner pressing on the tendon of the left thumbb, in the fleshy part of the thumb. With olde people, the tendon sheath, or rather the inner lubricant, has become a bit aged and the constant pressure leads to a chronic inflammation. This is readily treated by a small operation which cuts open the tendon sheath. Both Dame Kathleen Ollerneshaw and Beryl Fletcher had this. When I was working on my Notes, I did a lot of checking of move sequences and typing and got definite pains in the wrist. Since then, word processing has also occasionally produced RSI problems. Fortunately, rest lets it go away, but I have had physiotherapy several times. There were several periods when I had to stop typing for several weeks! The most unusual diagnosis was stiff neck due to tension while typing. Physiotherapy helped that. All the warnings/instructions about RSI are worth heeding. Take breaks. Stretch regularly. Make sure your work station is comfortable. Etc. RSI is real and I've known several people semi-permanently disabled by it. DAVID SINGMASTER, Professor of Mathematics and Metagrobologist School of Computing, Information Systems and Mathematics Southbank University, London, SE1 0AA, UK. Tel: 0171-815 7411; fax: 0171-815 7499; email: zingmast or David.Singmaster @sbu.ac.uk From cube-lovers-errors@mc.lcs.mit.edu Tue Mar 30 16:55:26 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id QAA25175 for ; Tue, 30 Mar 1999 16:55:25 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu To: cube-lovers@ai.mit.edu From: whuang@ugcs.caltech.edu (Wei-Hwa Huang) Subject: Re: Inventing your own techniques Date: 30 Mar 1999 14:55:07 GMT Organization: California Institute of Technology, Pasadena Message-Id: <7dqokb$43e@gap.cco.caltech.edu> References: wheeler@cipr.rpi.edu (Frederick W. Wheeler) writes: >For me, the most fun, and the ultimate challenge, in cubing comes from >figuring out how to solve the puzzle in the first place. I avoid >published and posted techniques. I'd really like to hear from people >on this list on how you go about inventing new moves and techniques or >how you feel about learning to solve a puzzle on your own. After I understood conjugation well enough, I have never invented a move that I can in all honesty call "new" -- although they may appear "new" to others. The only new part is just applying it to different types of moves and seeing what the result is. -- Wei-Hwa Huang, whuang@ugcs.caltech.edu, http://www.ugcs.caltech.edu/~whuang/ --------------------------------------------------------------------------- She ran by screaming "No, I run by moving my feet rapidly, you idiot!" From cube-lovers-errors@mc.lcs.mit.edu Tue Mar 30 18:05:07 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id SAA25385 for ; Tue, 30 Mar 1999 18:05:07 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Tue, 30 Mar 1999 16:25:51 -0500 (EST) From: Nicholas Bodley To: Noel Dillabough Cc: "Cube Lovers (E-mail)" , WaVeReBeL@webtv.net Subject: RE: Wrist pains In-Reply-To: <000001be7a68$23427d20$040a0a0a@laptop> Message-Id: On Mon, 29 Mar 1999, Noel Dillabough wrote: }Any ideas would be appreciated and I'll try my best to implement the best }one. If simulators "felt" like a cube when you used them they would be more }fun (and move without jamming etc) Can you imagine force-feedback joystick technology? Hooray for the reset button! I very recently tried a demo at a computer store; pleasant surprise. |* Nicholas Bodley *|* Autodidact & Polymath * Electronic Tech. (ret.) |* Waltham, Mass. *|* |* nbodley@tiac.net *|* |* Amateur musician *|* -------------------------------------------------------------------------- From cube-lovers-errors@mc.lcs.mit.edu Tue Mar 30 19:30:45 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id TAA25856 for ; Tue, 30 Mar 1999 19:30:45 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <370168C9.9ECB5992@whitewolf.com.au> Date: Wed, 31 Mar 1999 10:14:01 +1000 From: Ryan Heise To: noel@mud.ca Cc: "Cube Lovers (E-mail)" , WaVeReBeL@webtv.net Subject: Keyboard cube [was: Re: Wrist pains] References: <000001be7a68$23427d20$040a0a0a@laptop> Noel Dillabough wrote: > As a programmer, I am no stranger to repetitive stress related aches and > pains. I even had cubist's thumb way back :) My simulator, puzzler, has > mainly a mouse interface and this given enough time can cause you to be > rather sore as well. I was wondering if anyone had an idea for a "hands on > keyboard" approach that would allow you to naturally move the puzzles' > slices. I had some ideas on this once. The first keyboard layout below is easier to learn but the second would be faster once you had mastered it. [QWERTY keyboard] 1) U = r U'= u D'= f D = j R = 7 R'= m L'= 4 L = v F = h F'= g B'= y B = t 2) Any mappings using this set of keys: er ui asdf jkl; The simulator input key should be configurable so you can try out these variations once its written. If you want help implementing it, feel free to ask me - just in case I ever have some free time on my hands! -- Ryan Heise http://www.progsoc.uts.edu.au/~rheise/ From cube-lovers-errors@mc.lcs.mit.edu Tue Mar 30 20:15:57 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id UAA25946 for ; Tue, 30 Mar 1999 20:15:56 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <199903302344.SAA11205@life.ai.mit.edu> From: Norman Richards To: "Cube Lovers (E-mail)" Subject: Keyboard cube [was: Re: Wrist pains] In-Reply-To: <000001be7a68$23427d20$040a0a0a@laptop> Date: Tue, 30 Mar 1999 17:47:33 -0600 > [...] I was wondering if anyone had an idea for a "hands on > keyboard" approach that would allow you to naturally move the puzzles' > slices. > > There is a macro interface for the cubes to enter moves in UDFBLR notation, > but I am thinking of something that you could, with practice, manipulate a > cube in realtime using a keyboard. Oddly enough, I have been thinking about a method to manipulate a cube by use of the numeric keypad. It seems most moves can be completed rather naturally, but I do not know if it works in practice. Anyways, take a keypad like this: 7 8 9 4 5 6 1 2 3 This corresponds to a face of a cube quite nicely. Suppose you wanted to rotate the right face clockwise. One could enter 36 or 69, for example, which you could conceptually think of as the direction your hand would move to rotate the right face clockwise. Counter clockwise would be the other direction. (96 or 63 or even 93) The same technique could be applied to the left face or top face or bottom face. The middle slices could be rotated just as easil: 52 would rotate the middle vertical slice down. The question is how to effect rotating the front and rear faces. For me, 19 and 91 seem natural for F and F' because they basically mimic the twisting motion. The rear is more troublesome, but perhaps for symetry 73 and 37 might be used? Anyways, that could take care the turns, Cube rotations could be as simple as a shift followed by a direction. shift-5-2 might rotate the cube along the X axis such that U is now F and F is now D, etc... I do not know if keypad entry is any more or less prone to these types of entry, but I think that the general mechanism might work. ___________________________________________________________________________ orb@cs.utexas.edu soli deo gloria From cube-lovers-errors@mc.lcs.mit.edu Wed Mar 31 12:38:08 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id MAA28949 for ; Wed, 31 Mar 1999 12:38:07 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <4.1.19990330184411.00932b80@mail.vt.edu> Date: Tue, 30 Mar 1999 18:52:17 -0500 To: Cube-Lovers@ai.mit.edu From: Kevin Young Subject: Future Rubiks Products Your Vote Counts! In-Reply-To: References: <000001be7a68$23427d20$040a0a0a@laptop> Hello- We talked in the past about Oddzon (Current distributor of Rubik's Products for Seven Towns - the holder of the Rubik's brand) and the version of the Rubik's Cube on the market. If you are tired of those stickers that fall apart and would like a well built cube...one that has a sprung indexing mechanism which would mean that a layer would gently "click" into place when aligned along with tiles instead of stickers, then it's time for you to place your vote and influence them. They are currently looking into making a "Deluxe" Rubik's Cube, but, need to see if the market will support such a product. Anyway, you can place your vote at the following link: http://www.rubiks.com/poll.html?q=6 Be sure to browse their web site while you are there. Check out their news link to find out more on the production of the "Deluxe" Rubik's Cube. Click on the following link to go directly to their web site: http://www.rubiks.com Happy Cubing! Kevin Young From cube-lovers-errors@mc.lcs.mit.edu Wed Mar 31 13:17:28 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id NAA29097 for ; Wed, 31 Mar 1999 13:17:28 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Wed, 31 Mar 1999 08:46:33 -0500 (Eastern Standard Time) From: Jerry Bryan Subject: Re : Keyboard cube [was: Re: Wrist pains] In-Reply-To: <199903302344.SAA11205@life.ai.mit.edu> To: Cube Lovers Message-Id: On Tue, 30 Mar 1999 17:47:33 -0600 Norman Richards wrote: > > > [...] I was wondering if anyone had an idea for a "hands on > > keyboard" approach that would allow you to naturally move the puzzles' > > slices. > > I fought with this issue back in about 1985 when I was originally working on the 2x2x2 and the corners of the 3x3x3. I created a data base for each, with a program which would allow you to manipulate the cube on the screen, and the program would always show you your exact distance from Start. Actually, the screen would show you two renderings of the cube -- one was the cube you were manipulating and the other was the representative of the same cube under reduction by symmetry. It was the representative that was looked up in the data base. I tried all kinds of input mappings, none of which were very satisfying. One obvious thing to try is U for Up, D for Down, etc., but on a QWERTY keyboard this is not very easy to deal with. Keyboards in 1985 only had a numeric pad, not the additional arrow and page up/down keys of modern keyboards. Within the numeric pad, I ended up using up arrow for U, down arrow for D, right arrow for R, and left arrow for L. That left the question of F and B. It *sounds* kind of dumb, but using the numeric pad + key for B and the numeric pad 0/INS key for F worked about as well as anything. With these mappings, I could manipulate the cube without looking at the keyboard and with very little movement of my hand. I used the shift keys for things like U' and U2. So left shift plus up arrow was U' and right shift plus up arrow was U2, etc. I read the shift keys directly from the keyboard hardware (this was early DOS, and you could do such things). I wouldn't necessarily recommend accessing the hardware so directly these days. However, I found that I almost never used the shift keys. Rather, I would tap the up arrow key quickly three times for U', and I would tap the up arrow key quickly two times for U2. I did not implement an interface for whole cube moves. Rather, to rotate the whole cube I would do something like RL' or R'L or UD' etc. Well, this works for the 2x2x2, but not for the corners of the 3x3x3. It's tricky to make the interface simple and intuitive, and also to make it functionally rich at the same time. ---------------------------------------- Jerry Bryan jbryan@pstcc.cc.tn.us Pellissippi State Technical Community College From cube-lovers-errors@mc.lcs.mit.edu Wed Mar 31 14:47:54 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id OAA29488 for ; Wed, 31 Mar 1999 14:47:54 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <4.1.19990331093309.0265e700@pop.ncsa.uiuc.edu> Date: Wed, 31 Mar 1999 09:48:07 -0600 To: cube-lovers@ai.mit.edu From: Tom Magliery Subject: Re: Keyboard cube [was: Re: Wrist pains] In-Reply-To: <199903302344.SAA11205@life.ai.mit.edu> References: <000001be7a68$23427d20$040a0a0a@laptop> i already sent this to noel directly, but since others are sending suggestions here i thought i'd toss in my thoughts about a keyboard cube interface... mag At 11:42 PM 3/29/99 -0500, Noel Dillabough unabashedly said: >There is a macro interface for the cubes to enter moves in UDFBLR notation, >but I am thinking of something that you could, with practice, manipulate a >cube in realtime using a keyboard. this is a wonderful user interface design challenge. i've thought about it before, because i have never been comfortable with any of the mouse-based interfaces for moving 3d objects around. i've never used one that seemed fully intuitive to me. i'd love to see an interface like this: * 5 faces of the cube visible at once (all except B), perhaps something like this (except square, and with the individual cubies showing of course): +------------------+ |\ /| | \ U / | | \ / | | +----------+ | | | | | | L | F | R | | | | | | | | | | +----------+ | | / \ | | / D \ | |/ \| +------------------+ * unshifted keys for turning each of the visible faces either CW or CCW, a total of 10 keys in all, and repeated on the left- and right-hand side of the keyboard. the following diagram shows the cube operations thus associated with various keys (though the diagram is laid out mostly like the keyboard, i've added space between the hands for clarity): w:L' e:U' r:U t:R y:L' u:U' i:U o:R s:F' f:F j:F' l:F x:L c:D' v:D b:R' n:L m:D' ,:D .:R' * shifted keys for turning the cube itself. again, available on both hands. 3 axes of rotation, two directions each ==> only 6 keys needed on each hand. but why not have even more duplication? for example, suppose (in real life) you want to roll the cube forward away from you. you might do it by either grabbing it from the R side or the L side. hence the same 10 keys as above, when shifted, work to turn the entire cube in the same direction as they turn the faces when unshifted. -- ///X Tom Magliery, Research Programmer 217-333-3198 .---o \\\ NCSA, 605 E. Springfield O- mag@ncsa.uiuc.edu `-O-. /// Champaign, IL 61820 http://sdg.ncsa.uiuc.edu/~mag/ o---' From cube-lovers-errors@mc.lcs.mit.edu Wed Mar 31 21:24:53 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id VAA00984 for ; Wed, 31 Mar 1999 21:24:53 -0500 (EST) Message-Id: <199904010224.VAA00984@mc.lcs.mit.edu> Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Tue, 30 Mar 1999 21:57:43 -0500 (EST) From: Nichael Cramer To: Norman Richards Cc: "Cube Lovers (E-mail)" Subject: Re: Keyboard cube [was: Re: Wrist pains] In-Reply-To: <199903302344.SAA11205@life.ai.mit.edu> Norman Richards wrote: > Oddly enough, I have been thinking about a method to manipulate a > cube by use of the numeric keypad. It seems most moves can be > completed rather naturally, but I do not know if it works in practice. > > Anyways, take a keypad like this: > > 7 8 9 > 4 5 6 > 1 2 3 > > This corresponds to a face of a cube quite nicely. Suppose you > wanted to rotate the right face clockwise. One could enter 36 or 69, > for example, which you could conceptually think of as the direction > your hand would move to rotate the right face clockwise. Counter > clockwise would be the other direction. (96 or 63 or even 93) The > same technique could be applied to the left face or top face or bottom > face. The middle slices could be rotated just as easil: 52 would rotate > the middle vertical slice down. Or a extension of your scheme might be to combine arrow keys with the keypad, in a two-handed approach. I.e. 6^ or 6v rather than 36 or 69; no order dependence this way. (Likewise, I find the arrow keys more mnemomic.) The model is that you're "grabbing" the specified cubie and rotating it in the specified direction. In its most natural form, this assumes that the numeric key-pad and the arrow keys are separate (as they are on my keyboard), although one could certainly use some other set of "directional" keys aside from the standard arrow keys. And as I say, this also assumes --most naturally, although not necessarily-- a two-handed approach. > The question is how to effect rotating the front and rear faces. > For me, 19 and 91 seem natural for F and F' because they basically > mimic the twisting motion. The rear is more troublesome, but perhaps > for symetry 73 and 37 might be used? For completeness, too, there is also the slice between the front and back face. Rather than muddy the paradigm, perhaps other (non-assigned) keys should be used. The handy "0" key might make a natural candidate for the front face. On the other hand since the back face and middle slice are rather "pathological" cases in this paradigm, might it perhaps make sense to use keys "outside" the model? For example "R" and "M". (Or, less mnemonically --and depending on the set-up of your keyboard-- "/" or "*" or ".", which on my keyboard are right beside the numeric keypad keys.) (For these last cases, perhaps on the <- and -> keys should by operational. The up and down arrows being less meaningful here.) > Anyways, that could take care the turns, Cube rotations could be as > simple as a shift followed by a direction. [...] This seems like a good scheme. N From cube-lovers-errors@mc.lcs.mit.edu Thu Apr 1 14:42:07 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id OAA03933 for ; Thu, 1 Apr 1999 14:42:07 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Thu, 1 Apr 1999 14:07:30 -0500 (EST) From: Nicholas Bodley To: Nichael Cramer Cc: Norman Richards , "Cube Lovers (E-mail)" Subject: Spaceball (tm) input to a Cube simulator In-Reply-To: <199904010224.VAA00984@mc.lcs.mit.edu> Message-Id: If anyone has a Spaceball, it should make quite a nice input device. It senses both torque about all 3 orthog. axes, and linear displacement forces ditto; a total of 6 channels. Displacement could select a layer, which could be highlighted (anyone for alpha-channel translucency?), and torque would rotate the selected layer. |* Nicholas Bodley *|* |* Waltham, Mass. *|* |* nbodley@tiac.net *|* |* Amateur musician *|* From cube-lovers-errors@mc.lcs.mit.edu Thu Apr 1 17:01:45 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id RAA05680 for ; Thu, 1 Apr 1999 17:01:45 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu From: Andrew John Walker Message-Id: <199904010348.NAA17158@wumpus.its.uow.edu.au> Subject: Mike Reid's Solver To: cube-lovers@ai.mit.edu Date: Thu, 1 Apr 1999 13:48:23 +1000 (EST) If anyone has compiled a PC version of Mike Reid's program set to find optimal solutions in the face turn metric please contact me (or better still the list). Andrew Walker From cube-lovers-errors@mc.lcs.mit.edu Fri Apr 2 03:11:29 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id DAA06917 for ; Fri, 2 Apr 1999 03:11:29 -0500 (EST) Message-Id: <199904020811.DAA06917@mc.lcs.mit.edu> Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Thu, 1 Apr 1999 15:56:33 -0500 (EST) From: Dale Newfield Reply-To: DNewfield@cs.Virginia.edu To: "Cube Lovers (E-mail)" Subject: Re: Spaceball (tm) input to a Cube simulator In-Reply-To: On Thu, 1 Apr 1999, Nicholas Bodley wrote: > If anyone has a Spaceball, it should make quite a nice input device. > It senses both torque about all 3 orthog. axes, and linear > displacement forces ditto; a total of 6 channels. Displacement could > select a layer, which could be highlighted (anyone for alpha-channel > translucency?), and torque would rotate the selected layer. Except that it is typically quite difficult to separately control translation and rotation with these devices. -Dale From cube-lovers-errors@mc.lcs.mit.edu Sun Apr 4 18:06:09 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id SAA15332 for ; Sun, 4 Apr 1999 18:06:09 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu To: cube-lovers@ai.mit.edu From: whuang@ugcs.caltech.edu (Wei-Hwa Huang) Subject: Keyboard cube [WAS Re: Wrist pains] Date: 3 Apr 1999 00:22:20 GMT Organization: California Institute of Technology, Pasadena Message-Id: <7e3mvs$q14@gap.cco.caltech.edu> References: "Noel Dillabough" writes: >Any ideas would be appreciated and I'll try my best to implement the best >one. If simulators "felt" like a cube when you used them they would be more >fun (and move without jamming etc) Immediately after reading this mail, my concept of a "keyboard interface" almost popped up immediately. It is similar to the 1-9 keypad interface mentioned already. [Assume that the person is using a standard American QWERTY keyboard; remap if necessary.] First, represent the front face by q w e a s d z x c A "move" is represented by any two ordered keystrokes. If the two keystrokes are in the same row, it represents a horizontal layer moving, else if they're in the same row, it represents a vertical layer moving. Example: "ed" = R' "cd" = R "sd" = slice move "we" = U' "qe" = U' "qw" = U' This method does not have moves for rotating the three front to back layers nor 180-degree moves. Extension A: Make a gap of a key represent a 180-degree move. So, "qe" is now U2 instead of just U'. Extension B: Represent front-to-back layers by the unused key combinations. This will necessarily be idiomatic (so I don't like it). For example, you could have "knight moves" represent F and B turns, and combinations with the "s" be slice moves. Extension C: Add another grid for the right side of the cube: r t y f g h v b n This solves the problem of the front-to-back layers nicely, and adds some redundancy. Most cube programs should display more than one face to the user anyway! Extension D: Use the arrow keys to rotate the entire cube. This can be done by the right hand while the left hand is just turning faces, which is similar to how a lot of people solve the cube anyway. This also alleviates the problem of the front-to-back layers. I would implement all extensions, but leave A and B as "optional" for the user to turn off as desired. -- Wei-Hwa Huang, whuang@ugcs.caltech.edu, http://www.ugcs.caltech.edu/~whuang/ --------------------------------------------------------------------------- She ran by screaming "No, I run by moving my feet rapidly, you idiot!" From cube-lovers-errors@mc.lcs.mit.edu Mon Apr 5 14:06:24 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id OAA17906 for ; Mon, 5 Apr 1999 14:06:24 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <3706F677.EDD8C59E@okanagan.net> Date: Sat, 03 Apr 1999 21:19:54 -0800 From: karen loewen Reply-To: loewens@okanagan.net To: cube-Lovers@ai.mit.edu Subject: square-1 and megeminx Is there a world record for the the 4x4x4 and the 5x5x5 rubiks cubes? If so what is it? I was wondering what in your opinion is the hardest rubiks like cube available right now. On a web page several people from rated the greatest to least in difficulty: 1)square-1 2)megaminx 3)5x5x5 4)4x4x4 5)? 6)? Anyway it went something like that. Would you agree? I learnt how to do square-1 all by myself. Would you consider Square-1 one of the hardest cubes to do? If so would this be considered good of me to learn? Although I only tried about 4 times my record when it was in a cube is 2 minutes. Do you know of a world record for Square-1 or any good websites? Do you know what an average would be for the best time? (perhaps 90 seconds for those really into it?) I was wondering how this compares to others times and acomplishments. At http://byrden.com/puzzles/ I almost figured out the megaminx. I got everything except the last row. Is the Megaminx one of the hardest Rubiks like puzzles available? After I get bored of my 5x5x5 that I orderd thinking about buying the megaminx. Do you know of a world record on the megaminx? What would be a average time (perhaps 3-4 minutes?) If you are not sure of answers thats fine. Then do you know of any good websites I can go to? Thank you very much. From cube-lovers-errors@mc.lcs.mit.edu Mon Apr 5 14:57:39 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id OAA18074 for ; Mon, 5 Apr 1999 14:57:38 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <3707EF11.3F51A90@t-online.de> Date: Mon, 05 Apr 1999 01:00:33 +0200 Reply-To: Rainer.adS.BERA_GmbH@t-online.de Organization: BERA Softwaretechnik GmbH To: Andrew John Walker Cc: cube-lovers@ai.mit.edu Subject: Re: Mike Reid's Solver References: <199904010348.NAA17158@wumpus.its.uow.edu.au> From: Rainer.adS.BERA_GmbH@t-online.de (Rainer aus dem Spring) I have-the version that requires 80MB, NOT the version that requires 800MB :) Rainer adS Andrew John Walker wrote: > > If anyone has compiled a PC version of Mike Reid's program > set to find optimal solutions in the face turn metric please > contact me (or better still the list). > > Andrew Walker -- -------------------------------------------------------------------------- Rainer aus dem Spring email Rainer.adS.BERA_GmbH@t-online.de (home) Schimmelbuschstr. 10 email TEEADS@TEE.toshiba.de (business only) 40699 Erkrath tel. +49 (0)02104 35157 (private) Germany tel. +49 (0)02104 936150 (business) --------------------------------------------------------------------------- From cube-lovers-errors@mc.lcs.mit.edu Mon Apr 5 21:30:54 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id VAA18890 for ; Mon, 5 Apr 1999 21:30:53 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <3707EE0F.73ED160F@ibm.net> Date: Sun, 04 Apr 1999 15:56:15 -0700 From: "Jin 'Time Traveler' Kim" Reply-To: chrono@ibm.net To: cube-lovers@ai.mit.edu Subject: Re: Spaceball (tm) input to a Cube simulator References: If anybody wants a SpaceOrb 360 (for experimentation please, I generally don't just give away stuff out of the kindness of my heart, although that's not unknown either) just drop me an email with a mailing address. I still have the box around here somewhere, just don't remember where. If I dig around long enough I know I can find the instructions too. I don't have it in front of me, but I'm sure it's just a serial device like a mouse. Nicholas Bodley wrote: > > If anyone has a Spaceball, it should make quite a nice input device. > It senses both torque about all 3 orthog. axes, and linear > displacement forces ditto; a total of 6 channels. Displacement could > select a layer, which could be highlighted (anyone for alpha-channel > translucency?), and torque would rotate the selected layer. -- Jin "Time Traveler" Kim chrono@ibm.net http://www.chrono.org '95 PGT - SCPOC From cube-lovers-errors@mc.lcs.mit.edu Mon Apr 5 22:59:11 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id WAA19027 for ; Mon, 5 Apr 1999 22:59:10 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Reply-To: From: "John Burkhardt" To: "Cube-Lovers (E-mail)" Subject: Different versions of the Ideal cube Date: Mon, 5 Apr 1999 08:23:22 -0400 Message-Id: <000e01be7f5f$19623600$3cca8018@octopod.ne.mediaone.net> Recently I've acquired a couple of older cubes from ebay. One was sold as "the original rubik's cube" by Ideal. When I opened it up I noticed that the quality was not the same as my original cube that I bought in 1980 or so. The stickers were not as bright for one thing. On my "original" cube the orange stickers are almost fluorescent, whereas on this version the color is dull, and its not a faded version of the original color. Its clearly a different shade of orange. The yellow and green colors are not as bright. And then there is the center white sticker. On some older Ideal cubes there is a logo on it, on this one I just got the logo was a separate decal. On my 1980's cube there is no logo at all. Next we come to differences in the actual pieces. On some Ideal cubes the cubies are solid, well, probably hollow in the center, but there is no openining. But on others there is an opening. Does anyone know anything about the history of the Ideal cube? Were there different runs of production? Did they start "cutting corners" to lower cost? Is there any way to tell from the packaging, which cube is the version that has the nice bright colors? Sorry if this has been discussed in the past, I'm relatively new to this list... [ Moderator: The archives have quite a bit about various types of cubes. Are you sure the open-corner cubes were from Ideal? I thought those were the pirated knockoffs. ] -JRB From cube-lovers-errors@mc.lcs.mit.edu Tue Apr 6 14:31:56 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id OAA21857 for ; Tue, 6 Apr 1999 14:31:55 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu From: wheeler@cipr.rpi.edu (Frederick W. Wheeler) Message-Id: <14088.45800.718995.311244@cipr.no_spam.rpi.edu> Date: Mon, 5 Apr 1999 08:56:08 -0400 (EDT) To: Cube-Lovers@ai.mit.edu Subject: Re: Inventing your own techniques In-Reply-To: <14080.1711.289304.134028@cipr.no_spam.rpi.edu> References: <14080.1711.289304.134028@cipr.no_spam.rpi.edu> Dear Cube-Lovers list: I received several very interesting replies to my e-mail last week regarding inventing techniques to solving cube puzzles. Here are some excerpts of note that were e-mailed to me but not the list. First, part of what I wrote ... Fred Wheeler writes: > For me, the most fun, and the ultimate challenge, in cubing comes > from figuring out how to solve the puzzle in the first place. I'd > really like to hear from people on this list on how you go about > inventing new moves and techniques or how you feel about learning to > solve a puzzle on your own. Wei-Hwa Huang sent me this teaser about conjugation. whuang@ugcs.caltech.edu (Wei-Hwa Huang) wrote: > After I understood conjugation well enough, I have never invented a > move that I can in all honesty call "new" -- although they may > appear "new" to others. The only new part is just applying it to > different types of moves and seeing what the result is. Later, at my request, Wei-Hwa Huang was kind enough to elaborate on conjugation. whuang@ugcs.caltech.edu (Wei-Hwa Huang) wrote: > I keep on meaning to write a more detailed explanation but can never > seem to find the time. > > Essentially, by conjugation I mean taking two routines (call 'em A > and B), consider their reverses (a and b), and juxtapose them (do > the move ABab). When A and B have a small intersection the results > of the conjugation is a simple permutation. And pretty much more > cube puzzles can be solved if you have the simplest permutations. > > Eg, to rotate two corner pieces, let > A = R'DRFDF' (rotate one corner in the top face without affecting > the rest of the top face) > B = U (rotate the top face) > > As A and B have a small intersection (one corner cubie), the move > ABA'B' is quite useful. > > Note that A is itself a move arrived at by conjugation. Tom Magliery also has a system for discovering solution techniques. Tom Magliery wrote: > rather than telling you my actual operation for fixing the "switched wings" > problem on the 4x and 5x cubes, i'll tell you how i discovered it: one of > the things i experiment with is repeated applications of short(ish) > sequences of moves. for example, i'll just take a particular 2 or 3-move > sequence, and apply it over and over again until the cube arrives back at a > state very similar to (but hopefully slightly different than) where it was > when i started. i was doing this (starting from a solved cube) one day > when i discovered with much jubilation that i had arrived at a state with > one switched wing pair. (there was also another slight jumble, but i > already knew an independent move to fix that by itself.) I also received a good suggestion that discovering new sequences may be easier on a computer simulator. This, way the cube can be reset to the solved state quickly before each new attempt to make it easier to see what the trial sequence actually changes. Unfortunately, I lost this particular e-mail and forget who sent it, so I cannot attribute it. My apologies to the author. Regards, Fred Wheeler -- Fred Wheeler wheeler@cipr.rpi.edu www.cipr.rpi.edu/wheeler From cube-lovers-errors@mc.lcs.mit.edu Wed Apr 7 16:04:40 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id QAA26207 for ; Wed, 7 Apr 1999 16:04:40 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <003001be7fad$445a7040$53c4b0c2@home> From: roger.broadie@iclweb.com (Roger Broadie) To: "Cube Lovers (E-mail)" Subject: Re: Keyboard cube [was: Re: Wrist pains] Date: Mon, 5 Apr 1999 21:57:13 +0100 For anyone who is interested in trying out a simulator that can be operated in an instant-response keyboard mode, I have christened my web-pages by uploading a copy of my cube simulator. In this mode, the function keys do face, centre-slice and whole-cube turns for the 3x3x3, and alphabetic keys can also be used for the same purpose. L, U, F and R are assigned to F5 to F8, so it's reasonably easy to work up a rhythm. Squares and inverses are done with Shift and Control, though as Jerry Bryan pointed out repeated jabbing is at least as easy. These keys also work for 4x4x4 and 5x5x5 cubes, with the alphabetic keys b f u d l r used for the off-centre slices. I mainly wrote the simulator to show me the effects of turns in Singmaster notation and common variants such as are found in cube-lovers. It's in Qbasic, which is the limit of my knowledge, and is a lot less sophisticated in appearance than the simulators available on the web - no mouse operations and no nice visible turning of the layers while you watch for instance, and distinctly rudimentary interactions with external files - so I am not offering it to the world in general, but it does have some features I haven't seen elsewhere that may appeal to Cube-lovers readers. Among them are that it can be set to show the effect of the turns on the centre pieces: it shows their orientation as little clock-hands that point to 12 o'clock in their home positions. The orientation of each piece's pointer then allows its identity to be deduced. I don't really feel I've understood the effects of a sequence unless I can see what it does to the centres. Also (this is a party trick, really) it can be set to work as a cube with any number of pieces per edge from two to 15, using an extension of normal Singmaster notation - no keyboard mode for these cubes. The program can be downloaded from home.iclweb.com/icl1/roger.broadie I won't necessarily keep it there all that long. Roger Broadie From cube-lovers-errors@mc.lcs.mit.edu Wed Apr 7 16:33:55 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id QAA26292 for ; Wed, 7 Apr 1999 16:33:55 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Reply-To: From: "John Burkhardt" To: "'Cube-Lovers (E-mail)'" Subject: RE: Different versions of the Ideal cube Date: Tue, 6 Apr 1999 06:29:31 -0400 Message-Id: <001001be8018$5c165350$3cca8018@octopod.ne.mediaone.net> > [ Moderator: The archives have quite a bit about various types of > cubes. Are you sure the open-corner cubes were from Ideal? I > thought those were the pirated knockoffs. ] > Yes, I'm sure the open corner cubes I have are Ideal. Unless the pirates put them in Ideal boxes. I own three Ideal cubes. I also have a siamese cube, which looks like it started life as regular Ideal cubes and those corners are closed. And the new OddzOn cubes are solid too. -JRB From cube-lovers-errors@mc.lcs.mit.edu Wed Apr 7 17:25:37 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id RAA26422 for ; Wed, 7 Apr 1999 17:25:36 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <4.1.19990404175025.02471a60@pop.ncsa.uiuc.edu> Date: Sun, 04 Apr 1999 18:12:32 -0500 To: cube-lovers@ai.mit.edu From: Tom Magliery Subject: Fwd: Keyboard cube [WAS Re: Wrist pains] >From: whuang@ugcs.caltech.edu (Wei-Hwa Huang) >First, represent the front face by > >q w e >a s d >z x c > >A "move" is represented by any two ordered keystrokes. If the two keystrokes >are in the same row, it represents a horizontal layer moving, else >if they're in the same row, it represents a vertical layer moving. ^^^ you meant to say "column" here > >Example: > "ed" = R' > "cd" = R > "sd" = slice move > "we" = U' > "qe" = U' > "qw" = U' this is sort of a grab-and-move interface (in my mental picture, one keypress "grabs" a face, and the next "moves" it). i think i might like this paradigm better than my own suggestion of before (unshifted single keystrokes for face moves, shifted single keystrokes for cube rotations). one nice advantage is that it makes it as easy on the keyboard interface as it is in real life to do RL' and R'L, for which i suspect most people's mental model is really a single turn of the middle slice. i think i'd prefer some different key assignments than wei-hwa suggests, though. for example, i think i'd like to "grab" with the middle key in the line, and then "move" with the outer one. for example: "de" = R "dc" = R' (according to wei-hwa's definition of "move", our two suggestions are compatible. mine only adds redundancy.) >This method does not have moves for rotating the three front to back layers >nor 180-degree moves. another suggestion for 180-degree moves: allow the user to tap the second key in the sequence 2 (or 3) times for 180 (or 270 aka 90') degree moves. thus, e.g., "wee" = U2. this is intuitive not only to me: someone else posted that in their keyboard interface of years ago, they didn't use the specially-assigned 180 keys, but in practice just tapped the 90-keys twice anyway. an additional suggested extension: let me do things with both hands! (this is my favorite aspect of my own keyboard interface, posted a few days ago.) perhaps a similar nonad(?) of keys could be used for R-face-relative operations analogous to the F-face-relative ones above. this is like wei-hwa's extension C, except i'd rather use my right hand in its "normal" typing position. how about a third set, in the middle of the keyboard somewhere, for doing D-relative things? mag -- ///X Tom Magliery, Research Programmer 217-333-3198 .---o \\\ NCSA, 605 E. Springfield O- mag@ncsa.uiuc.edu `-O-. /// Champaign, IL 61820 http://sdg.ncsa.uiuc.edu/~mag/ o---' From cube-lovers-errors@mc.lcs.mit.edu Wed Apr 7 18:00:36 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id SAA26538 for ; Wed, 7 Apr 1999 18:00:36 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Mon, 5 Apr 1999 00:49:14 -0400 (EDT) From: der Mouse Message-Id: <199904050449.AAA08526@Twig.Rodents.Montreal.QC.CA> To: cube-lovers@ai.mit.edu Subject: Re: Keyboard cube [WAS Re: Wrist pains] > [Assume that the person is using a standard American QWERTY keyboard; > remap if necessary.] Gotcha. And your idea seems sound. But... > Extension D: Use the arrow keys to rotate the entire cube. Arrow keys are sufficiently nonstandard I would very much prefer something else - say, a shifted slice move to rotate the whole cube. (Under some reasonable circumstances it can be hard to even tell what you'll see for "the arrow keys", if they even exist.) In passing, > Extension C: Add another grid for the right side of the cube: > r t y > f g h > v b n I'd probably prefer u i o j k l m , . I might even argue in favor of w e r / s d f / x c v for the other set, simply because they're the home keys for the three principal fingers of the left hand. Other than that, it sounds like an eminently reasonable approach. der Mouse mouse@rodents.montreal.qc.ca 7D C8 61 52 5D E7 2D 39 4E F1 31 3E E8 B3 27 4B From cube-lovers-errors@mc.lcs.mit.edu Wed Apr 7 18:42:26 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id SAA26689 for ; Wed, 7 Apr 1999 18:42:25 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <19990406235847.6438.rocketmail@web601.yahoomail.com> Date: Tue, 6 Apr 1999 16:58:47 -0700 (PDT) From: Han Wen Subject: Re: Keyboard cube [Layout for Speed Cubing] To: noel@mud.ca Cc: Cube Lovers Hi, This is a very interesting problem. I've been scratching my head for a while, and I've cooked up with a keyboard combination that could work for virtual speed cubing. I tried to follow a few guidelines: speed cubing friendly; ergonomic and intuitive. There are of course, two types of rotations that are required to solve the cube: body rotations (rotate the whole cube) and slice rotations (rotate individual faces). For each type of rotation there are three additional sub-types. For body rotations, there are three axes x, y and z. For slice rotations, there are 1/4-turn clockwise, 1/4-turn counterclockwise and 1/2-turn. Let's define the three body axes as follows: the z-axis will intersect the U and D faces. The x-axis will intersect the F and B faces. The y-axis will intersect the R and L faces. Okay, now ergonomics. When I solve the cube, I notice that my left hand does most of the body rotations and my right hand does most of the slice rotations. I tried to keep this intuition in assigning keyboard keys by making the left hand perform body rotations and the right hand perform slice rotations (well, sort of...). The most intuitive form that I could think of for your hands to be in is the fetal or "clawed" position. This can be satisfied by placing the left-hand fingers on the A, W, E and F keys and right-hand fingers on the J, I, O and ; keys (assuming a QWERTY keyboard layout). To be speed cubing friendly, these 8 fingers should never have to leave these keyboard key assignments. __________________________________________________________________________________ For body rotations, the keyboard key assignments could be: F - clockwise body rotation about the y-axis (i.e. if we were rotating a face it would be R) E - clockwise body rotation about the x-axis (i.e. if we were rotating a face it would be F) W - clockwise body rotation about the z-axis (i.e. if we were rotating a face it would be U) To perform a counter-clockwise body rotation, hit the SPACEBAR key with the right thumb in combination with the key assigment (e.g. F and SPACEBAR) __________________________________________________________________________________ For the slice rotations, the keyboard 2-key assignments could be: F and J - 1/4-turn clockwise of the L-face F and I - 1/4-turn clockwise of the R-face F and O - 1/4-turn clockwise of R-face and 1/4-turn counterclockwise of the L-face E and J - 1/4-turn clockwise of the F-face E and I - 1/4-turn clockwise of the B-face E and O - 1/4-turn clockwise of the F-face and 1/4-turn counterclockwise of the B-face W and J - 1/4-turn clockwise of the U-face W and I - 1/4-turn clockwise of the D-face W and O - 1/4-turn clockwise of the U-face and 1/4-turn counterclockwise of the D-face To perform 1/4-turn counterclockwise slice rotations, hit the SPACEBAR key with the right thumb in combination with the 2-key assignment (e.g. F and J and SPACEBAR) To perform 1/2-turn slice rotations, hit the N key with the right thumb in combination with the 2-key assignment (e.g. F and J and N) __________________________________________________________________________________ I've ordered the keys in order of their importance. As you can see the J key is responsible for "LEFT-LIKE" slice rotations I key is responsible for "RIGHT-LIKE" slice rotations O key is responsible for middle slice rotations You might ask, why make O the middle slice and not I, since it's the middle key? Well, when you actually solve the cube, you never move the middle slice. You only move the left and right slices to effectively move the middle slice. Furthermore, this operation is performed much more seldomly than normal R and L slice rotations. Anyways, you can see with this keyboard mapping you only need a total of 8 keys to perform all of possible rotations you need to solve the cube. If we really want to make this speed cubing friendly we could also do the following: -body rotations should be performed in real-time; the speed of rotation should be an adjustable constant that the user can tweak to his or her preference -slice rotations should be instantaneous. There's really no point in watching a slice rotate. Just wasting time... > "Noel Dillabough" writes: > >Any ideas would be appreciated and I'll try my best > to implement the best > >one. If simulators "felt" like a cube when you > used them they would be more > >fun (and move without jamming etc) > === _________________________________________________________ Dr. Han Wen Applied Materials 3100 Bowers Ave, MS 1158 Santa Clara, CA 95054 e-mail: Han_Wen@amat.com / hansker@yahoo.com From cube-lovers-errors@mc.lcs.mit.edu Wed Apr 7 21:38:40 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id VAA27186 for ; Wed, 7 Apr 1999 21:38:39 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu From: Jerry Bryan To: Cube Lovers Subject: Re : Re: Inventing your own techniques In-Reply-To: <14088.45800.718995.311244@cipr.no_spam.rpi.edu> Message-Id: Date: Tue, 6 Apr 1999 20:49:37 -0400 (Eastern Daylight Time) On Mon, 05 Apr 1999 08:56:08 -0400 (EDT) "Frederick W. Wheeler" wrote: > Wei-Hwa Huang sent me this teaser about conjugation. > > whuang@ugcs.caltech.edu (Wei-Hwa Huang) wrote: > > After I understood conjugation well enough, I have never invented a > > move that I can in all honesty call "new" -- although they may > > appear "new" to others. The only new part is just applying it to > > different types of moves and seeing what the result is. > > Later, at my request, Wei-Hwa Huang was kind enough to elaborate on > conjugation. > > whuang@ugcs.caltech.edu (Wei-Hwa Huang) wrote: > > I keep on meaning to write a more detailed explanation but can never > > seem to find the time. > > > > Essentially, by conjugation I mean taking two routines (call 'em A > > and B), consider their reverses (a and b), and juxtapose them (do > > the move ABab). When A and B have a small intersection the results > > of the conjugation is a simple permutation. And pretty much more > > cube puzzles can be solved if you have the simplest permutations. > > > > Eg, to rotate two corner pieces, let > > A = R'DRFDF' (rotate one corner in the top face without affecting > > the rest of the top face) > > B = U (rotate the top face) > > > > As A and B have a small intersection (one corner cubie), the move > > ABA'B' is quite useful. > > > > Note that A is itself a move arrived at by conjugation. There are two separate ideas here. A process of the form XYX'Y' is called a commutator rather than a conjugate. As you say, a commutator which moves very few cubies can be a very useful process. In fact, the number of cubies moved by XYX'Y' can be used as a sort of informal measure of how close X and Y come to commuting. In the extreme case where X and Y do commute, we have XYX'Y'=YXX'Y'=YY'=I so that no cubies are moved. And conversely, two processes X and Y which "nearly" commute and/or which intersect in very few cubies are good candidates for forming a useful commutator. A process of the form Y'XY is called a conjugate, and in particular is called the conjugate of X by Y. Note that YXY' is also a conjugate, and in particular is called the conjugate of X by Y'. This can be a little confusing because a few books (incorrectly in my opinion) call YXY' the conjugate of X by Y. Of Y and Y', which is the "real" process and which is the inverse is totally arbitrary. For example, if Z=Y', then Z'=Y. So we could write a conjugate as YXZ (the conjugate of X by Z) and another conjugate as ZXY (the conjugate of X by Y) if we know that Y and Z are respectively the inverses of each other. It is sometimes said that the conjugate Y'XY results in X shifted by Y, which is the real utility of using conjugates to solve a cube. Use a process you know, but shift it to apply to a slightly different set of cubies. Your process A=R'DRFDF' consists of the conjugates R'DR (the conjugate of D by R) and FDF' (the conjugate of D by F'). It is often the case that useful processes can be formed from both commutators and conjugates. I am perversely proud that my own personal solution technique for solving the cube consists of only two processes -- one for the corners and one for the edges -- plus conjugates of those two processes. I think it is indicative of the power of conjugates that a cube can be solved with so few processes provided only that they are combined with conjugation. I am "perversely proud" because my "two processes" technique probably yields one of the slowest solution times of anybody on Cube-Lovers. I am always embarrassed to read about those people who can do it in under 30 seconds. I have taught myself some of the faster techniques, but I always find that after a few months the only technique my hands can remember is the old, slow one which I invented myself many years ago. ---------------------------------------- Jerry Bryan jbryan@pstcc.cc.tn.us From cube-lovers-errors@mc.lcs.mit.edu Thu Apr 8 11:48:13 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id LAA29548 for ; Thu, 8 Apr 1999 11:48:12 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu From: WaVeReBeL@webtv.net Date: Wed, 7 Apr 1999 09:02:51 -0700 (PDT) To: Cube-Lovers@ai.mit.edu Subject: Re: Keyboard cube [WAS Re: Wrist pains] Message-Id: <28684-370B81AB-994@mailtod-123.bryant.webtv.net> In-Reply-To: whuang@ugcs.caltech.edu (Wei-Hwa Huang)'s message of 3 Apr 1999 00:22:20 GMT How about giving the player a choice between using a default configuration, or customizing his/her own buttons, like in certain home video games such as Street Fighter? Another cool feature would be two simultaneous cubes, so players can battle head to head, also like Street Fighter. (I really like Street Fighter) -Alex Montilla- From cube-lovers-errors@mc.lcs.mit.edu Thu Apr 8 12:10:06 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id MAA29589 for ; Thu, 8 Apr 1999 12:10:05 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Reply-To: From: "Noel Dillabough" To: Subject: SpaceOrb 360 and Simulators Date: Wed, 7 Apr 1999 13:16:14 -0400 Message-Id: <000001be811a$572c33c0$020a0a0a@pprodual> I added support for the SpaceOrb 360 by SpaceTec to Puzzler, grab this version at: http://www.mud.ca/puzzler/Puzzler.EXE You must have a SpaceOrb 360 to try it out, but it is very very nice to use compared to the mouse. Twist the orb to rotate the puzzle, and press the buttons and twist to do moves. After a little practice you'll be able to solve a cube like it was in your hands! Only the cubes (all sizes) have support for the SpaceOrb, I may add support for the other puzzles at a later date. -Noel Dillabough From cube-lovers-errors@mc.lcs.mit.edu Thu Apr 8 13:14:00 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id NAA29818 for ; Thu, 8 Apr 1999 13:13:59 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu From: Andrew John Walker Message-Id: <199904080113.LAA02581@wumpus.its.uow.edu.au> Subject: Solvers To: cube-lovers@ai.mit.edu Date: Thu, 8 Apr 1999 11:13:10 +1000 (EST) Regarding Mike Reid's program, I compiled it fine with DJGPP, an MSDOS compiler, but it didn't run. Any ideas? I'll probably get a windows compiler soon. Anyway, two other points I was thinking of recently. Firstly, do any of the kociemba algorithm search programs use the fact that you can perform a depth n search by 3 depth n-1 searches using the 3 orthogonal orientations? (if my logic is correct!) This is because if you are using the group for the final phase, the last move of any depth n sequence must end in a square move, in which case the n-1 will easily find it, or else a quarter turn in which case the three orientations are required to make it found in the second phase. Unfortuneately I doubt the n-1 searches could be replaced by n-2 searches. Also when a cube is being scrambled adjacent cubes tend to stay together for a while. Has this been of any use in search methods? (eg. to help prune the search tree). Obvously a sequence like F2 B2 U2 D2 L2 R2 separates all adjoining pairs, but there is still a high degree of order with next to adjacent cubes, so maybe they could be used as well. Andrew Walker From cube-lovers-errors@mc.lcs.mit.edu Thu Apr 8 20:23:30 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id UAA01802 for ; Thu, 8 Apr 1999 20:23:29 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Thu, 8 Apr 99 19:45:22 EDT Message-Id: <9904082345.AA16179@aic.nrl.navy.mil> From: Dan Hoey To: Jerry Bryan , Cube Lovers Subject: Conjugation done right [Re: Inventing your own techniques] First, let's make sure everyone remembers that we're using X' as an abbreviation for X^(-1) for inverses of permutations. People really should read the archives, at so they know this sort of thing, but that's getting to be a lot to ask. Still, remember that address, because it's a good place to go for things you forgot about the list (in fact, it would be nice if the README mentioned that cube-lovers-request@ai.mit.edu is the e-mail address for administrative requests to the list management, just in case someone loses their greeting message.) Jerry Bryan wrote: > A process of the form Y'XY is called a conjugate, and in particular is called > the conjugate of X by Y. Note that YXY' is also a conjugate, and in particular > is called the conjugate of X by Y'. This can be a little confusing because a > few books (incorrectly in my opinion) call YXY' the conjugate of X by Y. I tried to explain this a while ago, but it's such a subtle, counterintuitive point that I had better try again. One form of conjugate is correct, and the other form is incorrect, but just which is correct depends on how you write function composition. The point is that there are two schools of function composition, "leftward" and "rightward", and the choice of your function composition determines how you define conjugates. It's surprising that a notational convention can have this sort of effect, but we'll see it does. First, I'll describe the two schools of composition. It will be convenient to consider a set X and two permutations f and g on X. Let h:X->X be the unique permutation that satisfies h(x) = f(g(x)) for all x in X. We could let f, g, and h be any functions, not just permutations, but we will need for them to be permutations later, when we use the group structure. How do we write h in terms of f and g? The rightward school says h = g f. This is the way we have been writing things on cube-lovers all along: we write g f for applying a permutation g to something and then applying f to the result. But remember that we write h(x) = f(g(x)), which is to say that (g f)(x) = f(g(x)). The fact that the order of f and g depends on the parenthesization is often considered ugly, so some seriously rightward people write the function name after the arguments: That is to say, they write (x)f instead of f(x), (x)g instead of g(x), and (x)h = ((x)g)f = (x)(g f). This makes function composition a kind of associative law. If you're seeing this for the first time, I'm sure you consider it a bizarre and useless and gratuitously confusing complication, but I assure you that rightward functions are in wide use in some branches of the mathematical community, chiefly in abstract algebra. But cube-lovers was started by computer programmers, not algebraists, and programmers have f(x) very tightly wired into their minds and parsers. So cube-lovers uses rightward composition with leftward functions, and we say (g f)(x) = f(g(x)). As for swapping the order of f and g, we just get over it, but there are some people out there who will call us disfunctional. The leftward composition school takes a different approach: they say h(x)=f(g(x)) means h = f g. When you follow a cube process written by these people, you have to perform it from the right to the left. This is also a little hard to get used to, but at least we have an "associative" rule, (f g)(x) = f(g(x)), with f and g in the same order, without having to write our functions after the arguments. For this reason, most mathematicians other than algebraists find leftward composition to be more natural. You probably learned leftward composition in calculus or whenever. But on cube-lovers no-one wanted to write all their cube processes from right to left, so we've pretty much forgotten about leftward composition on the list. Remember, though, leftward composition is pretty standard for a lot of mathematics, and it works better for the way we write functions, so you can't really call it wrong. And there are people who say that if we are going to write our functions to the left we also ought to compose them to the left. So far so good. The rightward and leftward schools write the composition of functions in opposite orders, but either way the permutations still form a group under composition. As long as you don't mix them, it shouldn't change anything else, should it? But it really does change the definition of conjugation. (Remember conjugation? This is a message about conjugation.) Suppose we have a group G, not necessarily a permutation group. Conjugation is one way of mapping G to a permutation group, where the set being permuted is the set of group elements of G. For an element s, I'll define the right conjugate of s, R_s, as the permutation for which R_s(g) = s' g s for all g in G. Similarly, the left conjugate of s, L_s is defined by L_s(g) = s g s' for all g. It's important to notice that in either case, conjugation by a product is the composition of conjugations. For letting s and t be two specific elements of G, we can carry out manipulations that hold for all elements g of G. I'll calculate with the left conjugate in the left column and the right conjugate in the right column: L_s(g) = s g s'; R_s(g) = s' g s; L_t(g) = t g t'; R_t(g) = t' g t; L_st(g) = (st) g (st)' R_st(g) = (st)' g (st) = s t g t' s' = t' s' g s t = L_s(t g t') = R_t(s' g s) = L_s(L_t(g)) = R_t(R_s(g)) (*) These calculations were carried out using the group operation of G, independently of how we write function composition. But let's look at how we write the composition in our two notations. In the rightward composition that cube-lovers has been using all along, (*) shows that L_st = L_t L_s and R_st = R_s R_t. So the mapping s |-> L_s is an _antihomomorphism_--it reverses the order of multiplication--but s |-> R_s is a homomorphism. Homomorphisms are a lot nicer than antihomomorphisms, so we should use right conjugation all the time, right? But consider the people who use leftward composition, (f g)(x)=f(g(x)). So the function composition in (*) is now written L_st = L_s L_t and R_st = R_t R_s. So with leftward composition, _left_ conjugation is the homomorphism, and _right_ conjugation is the antihomomorphism. It is so very convenient for conjugation to be a homomorphism that people who use rightward composition always use right conjugation, and people who use leftward composition always use left conjugation (unless they think it doesn't matter and guess wrong). We're rightward composers on cube-lovers, so conjugation by s is g |-> s' t s, but remember that most math texts (other than algebra) will use the leftward composition, and so they will correctly use left conjugation, g |-> s g s'. I learned this from Jim Saxe, when I tried using left conjugation in the Symmetry and Local Maxima message. Jim told me that unless I wanted to start using leftward composition I had better use right conjugation, but I was pretty sure it really didn't matter. Jim just splained and splained until he got across how much it really does matter, and why the only right answer is different in different books. Now I've done it for you, and I hope it helps. And they said that consistency was the hobgoblin of little minds.... Dan Hoey@AIC.NRL.Navy.Mil From cube-lovers-errors@mc.lcs.mit.edu Fri Apr 9 13:06:46 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id NAA05235 for ; Fri, 9 Apr 1999 13:06:45 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <000701be8238$8c026820$92121fc8@lucentmd> From: "Jorge E. Jaramillo" To: "cube" , Subject: Cube program by Roger Broadie Date: Thu, 8 Apr 1999 22:24:23 -0500 I'd like to say that the cube program from Mr. Broadie is quite nice, actually is something I have been searching for for a while and something I requested to several Web based cube programers and never found, the ability to have a sequence interfase is something very useful mostly when you are looking for patterns and you find these lists on the web that don't show the actual result but just describe it with some sort of complicated notation, trying to do it with a real cube is a real pain since you have to do all the moves and if you make a mistake you have to start all over again by solving the cube and then making the moves that would take you to the final pattern. Well done Mr. Broadie and keep up the good work, please let the list know when you have the Windows version ready. ;-) ======= Jorge E. Jaramillo jejarami@usa.net Cut the chain and chase the dream Savatage 1984 From cube-lovers-errors@mc.lcs.mit.edu Fri Apr 9 13:52:13 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id NAA05408 for ; Fri, 9 Apr 1999 13:52:13 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu From: WaVeReBeL@webtv.net Date: Sat, 27 Mar 1999 00:03:32 -0800 (PST) To: Cube-Lovers@ai.mit.edu Subject: Lubricant Message-Id: <10861-36FC90D4-6028@mailtod-121.bryant.webtv.net> Many people have suggested different lubricants on their web pages. Many have referred to silicon. Where can I get this? What other ones are good? Where can I find them? -Alex Montilla- [Moderator's note: I skipped sending this message two weeks ago because discussing cube lubrication with someone complaining of RSI symptoms seemed like a bad idea. Then I got a large pile of interface-related messages. But now that the backlog is mostly sent out, we might want to return to considering what lubricants to use. The lubes I remember from the archives are vaseline (greasy, erodes plastic slowly), soap (temporary), candle wax (drips flakes), and molybdenum disulfide (doesn't help, destroys cube quickly). The only silicone product I've used is Armor-All, which is a protectant that provides a very little lubrication. Does anyone know what silicone Alex is discussing? Any other good ideas on lubricants? -- Dan ] From cube-lovers-errors@mc.lcs.mit.edu Fri Apr 9 17:58:59 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id RAA07206 for ; Fri, 9 Apr 1999 17:58:59 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <370E49B3.E058A9D8@u.washington.edu> Date: Fri, 09 Apr 1999 18:40:51 +0000 From: David Barr To: cube-lovers@ai.mit.edu Subject: Re: Lubricant References: <10861-36FC90D4-6028@mailtod-121.bryant.webtv.net> > [ ... Does anyone know what silicone > Alex is discussing? Any other good ideas on lubricants? -- Dan ] I think most auto parts stores sell a silicone spray lubricant. I don't know what the brand names are. I have used this on my cubes and it works well. After you first apply it, the cube will seem stiff, but if you keep turning it for a while it starts working. David From cube-lovers-errors@mc.lcs.mit.edu Fri Apr 9 19:43:01 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id TAA08480 for ; Fri, 9 Apr 1999 19:43:00 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu From: Jerry Bryan To: "Jorge E. Jaramillo" Cc: cube , Roger.Broadie@iclweb.com Subject: Cube Explorer 1.5 by Herbert Kociemba In-Reply-To: <000701be8238$8c026820$92121fc8@lucentmd> Message-Id: Date: Fri, 9 Apr 1999 18:04:29 -0400 (Eastern Daylight Time) On Thu, 08 Apr 1999 22:24:23 -0500 "Jorge E. Jaramillo" wrote: > Well done Mr. Broadie and keep up the good work, please let the list know > when you have the Windows version ready. ;-) Another alternative for Windows is Herbert Kociemba's Cube Explorer 1.5, which is easily found with Web based search engines, and which I think can also be found on the download section of the Cube-Lovers site. Cube Explorer 1.5 does not allow you to type in a maneuver directly, which I think is what you are after. But it will do something just about as good, and in some ways even better. It will read in a standard ASCII text file which contains maneuvers in standard Singmaster notation (the BFUDLR notation), and it will then show you the end product. The file can contain any (reasonable) number of maneuvers, and the program will show you the end product for each maneuver all in one fell swoop (or swell foop, if you prefer). One thing Cube Explorer 1.5 does not support that you may be looking for is to manipulate the cube and look at each intermediate position. But that's usually not what I am looking for. I am usually looking for the end product of a maneuver. (Of course, you could put each intermediate position into your ASCII text file.) You can create the ASCII text file for Cube Explorer 1.5 by typing maneuvers into the file with the text editor of your choice. But most typically I just cut and paste maneuvers out of an E-mail into the text file, and then have Cube Explorer 1.5 read the file. It's much easier and less error prone than typing the maneuvers myself. Here is a case where Cube Explorer 1.5 may be "even better". Take a Cube-Lovers message with lots of maneuvers, cut and paste the whole thing into an ASCII text file, and read the file into Cube Explorer 1.5. Instantly, you see the positions for all the maneuvers. You don't even have to worry about deleting the extraneous non-maneuver text from the E-mail. For example, take Mike Reid's lists of minimal maneuvers for highly symmetric positions, or take my lists of local maxima and put them into Cube Explorer 1.5 in this fashion. The results are quite pretty. There are many other messages in the Cube-Lovers archives with lots of pretty patterns, but these two come to mind quickly. (By the way, converting BFUDLR strings to a graphical representation of a position is an extremely useful feature of Cube Explorer 1.5, but it has several other nice features. For example, you can give it a graphical representation of a position and get back very quickly -- in a matter of seconds -- a very good suboptimal maneuver for that position.) ---------------------------------------- Jerry Bryan jbryan@pstcc.cc.tn.us From cube-lovers-errors@mc.lcs.mit.edu Mon Apr 12 12:16:29 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id MAA15917 for ; Mon, 12 Apr 1999 12:16:28 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Fri, 9 Apr 1999 19:06:08 -0400 (EDT) From: der Mouse Message-Id: <199904092306.TAA25503@Twig.Rodents.Montreal.QC.CA> To: Cube-Lovers@ai.mit.edu Subject: Re: Lubricant > Many people have suggested different lubricants on their web pages. > Many have referred to silicon. Silicon in its (relatively) pure form is somewhat difficult to get hold of and probably not a very good lubricant. You probably mean silicone. > [Moderator's note: [...] Any other good ideas on lubricants? -- Dan ] I don't know how well it works - I haven't perceived a need for lubricants for my Cubes - but one I wouldn't write off without trying is graphite, available easily and cheaply as pencil lead, the softer the pencil the better. The major downside I would expect is black dust rubbing off on fingers and to a lesser extent everything you set the Cube down on. (But it's a kind of black dust that washes off easily.) der Mouse mouse@rodents.montreal.qc.ca 7D C8 61 52 5D E7 2D 39 4E F1 31 3E E8 B3 27 4B [Moderator's note: John Bailey also advises graphite, applied carefully and sparingly.] From cube-lovers-errors@mc.lcs.mit.edu Mon Apr 12 14:10:19 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id OAA16364 for ; Mon, 12 Apr 1999 14:10:19 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Sat, 10 Apr 1999 00:38:26 -0400 (EDT) From: Nicholas Bodley To: WaVeReBeL@webtv.net Cc: Cube-Lovers@ai.mit.edu Subject: Re: Lubricant In-Reply-To: <10861-36FC90D4-6028@mailtod-121.bryant.webtv.net> Message-Id: On Sat, 27 Mar 1999 WaVeReBeL@webtv.net wrote: }Many people have suggested different lubricants on their web pages. }Many have referred to silicon. Where can I get this? What other ones }are good? Where can I find them? White powder, used like graphite, sometimes for locks? Possibly Tri-Flow (tm), which (iirc) is a Teflon (tm) particle suspension. I experimented with quite a variety of lubricants, found a good one, and then one of the periodic disruptions of my life came along and I failed to note which it was! :( "Teflon" is a Du Pont trade name for PTFE, polytetrafluoroethylene. Btw, in case you do a Web search, watch "silicon" vs. "silicone". The chemist who coined the term "silicone" was wildly optimistic about people's ability to keep the two straight. Silicon, the chemical element, is gray, opaque to visible light, brittle like glass, and a lousy lubricant. You don't normally see it, nor can you normally buy it. Silicones are chemical compounds that include the chemical element, silicon. |* Nicholas Bodley *|* Autodidact & Polymath * Electronic Tech. (ret.) |* Waltham, Mass. *|* ----------------------------------------------- |* nbodley@tiac.net *|* Silicon oil and grease do not exist. |* Amateur musician *|* IC chips made of silicone do not exist. -------------------------------------------------------------------------- From cube-lovers-errors@mc.lcs.mit.edu Mon Apr 12 17:15:33 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id RAA18027 for ; Mon, 12 Apr 1999 17:15:32 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Sat, 10 Apr 1999 02:39:35 -0400 (EDT) From: der Mouse Message-Id: <199904100639.CAA26973@Twig.Rodents.Montreal.QC.CA> To: Cube-Lovers@ai.mit.edu Subject: Cube-manipulation programs Well, with the current discussion going on about Cube manipulation programs, I'll toss out my minor contribution the genre. It's a C program that takes simple text lines describing maneuvers and prints out a text representation of the resulting cube, together with its cycle structure. (I specifically chose to make it text-only because I'm comparatively often on text-only links.) It also allows you to define names for operations and then use them as primitives. A sample transcript, which defines the Spratt wrench as an operator and then uses it to flip the four F-face edges: > .set WRENCH (SLICER F)4 `WRENCH' defined > WRENCH F2 WRENCH F2 Cube: u u u u u u u f u l l l f u f r r r b b b l l f l f r f r r b b b l l l f d f r r r b b b d f d d d d d d d Cycles: (uf)+ (lf)+ (fr)+ (fd)+ [2] Already centered > Another example: > F SLICER F' Cube: u f u u f u u u u l l l f f f r r r b l b l l f r d d b r r b u b l l l f f f r r r b u b d d d d b d d b d Cycles: (u,b,d,f) (ub,bd,rf,fl) [4] Centred: (ul,fl,fu,df,bd,rd,rb,ru,rf,dl,bl) (ulb,flu,dlf,bld) (ubr,fur,dfr,bdr) [44] > The numbers in [ ] are the smallest power to which that operator must be raised to get the identity. While I don't expect it ever attain the popularity of slick graphics programs, there may be a few people interested in it; if anyone is, you have only to drop me a line asking for a copy.... der Mouse mouse@rodents.montreal.qc.ca 7D C8 61 52 5D E7 2D 39 4E F1 31 3E E8 B3 27 4B From cube-lovers-errors@mc.lcs.mit.edu Mon Apr 12 21:07:29 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id VAA18436 for ; Mon, 12 Apr 1999 21:07:29 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Reply-To: From: "Noel Dillabough" To: "Cube Lovers List (E-mail)" Subject: Cube moves macros in simulators Date: Sat, 10 Apr 1999 10:17:49 -0400 Message-Id: <000a01be8362$9646ab40$040a0a0a@laptop> In-Reply-To: It seems my help file is poorly written, I've gotten some surprise replies from people who I have told... On Friday, April 09, 1999 6:04 PM Jerry Bryan [mailto:jbryan@pstcc.cc.tn.us] wrote: >Cube Explorer 1.5 does not allow you to type in a maneuver directly, which I >think is what you are after. Puzzler does support cube move macros, in standard UDFBLR notation (use udfblr in lowercase for inner slices and meM for central slices in the 5x5x5 cube). To use this feature hit enter and enter the move...F2 will move the F slice 2 times, F3 and F' are equivalent and will move counterclockwise 1 time, F1 and F move clockwise 1 time. You can enter any number of moves in sequence in a string then by hitting enter again the move will be executed. One more note: these macros assume the cube is oriented so that you can see three faces (exactly like the initial orientation of the cube). So F refers the the bottom left face, R is the bottom right face and U is the upper face. /\ / \ |\U /| | \/ | \F|R/ \|/ Last note: I assumed that UDFBLR was the notation used by most people. However if there is another notation that is used or if some other notation is required for experimentation, let me know and I'll put it in. -Noel From cube-lovers-errors@mc.lcs.mit.edu Tue Apr 13 12:28:58 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id MAA20809 for ; Tue, 13 Apr 1999 12:28:58 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <37134515.4AD5@zeta.org.au> Date: Tue, 13 Apr 1999 23:22:29 +1000 From: Wayne Johnson Reply-To: sausage@zeta.org.au To: Cube-Lovers@ai.mit.edu Subject: Building a twisty puzzle I have been in the process of building plans for a twisty puzzle that is no longer available. I have been re-doing the design for a few weeks now and I want to start molding or crafting the pieces soon. This is where I am coming undone. I believe I will have some success crafting the three different pieces required using clay, and filing back the pieces once dry. >From here, I believe making plaster cast molds of the clay pieces will allow me to start making all the identical pieces. Now, the problem... what can I use to fill the mold? Can I use plastics or a type of resin? I would greatly appreciate any ideas or input. I'll be posting the design on my site as soon as they are nearing completion. Maybe I can get comments on whether the whole thing will work at all. Many thanks, Wayne www.zeta.org.au/~sausage [ Moderator's note: Should this turn out to be a puzzle covered by a patent, I'll have to drop discussion of the subject. It is my under- standing that construction of patented objects is an infringement even if the object is made for personal use, and even if the patent holder has ceased production. But I have no objections to the general topic of materials and construction techniques suitable for puzzles, though if any subscribers find this drifting too far from the topic, please let cube-lovers-request@ai.mit.edu know. --Dan ] From cube-lovers-errors@mc.lcs.mit.edu Tue Apr 13 13:25:11 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id NAA21055 for ; Tue, 13 Apr 1999 13:25:10 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Tue, 13 Apr 1999 16:19:14 +0100 From: David Singmaster Computing To: noel@mud.ca Cc: cube-lovers@ai.mit.edu Message-Id: <009D6951.D5AB9641.72@ice.sbu.ac.uk> Subject: RE: Wrist pains When I went to a meeting on RSI problems, the speaker mentioned 'mouse finger' which is about as debilitating as the white finger suffered by people who use pneumatic drills (or jack-hammers). When the speaker went to one small computer design firm, she found two people suffering from it, one having essentially lost the use of his right hand and having had to change to using his left hand! DAVID SINGMASTER, Professor of Mathematics and Metagrobologist School of Computing, Information Systems and Mathematics Southbank University, London, SE1 0AA, UK. Tel: 0171-815 7411; fax: 0171-815 7499; email: zingmast or David.Singmaster @sbu.ac.uk From cube-lovers-errors@mc.lcs.mit.edu Wed Apr 14 22:38:03 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id WAA26294 for ; Wed, 14 Apr 1999 22:38:03 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Tue, 13 Apr 1999 16:46:33 +0100 From: David Singmaster Computing To: mag@ncsa.uiuc.edu Cc: cube-lovers@ai.mit.edu Message-Id: <009D6955.A6FEB505.56@ice.sbu.ac.uk> Subject: Re: Keyboard cube [was: Re: Wrist pains] Re: Tom Magliery's representation of the cube. A form of this was used by Kathleen Ollerenshaw in the early 1980s, but she also had all but the center facelet of the back face folded out to form an additional square ring around the figure so one knew what everything was. DAVID SINGMASTER, Professor of Mathematics and Metagrobologist School of Computing, Information Systems and Mathematics Southbank University, London, SE1 0AA, UK. Tel: 0171-815 7411; fax: 0171-815 7499; email: zingmast or David.Singmaster @sbu.ac.uk [Moderator's note: I couldn't help myself: ................................................. : : : : : : : : : +---------+---------------+---------+ : : |`. \ / .'| : : | `+.......\.........../.......+' | : : | :`. \ / .': | : : | : `+.....\......./.....+' : | : :.....+ : :`. \ / .': : +.....: : |`..: : `+---+---+---+' : :..'| : : | :`..: | : : | :..': | : : | : :`..+...:...:...+..': : | : : | : : | : : | : : | : : | : : ..+...:...:...+.. : : | : : | : ..:' | : : | `:.. : | : : | ..:' : +---+---+---+ : `:.. | : :.....+' : : .' / \ `. : : `+.....: : | : :'..../.......\....`: : | : : | : .' / \ `. : | : : | :'....../...........\......`. | : : | .' / \ `. | : : +'--------+---------------+--------`+ : : : : : : : : : :...............:...............:...............: I think something like this appears in Winning Ways, too. --Dan ] From cube-lovers-errors@mc.lcs.mit.edu Thu Apr 15 16:59:24 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id QAA29551 for ; Thu, 15 Apr 1999 16:59:24 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Wed, 14 Apr 1999 15:44:11 +0100 From: David Singmaster Computing To: jburkhardt@mediaone.net Cc: cube-lovers@ai.mit.edu Message-Id: <009D6A16.1B1880B4.26@ice.sbu.ac.uk> Subject: RE: Different versions of the Ideal cube Ideal certainly did use oriental suppliers when the Great Cube Craze was on and I recall several qualities of cube appeared here. I can't remember for sure if they ever sold the open cornered versions. I definitely don't recall examples with markedly different colors. When Rubik's Fourth Dimension was launched here, I saw that they were using distinctly poor quality cubes, presumably from China or thereabouts. One person at the launch said hers broke within an hour. DAVID SINGMASTER, Professor of Mathematics and Metagrobologist School of Computing, Information Systems and Mathematics Southbank University, London, SE1 0AA, UK. Tel: 0171-815 7411; fax: 0171-815 7499; email: zingmast or David.Singmaster @sbu.ac.uk From cube-lovers-errors@mc.lcs.mit.edu Thu Apr 15 19:31:56 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id TAA00230 for ; Thu, 15 Apr 1999 19:31:55 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu From: Douglas Zander Message-Id: <199904142338.SAA14966@solaria.sol.net> Subject: Building a twisty puzzle (fwd) To: cube-lovers@ai.mit.edu (cube) Date: Wed, 14 Apr 99 18:38:20 CDT In the US there exists a magazine called, "Inventor's Digest" which I have a subscribtion to and which is currently running a series of articles about building prototypes from molds. It would probably be just what you are looking for. It explains the whole process. If you want, I can get subscription information for you or information on how to order individual articles. You may wish to look in your local library to see if they carry the magazine (au = australia?) but I'm not sure your country would carry it. If you want I will send you excerpts just ask. (is this something the whole list would want to find out about?) -- Douglas Zander | dzander@solaria.sol.net | Shorewood, Wisconsin, USA | [ Moderator's note: I doubt we have that many molder/fabricator people on the list (but I could be wrong). It's also somewhat questionable how large typed-in excerpts can be before we run into copyright problems. So I'd suggest people who are looking for excerpts should contact Douglas Zander at the above address. Subscription/ordering information is more generally useful and less problematic, so please send cube-lovers that info. --Dan ] From cube-lovers-errors@mc.lcs.mit.edu Thu Apr 15 20:25:17 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id UAA00392 for ; Thu, 15 Apr 1999 20:25:16 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <199904151407.KAA00624@livia.East.Sun.COM> Date: Thu, 15 Apr 1999 10:07:53 -0400 (EDT) From: Guy Steele - Sun Microsystems Labs Reply-To: Guy Steele - Sun Microsystems Labs Subject: Winning Ways To: cube-lovers@ai.mit.edu Cc: Guy.Steele@east.sun.com Date: Tue, 13 Apr 1999 16:46:33 +0100 From: David Singmaster Computing ... [Moderator's note: I couldn't help myself: [ Picture ] I think something like this appears in Winning Ways, too. --Dan ] I just checked my copy; it does not contain this sort of diagram for the cube, at least on the pages cited in the index for "Rubik's Cube", but it does have some very nice isometric 3-D "cutaway/see-through" diagrams of the cube. --Guy From cube-lovers-errors@mc.lcs.mit.edu Thu Apr 15 21:06:50 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id VAA00504 for ; Thu, 15 Apr 1999 21:06:50 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <37165923.7ACC5D48@u.washington.edu> Date: Thu, 15 Apr 1999 21:24:51 +0000 From: David Barr To: cube-lovers@ai.mit.edu Subject: Re: Keyboard cube [was: Re: Wrist pains] References: <009D6955.A6FEB505.56@ice.sbu.ac.uk> David Singmaster Computing wrote: > > Re: Tom Magliery's representation of the cube. > A form of this was used by Kathleen Ollerenshaw in the early 1980s, but > she also had all but the center facelet of the back face folded out to form an > additional square ring around the figure so one knew what everything was. I've been playing around with something like this myself. It doesn't work yet, but you can look at http://home1.gte.net/davebarr/Cube/ I got inspired by all of the recent discussion of input methods and started thinking about visual representations. David From cube-lovers-errors@mc.lcs.mit.edu Fri Apr 16 13:08:36 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id NAA02446 for ; Fri, 16 Apr 1999 13:08:36 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu From: Douglas Zander Message-Id: <199904160046.TAA20588@solaria.sol.net> Subject: Inventor's Digest info To: cube-lovers@ai.mit.edu (cube) Date: Thu, 15 Apr 99 19:46:42 CDT Forwarded message: > [ Moderator's note: ... Subscription/ordering > information is more generally useful and less problematic, so please > send cube-lovers that info. --Dan ] Inventors' Digest Subscription Dept. PO BOX 70 Guffey CO 80820 FAX: (617) 723-6988 Email: InventorsD@aol.com WWW: www.inventorsdigest.com Volume XV, No. 1, January/February 1999 Part 1/3: "Casting Plastic Prototypes at Room Temperature" Author: Jack Lander Volume XV, No. 2, March/April 1999 Part 2/3: "Making a Rubber Mold For Casting Plastic" Volume XV, No.3, May/June 1999 Part 3/3: "Casting Plastic in Rubber Molds" -- Douglas Zander | dzander@solaria.sol.net | Shorewood, Wisconsin, USA | From cube-lovers-errors@mc.lcs.mit.edu Mon Apr 19 12:14:43 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id MAA07359 for ; Mon, 19 Apr 1999 12:14:43 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <3718413B.251EE6E0@okanagan.net> Date: Sat, 17 Apr 1999 00:07:29 -0800 From: karen loewen Reply-To: loewens@okanagan.net To: Cube-Lovers@ai.mit.edu Subject: Rubiks Cube, Megaminx and Square-1 Is there a world record for the the 4x4x4 and the 5x5x5 rubiks cubes? If so what is it? I was wondering what in your opinion is the hardest rubiks like cube available right now. On a web page several people from rated the greatest to least in difficulty: 1)square-1 2)megaminx 3)5x5x5 4)4x4x4 5)? 6)? Anyway it went something like that. Would you consider Square-1 one of the hardest cubes to do? If so would this be considered good of me to learn all by myself? My best time is 83 sec. As if now I am not sure what my average is. Do you know of a world record for Square-1 or any good websites? Do you know what an average would be for the best time? I was wondering how this compares to others times and accomplishments. At http://byrden.com/puzzles/ I almost figured out the megaminx. I got everything except the last row. Is the Megaminx one of the hardest Rubiks like puzzles available? After I get bored of my 5x5x5 that I ordered thinking about buying the megaminx. Do you know of a world record on the megaminx? What would be a average time (perhaps 3-4 minutes?) Currently I am more interested in the Rubiks cube. Lately I have been trying to improve my time. I have a personal record of 50 seconds, and an average time of about 80 seconds. However, I learned how to do the cube all by myself. I didn't get help from others, websites, books... I was wondering If you learned by yourself or if you got help? Then what is your time? I don't believe that I will ever get much faster. Learning by yourself is a really hard task. I was wondering if there is any one out there who agrees that getting help from resources is cheating? In my opinion they make the people who haved learned by themselves look bad. This is just my opinion, you don't have to agree. If you are not sure of answers that's fine. Then do you know of any good websites I can go to? Thank you very much. From cube-lovers-errors@mc.lcs.mit.edu Mon Apr 19 17:34:05 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id RAA07769 for ; Mon, 19 Apr 1999 17:34:05 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Mon, 19 Apr 1999 15:13:27 +0100 From: David Singmaster To: jbryan@pstcc.cc.tn.us Cc: cube-lovers@ai.mit.edu Message-Id: <009D6DFF.A3A1ABCB.24@ice.sbu.ac.uk> Subject: RE: Re : Re: Inventing your own techniques The technique of solving the cube by use of commutators and conjugates is what most people worked out in the early days. However, I can testify that it took us some time to realise that one could use second level commutation. That is, FRF'R' = [F,R] only affects seven pieces, but in fact it only affects one piece in the L face, so taking the commutator with the L face produces a 3-cycle of corners. Likewise [F,R]^2 only twists one corner in the L face and combining it with turns of L allows you to twist three corners the same way or two corners opposite ways. DAVID SINGMASTER, Professor of Mathematics and Metagrobologist School of Computing, Information Systems and Mathematics Southbank University, London, SE1 0AA, UK. Tel: 0171-815 7411; fax: 0171-815 7499; email: zingmast or David.Singmaster @sbu.ac.uk From david.singmaster@sbu.ac.uk Mon Apr 19 18:35:09 1999 Return-Path: Received: from smtp.interlog.com (root@smtp.interlog.com [207.34.202.37]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with ESMTP id SAA07922 for ; Mon, 19 Apr 1999 18:35:09 -0400 (EDT) Received: from crii.com (209-20-9-212.dialin.interlog.com [209.20.9.212]) by smtp.interlog.com (8.9.1/8.9.1) with SMTP id SAA25968 for ; Mon, 19 Apr 1999 18:35:07 -0400 (EDT) Received: from [127.0.0.1] by crii.com [192.168.0.47] with DomainPOP (MDaemon.v2.7.SP5.R) for ; Mon, 19 Apr 1999 18:36:59 -0400 Delivered-To: cr728635@mail-00 Received: from mc.lcs.mit.edu (mc.lcs.mit.edu [18.30.0.229]) by mail.9netave.com (8.9.2/8.8.8) with ESMTP id SAA50612; Mon, 19 Apr 1999 18:25:01 -0400 (EDT) Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id RAA07769 for ; Mon, 19 Apr 1999 17:34:05 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Mon, 19 Apr 1999 15:13:27 +0100 From: David Singmaster To: jbryan@pstcc.cc.tn.us Cc: cube-lovers@ai.mit.edu Message-Id: <009D6DFF.A3A1ABCB.24@ice.sbu.ac.uk> Subject: RE: Re : Re: Inventing your own techniques X-MDaemon-Deliver-To: cube-lovers-outbound@mc.lcs.mit.edu The technique of solving the cube by use of commutators and conjugates is what most people worked out in the early days. However, I can testify that it took us some time to realise that one could use second level commutation. That is, FRF'R' = [F,R] only affects seven pieces, but in fact it only affects one piece in the L face, so taking the commutator with the L face produces a 3-cycle of corners. Likewise [F,R]^2 only twists one corner in the L face and combining it with turns of L allows you to twist three corners the same way or two corners opposite ways. DAVID SINGMASTER, Professor of Mathematics and Metagrobologist School of Computing, Information Systems and Mathematics Southbank University, London, SE1 0AA, UK. Tel: 0171-815 7411; fax: 0171-815 7499; email: zingmast or David.Singmaster @sbu.ac.uk From cube-lovers-errors@mc.lcs.mit.edu Tue Apr 20 14:22:17 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id OAA09900 for ; Tue, 20 Apr 1999 14:22:16 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Mon, 19 Apr 1999 15:48:36 +0100 From: David Singmaster To: WaVeReBeL@webtv.net Cc: cube-lovers@ai.mit.edu Message-Id: <009D6E04.8CAE2B95.34@ice.sbu.ac.uk> Subject: RE: Lubricant I used to use silicone grease of the type used for O-ring seals in diving equipment, etc. I haven't seen any damage caused by this. WD-40 has also been suggested and I have used it, but I think it may damage some plastics. Note that the central spindle is often made of a different plastic than the other pieces and I think it is more subject to attack by some of the lubricants. DAVID SINGMASTER, Professor of Mathematics and Metagrobologist School of Computing, Information Systems and Mathematics Southbank University, London, SE1 0AA, UK. Tel: 0171-815 7411; fax: 0171-815 7499; email: zingmast or David.Singmaster @sbu.ac.uk From cube-lovers-errors@mc.lcs.mit.edu Thu Apr 22 11:18:36 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id LAA14447 for ; Thu, 22 Apr 1999 11:18:36 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu From: WaVeReBeL@webtv.net Date: Mon, 19 Apr 1999 16:30:06 -0700 (PDT) To: Cube-Lovers@ai.mit.edu Cc: loewens@okanagan.net Subject: Re: Rubiks Cube, Megaminx and Square-1 Message-Id: <8843-371BBC7E-10617@postoffice-123.bryant.webtv.net> In-Reply-To: karen loewen 's message of Sat, 17 Apr 1999 00:07:29 -0800 Hi, I think it's great that you learned to do the cube all by yourself. I give much respect to anyone who solved any of these twisty puzzles. Very few people have the ability and the time to figure them out. I'm curious if you are willing to share your methods? I personally learned from a book. Afterwards, I kind of wished I hadn't. Since then, I promised myself not to look at any more solutions for any new puzzles I encounter. So far, all I've managed to solve on my own is the pyraminx. (very easy compared to the cube) I can see how you might feel a little disgruntled about others achieving quick solving times with aid from outside resources. I am an example of that. In about 4 months I achieved a 36 second average after scouring the net for every bit of information I could find. You shouldn't think it makes you look bad. If anything, I feel bad knowing that people like you must put a lot of hard work into it, while I had a much easier time. It still takes a lot of hard physical and mental work on my part to achieve a fast average, but a lot of the mental work was already done for me. As far as cheating is concerned, in my and many others' defense, I must respond, as the majority of people in this group have referred to outside information at one point or another. Consider speed cubing as a sport just like any other in the Olympics. Everyone is going to use every resource available to win. No one in the Olympics is going to try and win (or succeed for that matter) all by themselves w/out any help or coaching at all. The use of outside help brings those who use it to a higher level playing field. These people are in an equal playing field among themselves having access to the same resources. If people choose to learn on their own, it is only fair to put them in a different group rather than lumping everyone in the same group. But just because people have accessed other resources, doesn't mean they will all of a sudden reach less than a minute averages, it still takes a lot of hard work to get there. I know your average is still better than a lot of people who got help. On the other hand, getting help on learning how to solve the cube might be considered cheating just as it would be when one gets hints to a riddle or looks in the back of the book for all the answers. I don't think there is anything wrong with help at all, unless your goal is to do it all on your own without any help. You said that you don't believe that you will ever get much faster. If your skill level plateaus, I don't see anything wrong with using any resources available to exceed your limits. That's what help is for! You can still be proud of your accomplishments, but everyone has their limits. There are very few people who have achieved what you have. -Alex Montilla- From cube-lovers-errors@mc.lcs.mit.edu Thu Apr 22 12:22:10 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id MAA14641 for ; Thu, 22 Apr 1999 12:22:10 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <3.0.32.19990420085812.009b2880@mail.spc.nl> Date: Tue, 20 Apr 1999 08:58:14 +0200 To: cube-lovers@ai.mit.edu From: Christ van Willegen Subject: RE: Re : Re: Inventing your own techniques At 15:13 19-4-1999 +0100, you wrote: > The technique of solving the cube by use of commutators and conjugates >is what most people worked out in the early days. However, I can testify that >it took us some time to realise that one could use second level commutation. >That is, FRF'R' = [F,R] only affects seven pieces, but in fact it only affects >one piece in the L face, so taking the commutator with the L face produces a >3-cycle of corners. Likewise [F,R]^2 only twists one corner in the L face >and combining it with turns of L allows you to twist three corners the same way >or two corners opposite ways. When I learned how to solve the cube (some 20 years back, I think...), I was taught a layer-by-layer solution, consisting of 'modular' moves. Most of the modularity occurs on the 3rd layer, namely: - In flipping the edges, I use (RE)^4 to flip the UR edge. Then, I move the top layer so that there's another edge to be flipped at the UR position and I repeat the same procedure. - In rotating the edges, I was taught the above-mentioned {R,F]^2 to rotate an edge by 120 degrees. Later, I 'discovered' that [F,R]^2 does the same thing backward. Most other layer-by-layer methods I've seen have formulas to flip 2 edges in the top layer, but you'll need two for the different confi- gurations. Also, these methods mostly have two, three or more formulas to rotate the edges in the toplayer, depending on configuration. My method may not be the fastest around (it takes me about 2 minutes to solve The Cube), but I don't need many formulas for it: 1st layer: on my own (make a cross, fill in the corners) 2nd layer: 2 formulas (standard layer 3 to layer 2 swing, two directions) 3rd layer: 4 (exchange edges, flip one edge, exchange corners, rotate one corner) Christ van Willegen From cube-lovers-errors@mc.lcs.mit.edu Thu Apr 22 18:11:24 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id SAA15583 for ; Thu, 22 Apr 1999 18:11:23 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: From: Paddy Duncan To: cube-lovers@ai.mit.edu Subject: Re: Lubricant Date: Tue, 20 Apr 1999 21:27:31 +0100 WD-40 will make it stick REALLY badly! Please don't do it. Not because it will dissolve the plastic (although it might), but because it's too thin. Also I have seen in the past a problem with the kind of solvents in this kind of product where it seems to 'realise' any small cracks in plastic, causing it to just fall to bits the next day. Silicone grease sounds good to me. Paddy Duncan Systems Engineer Intralan (UK) Ltd [ Moderator's note: I'll remind you that last month Alex Montilla suggested (for low-quality tiled cubes), "If you use WD-40, it'll eat away at the plastic resulting in really smooth turning. It'll be great for about 3-4 weeks of daily cubing, but the WD-40 will take its toll, and the cube will start falling apart. But for a few bucks every 3-4 weeks is worth it to me." So WD-40 is bad for the cube, but possibly good for the turning, at least temporarily. That's the way the cubie crumbles. --Dan ] From cube-lovers-errors@mc.lcs.mit.edu Fri Apr 23 11:39:54 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id LAA17131 for ; Fri, 23 Apr 1999 11:39:53 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <371FCBE9.6DE8069@ibm.net> Date: Thu, 22 Apr 1999 18:24:57 -0700 From: "Jin 'Time Traveler' Kim" Reply-To: chrono@ibm.net To: cube-lovers@ai.mit.edu Subject: Re: Rubiks Cube, Megaminx and Square-1 References: <3718413B.251EE6E0@okanagan.net> The only record for a 4x4x4 I saw was 117 or 170+ seconds, I can't remember which. BTW, that was my web page you visited. :) The reason I think that the Square-1 is rated so high is because it "mutates" in form and shape as you twist it. All other puzzles remain mechanically symmetrical to themselves (even the pyramorphix, while changing shape, is still the same basic architecture underneath). The Square-1's possible moves change as you mix it, causing an extra level of confusion. Does this make it tougher to solve? Learning to solve puzzles by yourself is great. Unlike some others on the cube list, I've always relied on intuition and mental picturing to make all of my moves. This has allowed me to solve puzzles since I was about six years old. The only puzzles I have been unable to solve this way are the Rubik's Cube series (2^3 through 5^3), specifically the corner moves. Everything else I was able to do independently at one Time or another including the center pieces on the 4x4x4 and 5x5x5. A quick anecdote. For the longest Time I didn't bother scrambling my Geomaster Masterball for fear of messing it up. That barrier was overcome when a friend of mine inadvertently scrambled it for me. 14 hours of hair pulling later I came up with a "logical" solution for it (that actually helped me solve the Dogic later). Of course, shortly afterwards they sold Masterballs with solutions far simpler than mine, but I still prefer using my method, because it's mine. -- Jin "Time Traveler" Kim chrono@ibm.net http://www.chrono.org '95 PGT - SCPOC From cube-lovers-errors@mc.lcs.mit.edu Mon Apr 26 19:06:53 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id TAA24971 for ; Mon, 26 Apr 1999 19:06:52 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu From: "Marius Loots" Organization: University of Pretoria To: Cube-Lovers@ai.mit.edu Date: Fri, 23 Apr 1999 09:36:26 CAT-2 Subject: Re: Lubricant Reply-To: mloots@medic.up.ac.za Message-Id: > Many people have suggested different lubricants on their web pages. > The lubes I remember from the archives are vaseline (greasy, erodes > plastic slowly), soap (temporary), candle wax (drips flakes), and > molybdenum disulfide (doesn't help, destroys cube quickly). The only >From these lubricants the only one I have ever used was Vaseline. At some stage I did try car grease but this was too much of a mess on the hands. For a real slippery slide, we sometimes dipped the Vaseline Cube in water. This would give you a few minutes of realy high speed cubing. This shouldn't have any effect on the plastic, I am not sure about the mechanisms although I still have my very first cube and it is still in working order (albeit a bit loose because of age). Groetnis Marius mloots@medic.up.ac.za +27-12-319-2144 Add some Chaos to your Life and put the World in Order http://www.geocities.com/Athens/6398/ From cube-lovers-errors@mc.lcs.mit.edu Mon Apr 26 19:39:09 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id TAA24989 for ; Mon, 26 Apr 1999 19:39:09 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: In-Reply-To: Date: Fri, 23 Apr 1999 09:12:13 -0600 To: cube-lovers@ai.mit.edu From: Steve LoBasso Subject: Re: Lubricant White lithium grease is pretty good, but I don't know about its long term effects on plastic. If anyone has ever changed a distributor / points on an old car, there is a small tube of grease that is intended to be used on a plastic metal contact point. It is actually absorbed by the plastic and allows it to remain quite frictionless. If you want some good advice on this stuff look for an auto parts store with people that know more than just what they read from the packages or an older mechanic. -Steve -- Steve LoBasso Digital Technology International mailto:slobasso@dtint.com 500 West 1200 South or mailto:slobasso@hotmail.com Orem, UT 84058 http://members.tripod.com/~slobasso (801)226-6142 ext.265 FAX (801)221-9254 [ Moderator's note: Be sure to read the tube or find a MSDS for warnings about prolonged contact with skin. If you can absorb Li+ from this, it's serious bad news. --Dan ] From cube-lovers-errors@mc.lcs.mit.edu Mon Apr 26 21:15:50 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id VAA25075 for ; Mon, 26 Apr 1999 21:15:50 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu To: cube-lovers@ai.mit.edu From: whuang@ugcs.caltech.edu (Wei-Hwa Huang) Subject: Reinventing (and some edge-flipping techniques) Date: 26 Apr 1999 18:03:02 GMT Organization: California Institute of Technology, Pasadena Message-Id: <7g29om$4ua@gap.cco.caltech.edu> I skimmed through Singmaster's "Notes on Rubik's Magic Cube" this weekend. It was rather disappointing to realize that the techniques I had invented five years ago had all been independently invented twenty years ago! In any case, I thought I might share my thoughts about monoflips with the list. -------------- [I shall use "E" to denote moving the center slice (between the U and D faces) to the left (so that the F center becomes the L center). E' I will use to denote its inverse. In other words, E is the same as U'D followed by rotating the entire cube clockwise from the point of view of the U face. Similarly, I will use M to denote moving the L-R slice "up". Traditionally, a slice is counted as two turns, although it is usually easier to perform than two orthogonal turns.] As you may know, a "monoflip" is a sequence of moves that flips one edge on a given face (usually the U face) while not affecting the rest of the face. For instance, this is a monoflip: F E F M FF M' (10 turns) This flips the FU edge cubie. If you do this sequence of moves, it is particularly easy to look at the FUL, FU, and FUR cubies and see how they move around to perform this monoflip. What makes a monoflip so useful is the fact that it can me commutated with moves of the face (U) to flip two edges. E.g., FEFMFFM' U MFFM'F'E'F' U' will flip the FU and RU edges. (The first FEFMFFM' flips FU while messing up the rest of the cube, then the U moves the RU to where the FU was, then MFFM'F'E'F' flips the "new" FU as well as undoing what was done to the rest of the cube. U' then restores what was done.) Commutating with other moves will, of course, allow you to flip other edges. Using UU instead of U will flip the FU and BU edges, for instance. If you add conjugation, you can get pretty much any two edge pieces to flip -- e.g., R' FEFMFFM' U MFFM'F'E'F' U' R will flip the FU and RB edges. -------- The drawback of FEFMFFM', however, is that it is not that easy to remember, since you also have to remember its inverse MFFM'F'E'F'. (Although the embedded conjugate MFFM' is its own inverse, which is nice.) Therefore, the monoflip I see more often in other people's repertoire is F E' F E' F E' F E' (12 moves) which has many advantages: 1. It is easier to remember; 2. It is its own inverse; 3. Its results are "elegant". (flips of FU,FL,BR,BL) Of course, this move is special enough that you don't NEED to use it as a monoflip if you rotate and reflect this move. To flip two adjacent edges, simply do FE'FE'FE'FE' R'ER'ER'ER'E and you'll flip the FU and RU edges. (The second part is just a reflection along the BL - FR plane.) Other variants of this move can pretty much let you flip any combinations of edge cubies you want. -------------- I used to use the previous "monoflip" a lot. The only drawback with the previous monoflip, however, is that it is too slow, especially those slice moves. Therefore, when I need to do edge flipping these days, I use this monoflip: R F' U R' F (5 moves) At first this doesn't look like a monoflip, since each face seems to be pretty messed up. But this is not your normal monoflip -- this is a SLICE-BASED monoflip, where the E slice is intact except for the FR edge. In fact, I'd conjecture that this is the shortest monoflip there is. To flip the FR edge, RUF is pretty much the quickest you can to it in. But this messes up two diagonally opposite edges on the slice, so at least two more moves are needed to restore this -- hence, the F' and R'. You can think of this as RF' conjugated with U -- I'm not sure it helps much though. The inverse, F' R U' F R', is just a reflection of the original move and so is pretty easy to remember. In any case, this makes edge flipping nice and quick: RF'UR'F E' F'RU'FR' E (flips FR and FL in 12 moves) RF'UR'F EE F'RU'FR' EE (flips FR and BL in 16 moves) But how about the other edge pair combinations? Conjugates, of course. I use these moves: 1. Adjacent edges, same face: F'R' RF'UR'F E' F'RU'FR' E RF which reduces a bit to: FFUR'F E' F'RU'FR' E RF (flips FU and RU in 16 moves) 2. Adjacent edges, same slice: (done above, 12 moves) 3. Opposite edges: (done above, 16 moves) 4. Skew edges: R' RF'UR'F E' F'RU'FR' E R which reduces a bit to: F'UR'F E' F'RU'FR' E R (flips FL and RU in 14 moves) These are the current edge flips in my repertoire, and they achieve a balance between being easy to remember and being fast to do. ---------- I'd appreciate if others could share the moves they use for 2-edge flips, as well as know of any results known of God's algorithm for 2-edge flips. -- Wei-Hwa Huang, whuang@ugcs.caltech.edu, http://www.ugcs.caltech.edu/~whuang/ --------------------------------------------------------------------------- She ran by screaming "No, I run by moving my feet rapidly, you idiot!" From cube-lovers-errors@mc.lcs.mit.edu Tue Apr 27 11:11:51 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id LAA26808 for ; Tue, 27 Apr 1999 11:11:51 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu From: "Chris and Kori Pelley" To: Subject: RE: Lubricant Date: Mon, 26 Apr 1999 22:38:57 -0400 Message-Id: In-Reply-To: > -----Original Message----- > From: Marius Loots [mailto:MLOOTS@medic.up.ac.za] > ...For a real slippery slide, we sometimes dipped the Vaseline Cube > in water. This would give you a few minutes of realy high speed cubing. I concur with Marius. I used to practice solving underwater in my swimming pool, back when I averaged 33 seconds! I would use a cube with just a small amount of vaseline. After taking the cube out and letting it dry a couple hours, it would turn VERY WELL. Also, the deleterious effect on the plastic seems to be negligible, as I still have those same cubes and they still operate smoothly some 15+ years later. Chris Pelley ck1@home.com http://www.chrisandkori.com/cubes.htm From cube-lovers-errors@mc.lcs.mit.edu Tue Apr 27 12:19:57 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id MAA27107 for ; Tue, 27 Apr 1999 12:19:56 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <3725DDD8.327E@hrz1.hrz.tu-darmstadt.de> Date: Tue, 27 Apr 1999 17:55:04 +0200 From: Herbert Kociemba Reply-To: kociemba@hrz1.hrz.tu-darmstadt.de To: cube-lovers@ai.mit.edu Subject: Re: Reinventing (and some edge-flipping techniques) References: <7g29om$4ua@gap.cco.caltech.edu> Wei-Hwa Huang wrote: > > I'd appreciate if others could share the moves they use for 2-edge flips, > as well as know of any results known of God's algorithm for 2-edge flips. > I did a quick run with my optimal solver program. Here are all maneuvers with shortest length (face-turn metric) for the four possible two-flips. Note that many of them are basically identical due to the symmetry of the two-flip patterns itself: uf,ur flips: F U2 F2 D' U' L' U L D F2 U' F' U' (13f*) F D U R2 U2 R' U R U R2 D' F' U' (13f*) F' U' F2 D R U R' D' U' F2 U2 F U' (13f*) F' D' L2 U L U L' U2 L2 D U F U' (13f*) R D B2 U' B' U' B U2 B2 D' U' R' U (13f*) R U R2 D' F' U' F D U R2 U2 R' U (13f*) R' U2 R2 D U B U' B' D' R2 U R U (13f*) R' D' U' F2 U2 F U' F' U' F2 D R U (13f*) U' R U2 R2 D' U' F' U F D R2 U' R' (13f*) U' R D U B2 U2 B' U B U B2 D' R' (13f*) B F U F' U' B' R2 F R F R' F2 R2 (13f*) F R' F' R' F2 L D R D' L' R' F2 R2 (13f*) L F R' F' L' U2 R U R U' R2 U2 R (13f*) U' R' U' R2 D B U B' D' U' R2 U2 R (13f*) L F2 R2 F' R F R F2 L' U' R' U R (13f*) U' R' D' F2 U F U F' U2 F2 D U R (13f*) F2 R2 B' F' D' F D B R2 F' R' F' R (13f*) B F U2 F2 U' F U F U2 B' R' F' R (13f*) F R' F' L' U2 R U R U' R2 U2 L R (13f*) F2 R2 F' R F R F2 L' U' R' U L R (13f*) B' R2 F2 R F' R' F' R2 B U F U' F' (13f*) U F D R2 U' R' U' R U2 R2 D' U' F' (13f*) B' R' F R B U2 F' U' F' U F2 U2 F' (13f*) U F U F2 D' L' U' L D U F2 U2 F' (13f*) R2 F2 L R D R' D' L' F2 R F R F' (13f*) L' R' U2 R2 U R' U' R' U2 L F R F' (13f*) R2 F2 R F' R' F' R2 B U F U' B' F' (13f*) R' F R B U2 F' U' F' U F2 U2 B' F' (13f*) L' R' U' R U L F2 R' F' R' F R2 F2 (13f*) R' F R F R2 B' D' F' D B F R2 F2 (13f*) U F' U2 F2 D U R U' R' D' F2 U F (13f*) U F' D' U' L2 U2 L U' L' U' L2 D F (13f*) R' U2 R2 U R' U' R' U2 L F R F' L' (13f*) R' U' R U L F2 R' F' R' F R2 F2 L' (13f*) F U F' U' B' R2 F R F R' F2 R2 B (13f*) F U2 F2 U' F U F U2 B' R' F' R B (13f*) uf,ub flips: L F' U L' B' F U R' F U' R B F' U' (14f*) L' R B U' L B' U L R' F' U L' F U' (14f*) R B' U R' B F' U L' B U' L B' F U' (14f*) L R' F U' R F' U L' R B' U R' B U' (14f*) R2 F D U' R B2 U2 B2 R' D' U F' R2 U2 (14f*) R2 F L R' D L2 B2 L2 D' L' R F' R2 U2 (14f*) R2 F' D' U L' F2 U2 F2 L D U' F R2 U2 (14f*) R2 F' L R' D' L2 B2 L2 D L' R F R2 U2 (14f*) R2 B D U' L B2 U2 B2 L' D' U B' R2 U2 (14f*) R2 B L' R D L2 F2 L2 D' L R' B' R2 U2 (14f*) R2 B' D' U R' F2 U2 F2 R D U' B R2 U2 (14f*) R2 B' L' R D' L2 F2 L2 D L R' B R2 U2 (14f*) F U2 L R F2 D R2 D' F2 L' R' U2 F' U2 (14f*) F R2 D U B2 R B2 R' B2 D' U' R2 F' U2 (14f*) F' U2 L' R' F2 D' L2 D F2 L R U2 F U2 (14f*) F' L2 D' U' B2 L' B2 L B2 D U L2 F U2 (14f*) L2 F D U' R F2 U2 F2 R' D' U F' L2 U2 (14f*) L2 F L R' D R2 B2 R2 D' L' R F' L2 U2 (14f*) L2 F' D' U L' B2 U2 B2 L D U' F L2 U2 (14f*) L2 F' L R' D' R2 B2 R2 D L' R F L2 U2 (14f*) L2 B D U' L F2 U2 F2 L' D' U B' L2 U2 (14f*) L2 B L' R D R2 F2 R2 D' L R' B' L2 U2 (14f*) L2 B' D' U R' B2 U2 B2 R D U' B L2 U2 (14f*) L2 B' L' R D' R2 F2 R2 D L R' B L2 U2 (14f*) B U2 L R B2 D L2 D' B2 L' R' U2 B' U2 (14f*) B L2 D U F2 L F2 L' F2 D' U' L2 B' U2 (14f*) B' U2 L' R' B2 D' R2 D B2 L R U2 B U2 (14f*) B' R2 D' U' F2 R' F2 R F2 D U R2 B U2 (14f*) L' R B' U R' B U' L R' F U' R F' U (14f*) L' B U' L B' F U' R B' U R' B F' U (14f*) R' F U' R B F' U' L F' U L' B' F U (14f*) L R' F' U L' F U' L' R B U' L B' U (14f*) L F U' R F' U L' R B' U R' B U' R' (14f*) F U' R B F' U' L F' U L' B' F U R' (14f*) L F' U L' F U' L' R B U' L B' U R' (14f*) F U' R F' U L' R B' U R' B U' L R' (14f*) F' U L' F U' L' R B U' L B' U L R' (14f*) U F' L U' F L' R U' B L' U B' L R' (14f*) U' F R' U F' L' R U B' R U' B L R' (14f*) F' L' U B' U B L F R U' B U' B' R' (14f*) L U F' L U' F L' R U' B L' U B' R' (14f*) F' U' F U' R B L F U F' U L' B' R' (14f*) U B F' L' U B' L U' B' F R U' B R' (14f*) L U' F R' U F' L' R U B' R U' B R' (14f*) F D U' R B2 U2 B2 R' D' U F' R2 U2 R2 (14f*) F L R' D L2 B2 L2 D' L' R F' R2 U2 R2 (14f*) F' D' U L' F2 U2 F2 L D U' F R2 U2 R2 (14f*) F' L R' D' L2 B2 L2 D L' R F R2 U2 R2 (14f*) B D U' L B2 U2 B2 L' D' U B' R2 U2 R2 (14f*) B L' R D L2 F2 L2 D' L R' B' R2 U2 R2 (14f*) B' D' U R' F2 U2 F2 R D U' B R2 U2 R2 (14f*) B' L' R D' L2 F2 L2 D L R' B R2 U2 R2 (14f*) U2 R2 F D U' R B2 U2 B2 R' D' U F' R2 (14f*) U2 R2 F L R' D L2 B2 L2 D' L' R F' R2 (14f*) U2 R2 F' D' U L' F2 U2 F2 L D U' F R2 (14f*) U2 R2 F' L R' D' L2 B2 L2 D L' R F R2 (14f*) U2 R2 B D U' L B2 U2 B2 L' D' U B' R2 (14f*) U2 R2 B L' R D L2 F2 L2 D' L R' B' R2 (14f*) U2 R2 B' D' U R' F2 U2 F2 R D U' B R2 (14f*) U2 R2 B' L' R D' L2 F2 L2 D L R' B R2 (14f*) L' B U' L B' U L R' F' U L' F U' R (14f*) B' U R' B F' U L' B U' L B' F U' R (14f*) L' B' U R' B U' L R' F U' R F' U R (14f*) L' U B' R U' B L R' U' F R' U F' R (14f*) U' B F' L U' F L' U B' F R' U F' R (14f*) L' U' B L' U B' L R' U F' L U' F R (14f*) B L U' F U' F' L' B' R' U F' U F R (14f*) B U B' U R' F' L' B' U' B U' L F R (14f*) B U' L B' U L R' F' U L' F U' L' R (14f*) B' U R' B U' L R' F U' R F' U L' R (14f*) U B' R U' B L R' U' F R' U F' L' R (14f*) U' B L' U B' L R' U F' L U' F L' R (14f*) L' B' R' U F' U F R B L U' F U' F' (14f*) U2 F U2 L R F2 D R2 D' F2 L' R' U2 F' (14f*) L' R U B' R U' B L R' U' F R' U F' (14f*) R U' B F' L U' F L' U B' F R' U F' (14f*) F' D' L' U' L D U F2 U2 F' U F U F' (14f*) L2 U2 L2 F D U' R F2 U2 F2 R' D' U F' (14f*) R2 U2 R2 F D U' R B2 U2 B2 R' D' U F' (14f*) L' B' U' B U' L F R B U B' U R' F' (14f*) U2 F R2 D U B2 R B2 R' B2 D' U' R2 F' (14f*) L2 U2 L2 F L R' D R2 B2 R2 D' L' R F' (14f*) R2 U2 R2 F L R' D L2 B2 L2 D' L' R F' (14f*) F' U F U F' U2 F2 D U R U' R' D' F' (14f*) F D R U R' D' U' F2 U2 F U' F' U' F (14f*) R2 U2 R2 F' D' U L' F2 U2 F2 L D U' F (14f*) L2 U2 L2 F' D' U L' B2 U2 B2 L D U' F (14f*) L' R U' B L' U B' L R' U F' L U' F (14f*) L' U B' F R' U F' R U' B F' L U' F (14f*) U2 F' U2 L' R' F2 D' L2 D F2 L R U2 F (14f*) R B L U' F U' F' L' B' R' U F' U F (14f*) L2 U2 L2 F' L R' D' R2 B2 R2 D L' R F (14f*) R2 U2 R2 F' L R' D' L2 B2 L2 D L' R F (14f*) F U' F' U' F U2 F2 D' U' L' U L D F (14f*) U2 F' L2 D' U' B2 L' B2 L B2 D U L2 F (14f*) R B U B' U R' F' L' B' U' B U' L F (14f*) R B U' L B' U L R' F' U L' F U' L' (14f*) R B' U R' B U' L R' F U' R F' U L' (14f*) B U' L B' F U' R B' U R' B F' U L' (14f*) B' R' U F' U F R B L U' F U' F' L' (14f*) R U B' R U' B L R' U' F R' U F' L' (14f*) B' U' B U' L F R B U B' U R' F' L' (14f*) R U' B L' U B' L R' U F' L U' F L' (14f*) U B' F R' U F' R U' B F' L U' F L' (14f*) F D U' R F2 U2 F2 R' D' U F' L2 U2 L2 (14f*) F L R' D R2 B2 R2 D' L' R F' L2 U2 L2 (14f*) F' D' U L' B2 U2 B2 L D U' F L2 U2 L2 (14f*) F' L R' D' R2 B2 R2 D L' R F L2 U2 L2 (14f*) B D U' L F2 U2 F2 L' D' U B' L2 U2 L2 (14f*) B L' R D R2 F2 R2 D' L R' B' L2 U2 L2 (14f*) B' D' U R' B2 U2 B2 R D U' B L2 U2 L2 (14f*) B' L' R D' R2 F2 R2 D L R' B L2 U2 L2 (14f*) U2 L2 F D U' R F2 U2 F2 R' D' U F' L2 (14f*) U2 L2 F L R' D R2 B2 R2 D' L' R F' L2 (14f*) U2 L2 F' D' U L' B2 U2 B2 L D U' F L2 (14f*) U2 L2 F' L R' D' R2 B2 R2 D L' R F L2 (14f*) U2 L2 B D U' L F2 U2 F2 L' D' U B' L2 (14f*) U2 L2 B L' R D R2 F2 R2 D' L R' B' L2 (14f*) U2 L2 B' D' U R' B2 U2 B2 R D U' B L2 (14f*) U2 L2 B' L' R D' R2 F2 R2 D L R' B L2 (14f*) F' U L' B' F U R' F U' R B F' U' L (14f*) R' F U' R F' U L' R B' U R' B U' L (14f*) R' F' U L' F U' L' R B U' L B' U L (14f*) U' B' F R U' B R' U B F' L' U B' L (14f*) R' U F' L U' F L' R U' B L' U B' L (14f*) R' U' F R' U F' L' R U B' R U' B L (14f*) F R U' B U' B' R' F' L' U B' U B L (14f*) F U F' U L' B' R' F' U' F U' R B L (14f*) R' F' L' U B' U B L F R U' B U' B' (14f*) U2 B U2 L R B2 D L2 D' B2 L' R' U2 B' (14f*) L2 U2 L2 B D U' L F2 U2 F2 L' D' U B' (14f*) R2 U2 R2 B D U' L B2 U2 B2 L' D' U B' (14f*) L U' B' F R U' B R' U B F' L' U B' (14f*) L R' U F' L U' F L' R U' B L' U B' (14f*) B' D' R' U' R D U B2 U2 B' U B U B' (14f*) L2 U2 L2 B L' R D R2 F2 R2 D' L R' B' (14f*) R2 U2 R2 B L' R D L2 F2 L2 D' L R' B' (14f*) B' U B U B' U2 B2 D U L U' L' D' B' (14f*) R' F' U' F U' R B L F U F' U L' B' (14f*) U2 B L2 D U F2 L F2 L' F2 D' U' L2 B' (14f*) R' U B F' L' U B' L U' B' F R U' B (14f*) L R' U' F R' U F' L' R U B' R U' B (14f*) R2 U2 R2 B' D' U R' F2 U2 F2 R D U' B (14f*) L2 U2 L2 B' D' U R' B2 U2 B2 R D U' B (14f*) B D L U L' D' U' B2 U2 B U' B' U' B (14f*) U2 B' U2 L' R' B2 D' R2 D B2 L R U2 B (14f*) L F R U' B U' B' R' F' L' U B' U B (14f*) L2 U2 L2 B' L' R D' R2 F2 R2 D L R' B (14f*) R2 U2 R2 B' L' R D' L2 F2 L2 D L R' B (14f*) U2 B' R2 D' U' F2 R' F2 R F2 D U R2 B (14f*) L F U F' U L' B' R' F' U' F U' R B (14f*) B U' B' U' B U2 B2 D' U' R' U R D B (14f*) uf,rb flips: R' U' R U2 R2 D' U' F' U F D R2 U' (13f*) B2 D L U L' D' U' B2 U2 B U' B' U' (13f*) R2 D' U' F' U F D R2 U' R' U' R U2 (13f*) R2 U' R U R U2 L' B' R' B L R U2 (13f*) L F2 R' F' R' F R2 F2 L' R' U' R U (13f*) R U2 L' B' R' B L R U2 R2 U' R U (13f*) U' R' U R2 U2 L' R' B' R B L U2 R' (13f*) F2 L D R D' L' R' F2 R2 F R' F' R' (13f*) U2 L' R' B' R B L U2 R' U' R' U R2 (13f*) U2 R' U R U R2 D' F' U' F D U R2 (13f*) D B2 U' B' U' B U2 B2 D' U' R' U R (13f*) U R2 D' F' U' F D U R2 U2 R' U R (13f*) L' U' R' U L R F2 R2 F' R F R F2 (13f*) R F R F' R2 F2 L R D R' D' L' F2 (13f*) R' U' R D U B2 U2 B' U B U B2 D' (13f*) B2 U' B' U' B U2 B2 D' U' R' U R D (13f*) U' R' U L R F2 R2 F' R F R F2 L' (13f*) F2 R' F' R' F R2 F2 L' R' U' R U L (13f*) D' R' U' R D U B2 U2 B' U B U B2 (13f*) U B U B' U2 B2 D U L U' L' D' B2 (13f*) uf,db flips: L2 R2 D B' L D' B L2 R2 F' U L' F U' (14f*) U' B' U' B' U B2 U2 B' F' L' B L F U' (14f*) U' F R B R' B' F' U2 B2 U B' U' B' U' (14f*) U B U B U' B2 U2 B F R B' R' F' U (14f*) L2 R2 D' B R' D B' L2 R2 F U' R F' U (14f*) U F' L' B' L B F U2 B2 U' B U B U (14f*) L2 D B' L D' B L2 R2 F' U L' F U' R2 (14f*) L2 D' B R' D B' L2 R2 F U' R F' U R2 (14f*) L2 B D' R B' D L2 R2 U' F R' U F' R2 (14f*) L2 B' D L' B D' L2 R2 U F' L U' F R2 (14f*) L2 U F' L U' F L2 R2 B' D L' B D' R2 (14f*) L2 U' F R' U F' L2 R2 B D' R B' D R2 (14f*) D B' L D' B L2 R2 F' U L' F U' L2 R2 (14f*) D' B R' D B' L2 R2 F U' R F' U L2 R2 (14f*) B D' R B' D L2 R2 U' F R' U F' L2 R2 (14f*) B' D L' B D' L2 R2 U F' L U' F L2 R2 (14f*) U F' L U' F L2 R2 B' D L' B D' L2 R2 (14f*) U' F R' U F' L2 R2 B D' R B' D L2 R2 (14f*) F U' R F' U L2 R2 D' B R' D B' L2 R2 (14f*) F' U L' F U' L2 R2 D B' L D' B L2 R2 (14f*) L2 F U' R F' U L2 R2 D' B R' D B' R2 (14f*) L2 F' U L' F U' L2 R2 D B' L D' B R2 (14f*) L2 R2 B D' R B' D L2 R2 U' F R' U F' (14f*) F' D' F' D' F D2 F2 D' U' R' D R U F' (14f*) F' U L D L' D' U' F2 D2 F D' F' D' F' (14f*) F D F D F' D2 F2 D U L D' L' U' F (14f*) L2 R2 B' D L' B D' L2 R2 U F' L U' F (14f*) F U' R' D' R D U F2 D2 F' D F D F (14f*) D' B R F R' B' F' D2 F2 D F' D' F' D' (14f*) L2 R2 U F' L U' F L2 R2 B' D L' B D' (14f*) D' F' D' F' D F2 D2 B' F' L' F L B D' (14f*) D B' L' F' L B F D2 F2 D' F D F D (14f*) D F D F D' F2 D2 B F R F' R' B' D (14f*) L2 R2 U' F R' U F' L2 R2 B D' R B' D (14f*) R2 D B' L D' B L2 R2 F' U L' F U' L2 (14f*) R2 D' B R' D B' L2 R2 F U' R F' U L2 (14f*) R2 B D' R B' D L2 R2 U' F R' U F' L2 (14f*) R2 B' D L' B D' L2 R2 U F' L U' F L2 (14f*) R2 U F' L U' F L2 R2 B' D L' B D' L2 (14f*) R2 U' F R' U F' L2 R2 B D' R B' D L2 (14f*) R2 F U' R F' U L2 R2 D' B R' D B' L2 (14f*) R2 F' U L' F U' L2 R2 D B' L D' B L2 (14f*) B' D L U L' D' U' B2 U2 B U' B' U' B' (14f*) L2 R2 F U' R F' U L2 R2 D' B R' D B' (14f*) B' U' B' U' B U2 B2 D' U' R' U R D B' (14f*) B D' R' U' R D U B2 U2 B' U B U B (14f*) B U B U B' U2 B2 D U L U' L' D' B (14f*) L2 R2 F' U L' F U' L2 R2 D B' L D' B (14f*) A few remarks to my optimal solver program. Its input is the output-textfile of my Cube Explorer program and it optimizes the maneuvers of this textfile. It is basically the phase1 of the Cube Explorer algorithm, but with Mike Reid's idea of reducing the number of cube-states by symmetries it is possible to put the whole phase1 in a pruning table of about 69MB (Mike already did this more than a year ago in his own optimal solver program). My optimal solver needs to generate about 20% less nodes than Mike's when searching the tree and in this way does the search a bit faster. I do some more cosmetical work on the source code and then give it to the public. The hardware requirements are about the same as for Mike's solver, but it runs on the windows platform. Herbert From cube-lovers-errors@mc.lcs.mit.edu Tue Apr 27 18:00:36 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id SAA28553 for ; Tue, 27 Apr 1999 18:00:35 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Tue, 27 Apr 1999 15:07:29 -0400 (Eastern Daylight Time) From: Jerry Bryan Subject: Conjugation done right [Re: Inventing your own techniques] To: Cube Lovers Message-Id: On Thu, 08 Apr 1999 19:45:22 -0400 (EDT) Dan Hoey wrote: > Jerry Bryan wrote: > > > A process of the form Y'XY is called a conjugate, and in particular is called > > the conjugate of X by Y. Note that YXY' is also a conjugate, and in particular > > is called the conjugate of X by Y'. This can be a little confusing because a > > few books (incorrectly in my opinion) call YXY' the conjugate of X by Y. ... and Dan wrote: > > I tried to explain this a while ago, but I guess it didn't quite work. > One form of conjugate is right, and the other form is wrong, but just > which is right depends on how you write function composition. My apologies for leaving out a couple of things in my note about conjugation and commutators. But if I hadn't left them out, I doubt that we would have received Dan's very nice little message about rightward and leftward composition. I should have mentioned the rightward vs. leftward composition issue. As Dan points out, it is certainly the case that Y'XY can be correct in one book while YXY' can be correct in another. However, what I *meant* to say was that I had seen books in which (unless I was missing something obvious) the author's definition of conjugation did not correspond to the author's composition direction. All I was really trying to say was that irrespective of the author's chosen direction, YXY' and Y'XY are both conjugates. It's just that in one case, you have the conjugate of X by Y and in the other you have the conjugate of X by Y', and which is which depends on the right vs. left system the author is using. I cited the reason "X shifted by Y" as a reason for preferring the conjugate of X by Y to be Y'XY in the Cube-Lovers system. I should also have mentioned the homomorphism vs. antihomomorhism issue. There are two reasons for preferring Y'XY to YXY' for the conjugate of X by Y in the Cube-Lovers system, and regrettably I only mentioned one of them. Homomorphism is the other. Dan covered the homomorphism issue extremely well, so I would like to make some additional comments about the "X shifted by Y" interpretation of conjugation. Let us suppose that we have a maneuver A = L2 F2 L2 U L' R B R2 D2 R2 B' L R' U' which flips the uf cubie and the df cubie while leaving the rest of the cube unchanged (the rest of the cubies are said to be fixed by A). The uf and df cubies are the edge cubies which are in the middle of the top row and the middle of the bottom row of the front face, respectively. (The given maneuver for A is minimal in the face turn metric, but the exact maneuver doesn't matter for our purposes.) Suppose that instead we want to flip the ul cubie and the df cubie. A maneuver which will do so is U'AU. The U' move brings the ul cubie into the uf cubie's place while leaving the df cubie where it was. The A maneuver flips the *contents* of the uf cubicle which is now the ul cubie and flips the df cubie as usual. The U moves returns the (now flipped) ul cubie to the ul cubicle. We might write the actions of the A maneuver as follows: A: uf -> fu (flips the uf cubie) df -> fd (flips the df cubie) We might write the actions of the U and U' moves on the edge cubies as follows: U: uf -> ul U': uf -> ur ul -> ub ur -> ub ub -> ur ub -> ul ur -> uf ul -> uf Hence, if we just consider the AU part of U'AU, we have that the uf cubie goes to fu which in turn goes to lu. (If U performs uf -> ul, then it equivalently performs fu -> lu). So the uf cubie is carried to the ul cubicle and flipped to be lu. This is the general idea of what we want (to flip the cubie which is in the ul cubicle), but it is the wrong cubie in the ul cubicle. So preceding AU by U' "cancels" the movement of the cubie (and also the movement of all the other cubies) and retains only the flip of the cube. The net result is that the cubie which is flipped is shifted from being the uf cubie to being the ul cubie, as desired. A is shifted by U, which is what we wanted. It should be clear that UAU' flips the ur and the df cubies. UAU' flips the ur rather than the uf cubie, which we can describe as saying that A has been shifted by U'. Essentially any two edge cubies can be flipped by variations on this basic theme. Our next example will involve whole cube moves. We denote the whole cube move of grasping the right face and turning the whole cube clockwise and counterclockwise by c_R and c_R', respectively. So c_R' would bring the bu and fu cubies into the uf and df cubicles (respectively), A would flip them, and c_R would return them to their original locations. The net result is that the maneuver (c_R' A c_R) flips the bu and the fu cubies. It is standard on Cube-Lovers to denote the 24 rotations of the cube by C, and we might write a C-conjugate as c'Ac where c is some fixed but arbitrary element of C. c_R and c_R' are just two particular elements of C. Working with a real cube, you probably wouldn't even think about C-conjugation in this particular context -- you would just do it. That is, if your hands knew how to perform the A maneuver to flip the uf and df cubies, and if you needed to flip two edge cubies which were on opposite sides of the same face, you would just rotate the whole cube in space to bring the two cubies which needed to be flipped into the uf and df locations and then you would perform the A maneuver -- simpler to do than to describe. It is more common on Cube-Lovers to talk about M-conjugation than to talk about C-conjugation, where M is the group of 24 rotations and 24 reflections of the cube. C is a subgroup of M. So c_R and c_R' just as well elements of M as they are of C, and our (c_R' A c_R) maneuver is a good example of M-conjugation. M-conjugation lets us deal with reflections in addition to rotations, which in effect means it let's us treat clockwise and counterclockwise moves as equivalent when appropriate for symmetry purposes. But when we are dealing with whole cube rotations of a real cube, we are just dealing with C-conjugation. In the case of our A maneuver, C-conjugation means that c'Ac lets us flip any two cubies anywhere on the cube which are opposite edge cubies on the same face of the cube. Finally, whole cube rotations are a convenient way to apply the maneuver A to any face of a real cube. But mathematically, we really do not have to perform whole cube rotations. We can use C-conjugation (and more generally, M-conjugation) to apply the "same" maneuver to a different face. Consider again (c_R' A c_R). If we write out A, we get c_R' (L2 F2 L2 U L' R B R2 D2 R2 B' L R' U') c_R But the maneuver (c_R c_R') is equal to the identity, so we can insert it between each face move thusly. c_R' L2 (c_R c_R') F2 (c_R c_R') L2 (c_R c_R') U (c_R c_R') etc. Now, we can re-associate thusly so that we have the c_R-conjugate of each face turn. (c_R' L2 c_R) (c_R' F2 c_R) (c_R' L2 c_R) (c_R' U c_R) etc. Finally, if we actually perform the calculations, we discover that conjugation by c_R leaves L, L', L2, R, R', and R2 alone; it takes F, F', and F2 to U, U', and U2, respectively; it takes U, U', and U2 to B, B', and B2, respectively;, it takes B, B', and B2 to D, D', and D2, respectively; and it takes D, D', and D2 to F, F', and F2, respectively. Hence, conjugation by r_C gives us a maneuver to flip the bu and fu cubies thusly. A = L2 F2 L2 U L' R B R2 D2 R2 B' L R' U' (flip uf and df) c_R' A C_R = L2 U2 L2 B L' R D R2 F2 R2 D' L R' B' (flip bu and fu) ---------------------------------------- Jerry Bryan jbryan@pstcc.cc.tn.us From cube-lovers-errors@mc.lcs.mit.edu Tue Apr 27 18:45:51 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id SAA28703 for ; Tue, 27 Apr 1999 18:45:51 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Tue, 27 Apr 1999 13:23:11 -0700 (PDT) From: Tim Browne To: cube-lovers@ai.mit.edu Subject: Square-1 problem Message-Id: Hey there. I've got a problem with my Square-1 puzzle. A few days ago, I got a whole bunch of sugar grains stuck inside which are screwing up the mechanism big time. At first it seemed as though the it was getting better as the sugar was ground down and flushed out during each rotation, but now it's getting affected by the dampness and the sugar's turning into a pretty decent adhesive. The only real solution seems to be to take the puzzle apart, clean it, dry it, and reassemble it. Someone on rec.puzzles suggested soaking it in water, but given that the stickers are laminated paper instead of plastic and the possibility of rusting the mechanism, I'd rather not do this. Besides, I'd really like to see the internal workings of this Machiavellian torture machine. :-) If anyone on this list knows how to disassemble/reassemble the puzzle, I'd really appreciate it if you could let me know how to do it. :-) Thanks in advance. L8r. Cubic Puzzles - The SIMPLEST Solutions http://www.victoria.tc.ca/~ue451/solves.html From cube-lovers-errors@mc.lcs.mit.edu Tue Apr 27 20:31:40 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id UAA29104 for ; Tue, 27 Apr 1999 20:31:40 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Thu, 22 Apr 1999 21:48:58 -0400 (EDT) From: Nicholas Bodley Reply-To: Nicholas Bodley To: Paddy Duncan Cc: cube-lovers@ai.mit.edu Subject: Re: WD-40 as a lubricant In-Reply-To: Message-Id: Although I'm not really sure of my info, I believe WD-40 was originally a Water Displacer, hence "WD". Fairly sure it was meant to displace water from mechanisms made of metal. It's possible that its lubricating properties were secondary. As a semi-amateur mechanical technician, I gather that it's not intended to be used as a long-term lubricant. Used as intended, it seems to be a very good product. As to compatibility with plastics, I once was cleaning the inside of a computer printer that had a clear plastic rack which engaged a gear on the print head drive motor (which, amazingly enough, was on the print head itself; no kidding). I was using rubbing alcohol, as I remember. Whether it was the alcohol itself, or an adiitive to dilute it, I don't know, but the rack crystallized, cracked, and fell apart in only a few minutes. Astonishing to watch. Alcohol is usually a safe solvent for electronic work, but apparently not for some plastic mechanical parts! Of course, I had knowingly ignored the warning not to use any solvents for cleaning. Lesson from this is that there's some risk in applying liquids of unknown compatibility to some plastics. HDPE won't be bothered by any liquid you're likely to apply. Silicones (not spelled "silicons") should be safe, very likely, and Teflon powder would be. (Just don't get that powder near a cigarette or flame; decomposition products are very poisonous.) |* Nicholas Bodley *|* Autodidact & Polymath * Electronic Tech. (ret.) |* Waltham, Mass. *|* ----------------------------------------------- |* nbodley@tiac.net *|* |* Amateur musician *|* From cube-lovers-errors@mc.lcs.mit.edu Tue Apr 27 21:05:47 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id VAA29184 for ; Tue, 27 Apr 1999 21:05:47 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu From: "Chris and Kori Pelley" To: "Tim Browne" , Subject: RE: Square-1 problem Date: Tue, 27 Apr 1999 20:50:46 -0400 Message-Id: > -----Original Message----- > From: Tim Browne [mailto:ue451@victoria.tc.ca] > of this Machiavellian torture machine. :-) If anyone on this list knows > how to disassemble/reassemble the puzzle, I'd really appreciate it if you I know how to disassemble it! First you get it into the original shape that it comes in, and turn 180 degrees. Then you twist it about 22 degrees and pry out one of the dart (edge) pieces. This can best be seen in a diagram, and I have a rough sketch at this address: http://members.home.net/chrisandkori/sq-disassem.jpg Once one piece is out, they all come out easily, similar to Rubik's Cube. Putting it back together is similar-- do the same thing in reverse. The mechanism is really neat! Chris Pelley ck1@home.com From cube-lovers-errors@mc.lcs.mit.edu Fri Apr 30 20:25:46 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id UAA07983 for ; Fri, 30 Apr 1999 20:25:46 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Mail-from: From cube-lovers-request@life.ai.mit.edu Fri Apr 30 07:35:29 1999 Date: Fri, 30 Apr 1999 12:33:43 +0100 From: David Singmaster To: whuang@ugcs.caltech.edu Cc: cube-lovers@ai.mit.edu Message-Id: <009D768E.2615E470.8@ice.sbu.ac.uk> Subject: RE: Reinventing (and some edge-flipping techniques) I've just spent three days being a Rubik's Cube demonstrator at a trade fair, using the method given the my Step by Step solution in the middle of the fifth edition of my Notes. The problems that Wei-Hwa Huang has described are ones that I found in trying to develop an easy method. Basically there is no 'simple' way to flip edges, where 'simple' means easily understood and remembered. There are simple ways to move edges, move corners and twist corners. Consequently I decided to get the edge orientations correct at the beginning of work on the last face, so that I wouldn't have to worry about what happened to the rest of the face. In case you haven't got my notes at hand, I used BLUL'U'B' which is a simple conjugate of the commutator [L,U]. This exchanges the four U corners as two pairs of exchanges and cycles three U edge, but effectively flips two of them on the way. Using the inverse process BULU'L'B' does the same thing, but one of them effectively flips two adjacent edges and the other flips two opposite edges. Two applications will flip all four edges. Then we know simple processes which do 3-cycles or pairs of 2-cycles of edges, preserving orientation, or of corners and we have simple processes for twisting corners. So we could carry out these three steps in any order giving six possible algorithms and I'm pretty sure I received examples of all of these. Indeed, of one considers doing the last face as having a fourth stage of orienting edges, there are 24 possible algorithms and at one point I was classifying algorithms into these 24 cases. I don't think I kept up with this long enough to have all 24 cases, but I expect all of them exist! Some personal comments and recollections, much of which is in my Notes. The ideas of monotwist and monoflip, though blindingly obvious, took well over a year to emerge! Despite the fact that lots of quite bright mathematicians were working on the cube (e.g. Conway, Penrose, Rubik), I remember first hearing about the idea in Jan 1980 (?) from Peter McMullen who said they were using the idea at Cambridge. At first it seemed unreasonable as we generally were looking for moves that only affected the U face and the mono-moves are almost all elsewhere. However once I realised that the idea gives a way of building simple moves, I realised that the commutator [F,R] was a mono-move in the L face and its square was a mono-twist in the L face. The Cambridge group had been using shorter, but less simple, moves. With these mono-moves, it was now pretty easy to build the algorithm that is my Step by Step solution and I think I did it within a few weeks as I recall the 5th ed. of my Notes was produced by March. (Remebering dates from 20 years ago is always a bit dodgy - check what's in the Notes, which I don't have a copy of here.) DAVID SINGMASTER, Professor of Mathematics and Metagrobologist School of Computing, Information Systems and Mathematics Southbank University, London, SE1 0AA, UK. Tel: 0171-815 7411; fax: 0171-815 7499; email: zingmast or David.Singmaster @sbu.ac.uk From cube-lovers-errors@mc.lcs.mit.edu Mon May 3 13:47:11 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id NAA17378 for ; Mon, 3 May 1999 13:47:10 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <372A817B.5825@zeta.org.au> Date: Sat, 01 May 1999 14:22:19 +1000 From: Wayne Johnson Reply-To: sausage@zeta.org.au To: cube-lovers@ai.mit.edu Subject: Rubiks Magic Strategy Rules Does anyone know how to play the Rubiks Magic Strategy game? I just bought it second hand and while there's some rough instructions on the back, the manual is missing and we don't know how to start off. I'd appreciate any help. Thanks, Wayne Johnson, www.zeta.org.au/~sausage From cube-lovers-errors@mc.lcs.mit.edu Mon May 3 15:29:40 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id PAA17694 for ; Mon, 3 May 1999 15:29:40 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Sat, 1 May 1999 13:37:32 -0400 (EDT) From: der Mouse Message-Id: <199905011737.NAA19339@Twig.Rodents.Montreal.QC.CA> To: cube-lovers@ai.mit.edu Subject: Re: Reinventing (and some edge-flipping techniques) > Basically there is no 'simple' way to flip edges, where 'simple' > means easily understood and remembered. On what point does the Spratt wrench fail? That's always been my favored edge-flipper. (On the 3-Cube, that is; when solving a dodecehedral puzzle I bought from Mr. Bandelow, I was forced to develop other edge-flippers, and the one I ended up with maps easily onto the Cube. In 3-Cube terms, it's based on R F' R' F, which induces a 3-cycle (fr,fd,dr) on edges. By applying this, rotating the cube 120 degrees about its rfd-lbu long diagonal, and applying the inverse, you can get a two-edge flipper at the price of disturbing four corners. The dodecahedron I solve by doing edges first with this procedure, then using (the dodecehedral analog of) (R F' R' F) 3, which leaves edges alone and produces two corner swaps, to fix up the corners. But when solving the 3-Cube, I still find the Spratt wrench more convenient.) What I'd like is a puzzle like the dodecahedron, but with an additional turning mode: 72 degrees on a cut through the center. The puzzle as it stands has face-cut lines that make it clear such turns are conceivable, though designing a mechanism for them would be interesting. Perhaps when we get force-reflecting datagloves.... :-) der Mouse mouse@rodents.montreal.qc.ca 7D C8 61 52 5D E7 2D 39 4E F1 31 3E E8 B3 27 4B From cube-lovers-errors@mc.lcs.mit.edu Mon May 3 17:26:27 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id RAA18386 for ; Mon, 3 May 1999 17:26:27 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <199905031954.VAA24148@bednorz.get2net.dk> From: "Klodshans" To: sausage@zeta.org.au Date: Mon, 3 May 1999 20:52:12 +0000 Subject: Re: Rubiks Magic Strategy Rules Reply-To: klodshans@get2net.dk Cc: cube-lovers@ai.mit.edu In-Reply-To: <372A817B.5825@zeta.org.au> Wayne wrote: > Does anyone know how to play the Rubiks Magic Strategy game? I just > bought it second hand and while there's some rough instructions on the > back, the manual is missing and we don't know how to start off. The game is similar/equivalent to Rubik's Eclipse. The rules are as follows: ------------------------------------------------------------------------- Set Up: At the beginning of the game, the board is empty. One player takes the 8 circle pieces, and the other player takes the 8 square pieces. Objective: To win the game you must get 3 of your game pieces of the same color (black or silver) in a "locked" row, either vertically, horizontally or diagonally. A row of 3 is "locked" when none of the game pieces in it can be flipped onto an adjacent square, because all the adjacent squares are occupied. Rules of play: Players alternate in taking turns. The Circle player starts the game by placing a circle piece, either side up, somewhere on the board. Subsequently, starting with the Square players's first move, each player's turn consist of two actions: Flip and Place, _in that order._ Flip: On each turn, the player must flip _any_ one of their opponent's pieces already on the board. Flipping a piece means moving it to any adjacent vacant square (horizontally or vertically, but not diagonally) while _reversing_ the sides. The grey becomes black and vice versa. Place: Each player must, on each turn, then place one of their pieces, either side up, on any vacant square on the board, _even if this results in a winning line for the opponent._ Note: A player _must_ flip an opponent's piece, even if this may result in a winning line for the opponent. If it is not possible to flip any of their opponent's pieces, the player still goes on to placing a piece of their own. Play goes on in this manner, with each player first flipping any of their opponent's pieces (not necessarily the last one placed), before placing a piece of their own. This means once placed on the board,, players will never touch their own pieces again, but they can change position and color of their opponent's pieces. A player may leave an opponent's row of 3 without loosing the game (provided it is not "locked"). Winning the Game: The first player to archieve a "locked" vertical, horizontal, or diagonal line of 3 of their _own_ game pieces, all with the same color (black or silver), is the winner. A "locked" line is one in which none of the 3 game pieces can be flipped because all the adjacent squares are occupied. If the game continues until the last piece is placed on the board, and both players end up with a winning line, or neither player has won, the game is a draw. ------------------------------------------------------------------------- ______________________________________ Philip K E-mail: philipk@bassandtrouble.com E-mail: klodshans@get2net.dk web: http://hjem.get2net.dk/philip-k From cube-lovers-errors@mc.lcs.mit.edu Tue May 4 15:15:59 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id PAA22863 for ; Tue, 4 May 1999 15:15:59 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <009301be95b5$fc951340$70c4b0c2@home> From: roger.broadie@iclweb.com (Roger Broadie) To: Cc: "David Singmaster" Subject: Re: Reinventing (and some edge-flipping techniques) Date: Mon, 3 May 1999 23:40:28 +0100 David Singmaster wrote (1 May 1999) >Consequently I decided to get the edge orientations correct at the >beginning of work on the last face, so that I wouldn't have to worry >about what happened to the rest of the face. In case you haven't got >my notes at hand, I used BLUL'U'B' which is a simple conjugate of the >commutator [L,U]. When I read David Singmaster's algorithm in his Notes on Rubik's Magic Cube I thought his idea of curing the orientations of the edge-piece before positioning them was a great one, and adopted it in my own algorithm. One may be able to get away with only 6 turns to cope with the orientation, which is quite a gain on the number of turns needed if one takes the obvious route and orients once the pieces are in position. I then went on to apply the same principle to the corner pieces, by orienting them next, which can be done in 7 or 14 face turns by selecting the first of the following (for three twists) or the first followed by the second suitably applied (for two or four twists): F U2 F' U' F U' F' L' U2 L U L' U L These processes, which I mentioned in my last post, move the corner pieces as well as twist them, and also move the edge pieces but preserve their orientation. So, if applied after the edge pieces have been oriented but not positioned, they get the top face of the cube the right colour, and it can then be solved by orientation-preserving moves of the edge and corner pieces. I may be rather bad at perceiving patterns, but I find the simplification of having to look only at the faces of the top-layer pieces that lie in the side faces of the cube in order to work out what needs to go where enough of an advantage to make this order of the stages worthwhile even if it did not take fewer moves in total. Roger Broadie From cube-lovers-errors@mc.lcs.mit.edu Tue May 4 16:04:16 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id QAA22965 for ; Tue, 4 May 1999 16:04:15 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <009201be95b5$f9cc7d60$70c4b0c2@home> From: roger.broadie@iclweb.com (Roger Broadie) To: Cc: "Frederick W. Wheeler" Subject: Re: Inventing your own techniques Date: Mon, 3 May 1999 23:40:04 +0100 I'd like to return to Fred Wheeler's interesting question (30 March 1999), for its own sake and partly as a prelude to my next posting. The processes I originally used to solve the cube - before I had been introduced to commutators by David Singmaster's little blue book - were based on a principle that formed itself in my head as I explored the cube. I called it "Out and back by a different route". If pieces were moved away from their original position by one process and then restored by a different one, the result would be a process that would only move pieces other than those moved out and back. Then it struck me that the different routes could be based on the obvious processes used in a bottom-up algorithm to move a bottom corner piece into position from the top corner vertically above it, depending on the orientation of the piece. Thus, taking the DLF piece as the one subject to the out-and-back movement, the out trip would take the piece to FLU using front face turns, and the return route would bring it back using left face turns: F U' F'. U' L' U L (1) This process, I discovered, moved an edge piece out of the top layer into the middle, UB > FL, but had no other effect on the middle layer. So, at once, it formed the basis for solving the middle layer. Besides inverses and reflections there is one other essentially different process of this type involving the DLF corner. It takes the piece to the far corner RUB on the out trip: F U2 F' . U2 L' U' L (2) And it too moves just one edge piece out of the top into the middle layer, from a different source position but to the same target position as (1), UF > FL. We can now repeat this approach, using these two processes and their inverses and reflections to take a piece out of the top layer and then return it. That generates a set of upper-layer processes that led me to my first solution. It was not very efficient, but one of these process is very attractive. It results from following (2) above with the reflection of (1) in the diagonal plane FL-BR: F U2 F' U2 L' U' L . L' U L U F U' F' = F U2 F' U' F U' F' (3) It is short, because of the cancellation, very easy to do, because all the turning can be done with one hand, and has a very useful cycle pattern, with an untwisted 3-cycle of edge pieces and a twisting pair of swaps of corner pieces. That leads on to another basic technique: looking at the cycle pattern of a process and seeing what can be done to suppress or simplify some of the cycles. If we take (3) above, by combining it with its reflection suitably applied, we can suppress either the movement of the edge pieces to give a double twist of the corners (4), or the movement of the corner pieces to give an untwisted edge 3-cycle (5): F U2 F' U' F U' F' B' U2 B U B' U B UF(L-, R+) (4) F U2 F' U' F U' F' L' U2 L U L' U L U(F, L, R) (5) There are shorter alternatives, of course, but (4) remains my favourite for the purpose, done as F U2 F' U' F U' F' [twist whole cube parallel to U'] L' U2 L U L' U L Of course, taking powers of a process is one way selectively to eliminate constituent cycles, and (1) above, if done four times, is a triple corner twist, because the edge pieces move through a 4-cycle which is eliminated, one corner piece undergo a twist with no change of position, which is preserved, and the other two undergo a twisted 2-cycle that leaves them in position but twisted. But powers tend to be rather lengthy, as this example illustrates. Then one can look for patterns in processes and apply them elsewhere. (3) above can be thought of as taking DLF up to the top and then round and home again, with the + and - turns of the F face cancelling out. One other process I discovered on the cube using this principle is the following, where M is the turn of the centre slice parallel to R: M2 U M2 U2 M U M2 (UF,UB) (UR, UL) (6) And the structure of (3) transfers directly to the tetrahedron as F U F' U F U F' 3-cycle round the vertical axis and the dodecahedron as F U2 F' U' F U' F' and F U2 F' U F U2 F' edge 3-cycles + corner double-swaps In these I am taking the puzzle to be sitting on a table, with U being the vertex (for the tetrahedron) or face (for the dodecahedron) at the top and F being a vertex or face adjacent to the top pointing towards you. For a discussion of designing 3-cycles using commutators and conjugates, see the message I posted in November 1997, which looked at processes of the type [P, TQT'] where P and Q are turns of layers that are parallel to one another, and T is a turn of a layer transverse to P and Q. These processes yield a result that can be expressed as second-level commutation, as mentioned by David Singmaster. Roger Broadie From cube-lovers-errors@mc.lcs.mit.edu Tue May 4 16:30:21 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id QAA23035 for ; Tue, 4 May 1999 16:30:20 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu From: WaVeReBeL@webtv.net Date: Mon, 3 May 1999 22:17:36 -0700 (PDT) To: Cube-Lovers@ai.mit.edu Subject: Attention Star Wars Fans! Message-Id: <2346-372E82F0-11792@postoffice-123.bryant.webtv.net> I just got back from Target & saw a new Rubik's product. It is a 2x2x2 puzzle of Darth Maul's head! (he's from Star Wars: Episode 1) It comes in the usual cardboard & plastic box except it is colored in Black & red. I think it is $14.99. I haven't had a chance to buy one and try out the mechanism though, because I spent all my money hoarding the action figures.... -Alex- May the force be with you... From cube-lovers-errors@mc.lcs.mit.edu Wed May 5 14:09:02 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id OAA26136 for ; Wed, 5 May 1999 14:09:01 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Tue, 4 May 1999 21:56:22 +1000 (EST) Message-Id: <199905041156.VAA09100@pcug.org.au> Content-Type: text/plain; charset="us-ascii" To: Cube-Lovers@ai.mit.edu From: pfoster@pcug.org.au (Peter Foster) Subject: Re: Speed cubing results - March 99 >Almost everybody responded w/ a different preview time (anywhere from no >preview to 15 seconds). People like me who started cold had a >disadvantage to those who had a preview. A 15 second preview sounds >good to me. This gives enough time to familiarize oneself w/ the cube, >look for pieces, and plan out the first few moves. I've been timing >myself cold which means much time is wasted at the beginning. Having a >preview helps a lot. I would prefer that there is no preview time. Solving the cube isn't just turning the faces, it's also deciding which faces to turn. Surely, time spent in examining the cube is therefore part of the solving time. >When it comes to averages, I guess there is no standard. I agree w/ >disregarding the high & low extremes though. They can distort the >average (arithmetic mean). This should give a more accurate >representation. Also, the more entries calculated into the average the >better. I used to do a run of 11, then take the median (middle) value. Cheers _______________________________________________________________ Peter Foster pfoster@pcug.org.au [Moderator's note: While would I avoid previews in principle, I understand that the official contests were carried out with a free preview period. It seems unavoidable that we qualify all our records with the conditions under which they are measured--with or without preview; best score, average, or median; by sight or by touch; in air or underwater; solo or mixed doubles; etc. --Dan ] From cube-lovers-errors@mc.lcs.mit.edu Wed May 5 14:48:26 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id OAA26205 for ; Wed, 5 May 1999 14:48:25 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu To: cube-lovers@ai.mit.edu From: whuang@ugcs.caltech.edu (Wei-Hwa Huang) Subject: Algorithm for the Antislice Group Date: 4 May 1999 14:11:57 GMT Organization: California Institute of Technology, Pasadena Message-Id: <7gmv7d$ncj@gap.cco.caltech.edu> In a small fit of playing around last week, I finally worked out a method of solving the Antislice Group. Of course, God's Algorithm is known, but since it's pretty hard for me to memorize it, here's mine. For those of you that don't know, the antislice group is all configurations that the cube can be in, provided that the only move you make is FB, with rotations and reflections. So, with fixed centers, the only allowed moves are FB, RL, and UD. I'll abbreviate these to F, R, and U. I'll even use the "clockwise quarter turn" metric, which means that F' = FFF is three moves, not one. Okay. The algorithm has four steps: A. Get the cube to be a subset of the half-face turn group. (up to 4 moves) B. Match the corners. (up to 6 moves) C. "HOt HOt HOt" (double-slice group). (up to 12 moves) D. Solve the cube. (up to 6 moves) This is a maximum of 28 moves. In practice, one can often avoid future extra moves by modifying the algorithm slightly. A. Get the cube to be a subset of the half-face turn group. This means that the UD faces only contain the UD colors, the FB faces only contain the FB colors, and the RL faces only contain the RL colors. Here's how to do it: A0. Pick any set of colors on opposite face centers. Let's call it the color "grud". (For instance, if blue is opposite white on the solved cube, "grud" can mean "blue or white".) We'll try to solve "grud" first. A1. Find a face with grud at the corners and reorient the cube so that it is the U face. A2. If the U center is grud but none of the U edges are grud, perform R, repeat step A1, and go to step A5. A3. If the U center is not grud but all of the U edges are grud, then either the F center is grud or the R center is grud. If the F center is grud, perform F; if the R center is grud, perform R. Then repeat step A1 and go to step A5. A4. If the U center is grud and two of the U edges are grud (so there is a grud "H" shape on the U side), then either F has two grud edges or R has two grud edges. If the former, perform F; if the latter, perform R. Then repeat step A1 and go to step A6. A5. If the U center is not grud, two of the U edges are grud, and every face has some grud on it, perform U and go to step A7. A6. If the U center is not grud and none of the U edges are grud, either the F center is grud or the R center is grud. If the F center is grud, perform F; if the R center is grud, perform R. Then repeat step A1 and go to step A7. A7. If the U center is not grud, two of the U edges are grud, and either F or R does not have grud on it, then perform F or R (whichever one did not have grud on it), repeat step A1, and go to step A8. A8. The U face should now be all grud. If the other four faces are "unsolved" (have colors of adjacent faces), perform U and it should be solved. B. Match the corners. In other words, does each face have four corners of the same color? If so, go on to step C. Otherwise, at least one face will have four corners of the same color. Orient the cube so that it is the U face, and then perform FRFRFR. This should match the corners. C. "HOt HOt HOt" (double-slice group) This step is to get rid of any face that looks like an "H" (all one color except for two opposite edges), an "O" (all one color except for the center), or a "t" (all one color except for the corners). This may have to be done up to three times, and after they are removed the cube should be in the double-slice group. Orient the cube so that the top face is "HOt". Then, perform FRRF. Repeat until no faces are "HOt". D. Solve the cube. The cube should now be in a very easy to solve state, if not already solved already. If the cube is not already solved, there must be some corner which does not match an edge next to it. Orient the cube so that said corner is the UFR corner and the edge is the RU edge. Then, perform FF. Repeat until the cube is solved. -- Wei-Hwa Huang, whuang@ugcs.caltech.edu, http://www.ugcs.caltech.edu/~whuang/ --------------------------------------------------------------------------- ..make lemonade and hope it also gives you a source of protein and vitamin A. From cube-lovers-errors@mc.lcs.mit.edu Fri May 7 11:26:58 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id LAA04662 for ; Fri, 7 May 1999 11:26:57 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Fri, 7 May 1999 12:27:25 +0100 From: David Singmaster To: mouse@rodents.montreal.qc.ca Cc: cube-lovers@ai.mit.edu Message-Id: <009D7C0D.6D45DA64.17@ice.sbu.ac.uk> Subject: Re: Reinventing (and some edge-flipping techniques) Der Mouse's message reminds me of a point which I had meant to include. In my algorithm, most of the moving involves just two adjacent faces, which I find easier to remember and to carry out. The Spratt wrench (which I don't really know, so I'll have to try it, BTW, who was/is Spratt?) doesn't have quite this simple structure. DAVID SINGMASTER, Professor of Mathematics and Metagrobologist School of Computing, Information Systems and Mathematics Southbank University, London, SE1 0AA, UK. Tel: 0171-815 7411; fax: 0171-815 7499; email: zingmast or David.Singmaster @sbu.ac.uk From cube-lovers-errors@mc.lcs.mit.edu Fri May 7 17:25:58 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id RAA06644 for ; Fri, 7 May 1999 17:25:58 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu From: "Chris and Kori Pelley" To: "Cube Lovers" Subject: Darth Maul 2x2x2 Cube Date: Fri, 7 May 1999 08:05:46 -0400 Message-Id: I've put a couple photos of the new Darth Maul Cube on my home page, in case anybody hasn't seen it yet. The cube turns very smoothly, and is basically just an oversized 2x2x2. I was surprised to discover they are made by OddzOn. http://www.chrisandkori.com/darthmaul.htm Chris Pelley ck1@home.com From cube-lovers-errors@mc.lcs.mit.edu Fri May 7 20:53:13 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id UAA07387 for ; Fri, 7 May 1999 20:53:13 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu From: WaVeReBeL@webtv.net Date: Fri, 7 May 1999 13:02:42 -0700 (PDT) To: Cube-Lovers@ai.mit.edu Subject: Thanks all! Message-Id: <9973-373346E2-9532@postoffice-121.bryant.webtv.net> Hello all, I just want to say thanks to all the great help & advice everyone has given me. I wish I had time to E-mail everyone personally. I'm so glad I found out about this mailing list & all of the great web pages. (Yay internet!) You have helped me reach my goal of beating the 30 second barrier. It all started w/ a little book fair where I picked up "The Simple Solution to Rubik's Cube" by James G. Nourse for $.25 last year. It then snowballed, and I learned everything I could about the cube, spent tons of money on different puzzles, & put a lot of time into it. After the first 4 months of intense cubing, my records are: LAYER METHOD 30" best 36" average CORNERS FIRST 26" best 37" average I've been on a break for a while now ever since my hands started to hurt. Already I've started to loose my edge, & forgot some of the moves. I'm slower now, but I can still solve it under 45" guaranteed. When the summer comes, school will be over and I'll have more free time to train again & hopefully reach my new goal of consistently finishing under 30". For now I'll give my hands a well deserved rest. I just bought that book for a quarter on a whim. Who knew a little cube would have such a great impact in my life. Thanks again for all of the support. -Alex Montilla- From cube-lovers-errors@mc.lcs.mit.edu Fri May 7 21:12:30 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id VAA07476 for ; Fri, 7 May 1999 21:12:30 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <372B283E.428F@hrz1.hrz.tu-darmstadt.de> Date: Sat, 01 May 1999 18:13:50 +0200 From: Herbert Kociemba Reply-To: kociemba@hrz1.hrz.tu-darmstadt.de To: Cube Lovers Subject: Optimal solver for Windows now available I finished my optimal solver program for Windows now. It optimizes the maneuvers written to the output file of the Cube Explorer program. I am quite satisfied with the performance. I searches 1,100,000 nodes per second on a P350. 90MB of RAM should be enough (though I run it on a machine with 256MB). A depth 17 search on random cubes typically takes less than one hour. I made a test run with 10 random cubes and optimal solutions for all of them were found within 35 hours (6 had length 18 and 4 had lenght 17). The exe file and the source code are available at http://home.t-online.de/home/kociemba/cube.htm Herbert Kociemba [ Moderator's note: This is also available in ftp://ftp.ai.mit.edu/pub/cube-lovers/contrib/opt09.zip If you've been waiting for the cube-lovers archives, the server is serving again. -- Dan ] From cube-lovers-errors@mc.lcs.mit.edu Tue May 11 13:03:08 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id NAA20945 for ; Tue, 11 May 1999 13:03:08 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu From: WaVeReBeL@webtv.net Date: Fri, 7 May 1999 13:52:12 -0700 (PDT) To: Cube-Lovers@ai.mit.edu Subject: "Negative" Turning Message-Id: <11000-3733527C-9578@postoffice-123.bryant.webtv.net> When the cube locks up on me, I have to turn the layer in the opposite of the desired direction anywhere from a little jiggle to over 90 degrees in order to straighten out the pieces. I'm sure all of you have to do this too. I'm calling it "negative" turning. Is there another term for this? I do this rather unconsciously now. All this locking up wastes time, especially with numerous unsuccessful efforts. I'm guessing when fractions of seconds count, time spent fixing could be spent doing more turns. I'm wondering, do any of you perform negative turning before starting any turns to prevent a lock up before it starts rather than try and fix it after it happens? Or do you incorporate these negative movements within combos in anticipation of frequent sticky situations? When practicing frequently used combos I have incorporated negative turns into them with some success. Does anyone do this to all moves? It would take a long time to achieve this w/ all of my combos, so I'm looking for someone who has. Would it take longer to do combos w/ negative moves "built in", or just fix the problem when in comes. Or maybe there is someone out there who makes turns so accurately he never experiences this. Thanks. -Alex Montilla- From cube-lovers-errors@mc.lcs.mit.edu Tue May 11 15:16:14 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id PAA21349 for ; Tue, 11 May 1999 15:16:14 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Sender: davidb@u.washington.edu Message-Id: <373875FF.5EBFA011@iname.com> Date: Tue, 11 May 1999 11:25:03 -0700 From: David Barr To: WaVeReBeL@webtv.net, cube-lovers@ai.mit.edu Subject: Re: "Negative" Turning References: <11000-3733527C-9578@postoffice-123.bryant.webtv.net> The reason that "negative turning" is necessary is because the prior turn did not get the faces lined up exactly. Let's look at the sequence "R U". You turn the right face a quarter turn, then you turn the upper face a quarter turn. If you make the R turn a fraction of inch too far, then the cube will correct itself when you try to make the U turn. But if you make the R turn a fraction of an inch too short, the upper face will lock if you first try to turn it clockwise. The "negative turn" doesn't lock up because it is counterclockwise. When you then start to turn the U face counterclockwise it straightens up the R face so that the U face is free to turn in either direction. "Negative turning" is sometimes necessary, but a better solution is to always either overturn or underturn by a fraction of an inch depending on which way you plan on making the next turn. So if you are planning on turning "R U", make sure your "R" is a fraction of an inch past a quarter turn, but if you are planning to turn "R U'", make sure your "R" is a fraction of an inch short of a quarter turn. David From cube-lovers-errors@mc.lcs.mit.edu Tue May 11 17:17:19 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id RAA21707 for ; Tue, 11 May 1999 17:17:19 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Thu, 6 May 1999 12:41:20 -0700 From: Gene Johannsen To: Wei-Hwa Huang Cc: cube-lovers@ai.mit.edu Subject: Re: Algorithm for the Antislice Group In-Reply-To: <7gmv7d$ncj@gap.cco.caltech.edu> Message-Id: On 4 May 1999, Wei-Hwa Huang wrote: > [snip] > > B. Match the corners. > > In other words, does each face have four corners of the same color? If so, > go on to step C. Otherwise, at least one face will have four corners of > the same color. Orient the cube so that it is the U face, and > then perform FRFRFR. This should match the corners. I am having problems with this step. My cube is in a configuration that this maneuver does not solve: YYY YYG <- Back face GGG BBW ORO BBW ROR BBB ROR WWW ORO <- Bottom face BWW ORO BWW ROR YYY YGG <- Front face GGG FRFRFR does not solve the corners for this position. gene From cube-lovers-errors@mc.lcs.mit.edu Wed May 12 16:54:45 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id QAA25198 for ; Wed, 12 May 1999 16:54:45 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu To: cube-lovers@ai.mit.edu From: whuang@ugcs.caltech.edu (Wei-Hwa Huang) Subject: Re: Algorithm for the Antislice Group Date: 11 May 1999 22:54:04 GMT Organization: California Institute of Technology, Pasadena Message-Id: <7hacec$rs6@gap.cco.caltech.edu> References: Gene Johannsen writes: > I am having problems with this step. My cube is in a > configuration that this maneuver does not solve: As I e-mailed Gene, I do not believe his configuration is part of the anti-slice group -- would any members care to give a quick heuristic to determine if a cube is in the anti-slice group? -- Wei-Hwa Huang, whuang@ugcs.caltech.edu, http://www.ugcs.caltech.edu/~whuang/ --------------------------------------------------------------------------- ..make lemonade and hope it also gives you a source of protein and vitamin A. From cube-lovers-errors@mc.lcs.mit.edu Wed May 12 18:20:43 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id SAA25497 for ; Wed, 12 May 1999 18:20:43 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Wed, 12 May 1999 00:19:21 -0400 (EDT) From: Nicholas Bodley To: WaVeReBeL@webtv.net Cc: Cube-Lovers@ai.mit.edu Subject: Re: "Negative" Turning In-Reply-To: <11000-3733527C-9578@postoffice-123.bryant.webtv.net> Message-Id: Sorry to say (because it's no longer made), the Deluxe Cube from Ideal had differently-shaped details inside so that with moderate amounts of misalignment, it would self-align as you began a move. It also had plastic colored tiles attached. "Negative" turning seemed to be unnecessary if you used ordinary care, but I wasn't trying for speed. |* Nicholas Bodley *|* Autodidact & Polymath * Electronic Tech. (ret.) |* Waltham, Mass. *|* ----------------------------------------------- |* nbodley@tiac.net *|* Keep smiling! It makes people wonder |* Amateur musician *|* what you've been up to. -------------------------------------------------------------------------- From cube-lovers-errors@mc.lcs.mit.edu Tue May 18 20:21:45 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id UAA20507 for ; Tue, 18 May 1999 20:21:45 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Reply-To: From: "John Burkhardt" To: Subject: "The" Hungarian cube ?? Date: Tue, 18 May 1999 05:41:10 -0400 Message-Id: <000301bea112$904d7070$3cca8018@octopod.ne.mediaone.net> I recently bought a rubik's cube from someone. It was in a blue cardboard box that has Hungarian all over it. The closest thing to a logo says: "Politoys" and under that it reads: Hungary Budapest. On one side of the box there is a long three paragraph description which I can't read and it's signed by E. Rubik. When I opened it up I found a cube that looks in every way identical to the Ideal version of the rubik's cube. Same colors. Same "Rubik's cube" logo in the center white square. Does anyone know if this is, in fact, a very early version of the cube or did someone put an Ideal cube in this box? What was the first and original cube? The guy who sold it to me is also very curious. Could it be that Ideal took over and this is a later production that was begin sold in Hungary? I'm wondering then why there is no indication of "Ideal" anywhere on it. -John [ See ftp://ftp.ai.mit.edu/pub/cube-lover/cube-mail-0.gz for discussions of early Hungarian and American cubes. -- Dan ] From cube-lovers-errors@mc.lcs.mit.edu Tue May 18 20:55:53 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id UAA20761 for ; Tue, 18 May 1999 20:55:51 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Tue, 18 May 1999 19:39:16 +0100 From: David Singmaster To: cube-lovers@ai.mit.edu Cc: chrisit@seventowns.com Message-Id: <009D84EE.93F50834.1@ice.sbu.ac.uk> Subject: Speed cubing A UK TV program is looking for a speedy cubist. I suppose anything under a minute would be considered speedy. Is there anyone in the UK who has this kind of current speed? If so, could they email chrisit@seventowns.com and send a copy to me since I've had some other possible inquiries. DAVID SINGMASTER, Professor of Mathematics and Metagrobologist School of Computing, Information Systems and Mathematics Southbank University, London, SE1 0AA, UK. Tel: 0171-815 7411; fax: 0171-815 7499; email: zingmast or David.Singmaster @sbu.ac.uk From cube-lovers-errors@mc.lcs.mit.edu Tue May 18 21:21:14 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id VAA20836 for ; Tue, 18 May 1999 21:21:13 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu From: "Jason Werner" Message-Id: <9905181213.ZM1550@sgi.com> Date: Tue, 18 May 1999 12:13:44 -0700 To: Cube-Lovers@ai.mit.edu Subject: Star Wars mania Picked this up at Target a couple days ago: http://reality.sgi.com/mrhip/dmrc.jpg If you haven't seen it in person, it appears to be just a 2x2x2. Haven't opened the package; don't plan to. :) -Jason -- Jason K. Werner Phone: 650.933.9393 Systems Administrator Fax: 650.932.9393 SGI, CSBU Division Pager: 650.317.7954, mrhip_p@sgi.com mrhip@sgi.com URL: http://reality.sgi.com/mrhip [ Moderator's note: This is the toy Chris Pelley mentioned a few days ago, but pictured in a box. ] From cube-lovers-errors@mc.lcs.mit.edu Wed May 19 13:49:11 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id NAA23513 for ; Wed, 19 May 1999 13:49:10 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <617C1EFE73F1D211A6700060B03CB9391BAA@HP_NETSERVER> From: Christine Trussell To: Subject: Customised Cubes Date: Wed, 19 May 1999 15:59:20 +0100 Have you customised your cube? If so please let me know what you have done to it to make it run faster, smoother etc. We will pay for this information. Thanks and look forward to hearing from you Regards, Chrisi Trussell Seven Towns Ltd 7 Lambton Place London W11 2sH Tel: 44 171 727 5666 Fax: 44 171 727 5666 Email: ChrisiT@SEVENTOWNS.COM [Moderator's note: This is more hucksterish than I usually pass through to cube-lovers, but in case anyone wants to know who's in the cube biz, this is one of them. She also wants to buy Rubik's Revenges. (Who doesn't? I've gotten a dozen such requests, either ignored or answered with the explanation that no one is selling them now except in one-off auctions. Be sure to let cube-lovers know if that changes.) Anyway, this is Chrisi's ad; if you want to read more ads from her, her addresses are above; the ads won't run on cube-lovers. --Dan ] From cube-lovers-errors@mc.lcs.mit.edu Thu May 20 13:56:11 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id NAA00253 for ; Thu, 20 May 1999 13:56:11 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <37440E6E.244C@zeta.org.au> Date: Thu, 20 May 1999 23:30:22 +1000 From: Wayne Johnson Reply-To: sausage@zeta.org.au To: cube-lovers@ai.mit.edu Subject: Huge Cube! My cousin came back from england on his recent trip and brought me home a cube. Most cubes are 57mm. This one is.. wait for it.. 90mm. Has anyone else got one of these? I'd never heard or read about one before. It's a tile cube that is of average quality. It was bought at a market near a place called Kensington. Wayne Johnson www.zeta.org.au/~sausage From cube-lovers-errors@mc.lcs.mit.edu Thu May 20 17:04:55 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id RAA01421 for ; Thu, 20 May 1999 17:04:54 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <37441ED1.2C5B3F5E@binghamton.edu> Date: Thu, 20 May 1999 10:40:17 -0400 From: Mirek Goljan Organization: SUNY Binghamton To: cube-lovers@ai.mit.edu Subject: Re: "The" Hungarian cube ?? References: <199905201405.QAA28449@ms.globe.cz> The cube is most likely the original Rubik's cube made in Hungary by Politoys in the early 80's. I bought many of those being in Czechoslovakia during the 80's. Basically two types wrapped in a blue cardboard box were sold. The first one has opposite colors w-y, g-b, r-o and it tends to fall apart after a few months of speed cubing. A positive thing is that this type is well suited for speed cubing, it doesn't require perfect aligning of cubicles. A negative thing is that stickers don't last long, the glue is bad. The second type has colors w-b, g-y, r-o, I think. I always changed stickers to get w-y oposite colors. There was a very slight difference between cardboard boxes. This cube requires better aligning of layers before a next move (the construction was a little bit improved), the glue is better, but the plastic used I rate lower. Mirek > -----Original Message----- > From: "John Burkhardt" > > I recently bought a rubik's cube from someone. It was in a blue cardboard > > box that has Hungarian all over it.... ******************************** Miroslav Goljan Watson School of Engineering and Applied Science, Dept. of EE State University of New York PO BOX 00238 Binghamton, NY 13902-6000 e-mail: bg22976@binghamton.edu ******************************** From cube-lovers-errors@mc.lcs.mit.edu Thu May 20 22:44:17 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id WAA04400 for ; Thu, 20 May 1999 22:44:17 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <015101bea311$641f58a0$60c4b0c2@home> From: roger.broadie@iclweb.com (Roger Broadie) To: Cc: Subject: Re: Huge Cube! Date: Thu, 20 May 1999 23:37:38 +0100 It is one of a series of three that are on sale in the UK in the cheaper toy shops. They were mentioned on Cube-lovers in March. The big one that you have works pretty well and makes a handsome display object. There is also a normal-sized cube also with tiles that is about the most horrible to turn I have ever met - the shop-keeper even felt compelled to warn of the fact me in advance. Then there is also a key-ring sized cube (30 cm) which turns tolerably well and has conventional stickers, though not firmly stuck on, for only 73 pence in my local shop. Apparently the children like them because they are so easy to solve by rearranging the stickers. Roger Broadie Wayne Johnson wrote (20 May 1999) >My cousin came back from england on his recent trip and brought me >home a cube. Most cubes are 57mm. This one is.. wait for >it.. 90mm.[...] From cube-lovers-errors@mc.lcs.mit.edu Fri May 21 13:55:13 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id NAA07307 for ; Fri, 21 May 1999 13:55:13 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Thu, 20 May 1999 20:41:56 -0700 (PDT) From: Tim Browne To: cube-lovers@ai.mit.edu Subject: Re: Huge Cube! In-Reply-To: <015101bea311$641f58a0$60c4b0c2@home> Message-Id: On Thu, 20 May 1999, Roger Broadie wrote: > The big one that you have works pretty well and makes a handsome > display object. There is also a normal-sized cube also with tiles > that is about the most horrible to turn I have ever met - the > shop-keeper even felt compelled to warn of the fact me in advance. The most problematic ones I've come across so far are the "Wisdom" Ball (everything has to be lined up exactly right), Alexander's Star (same), and the Pyramorphix (same). It's a neat puzzle, but it seems to have a mind of its own, many times forcing you to turn a half/direction you don't want to and gets jammed constantly. When you finally do get past the jams, it's completely unexpected and flies at super speed. On top of this, the centres are so sharp that when it happens, it often cuts your fingers. Has anyone managed to come up with a fix for this? My guess is all that would need to be done to fix all of these problems would be to make the edges of the centre pieces more rounded, but I can't be sure about that. > Then there is also a key-ring sized cube (30 cm) [...] Uh... I think you mean 30Mm cube, don't you? :-) L8r. -- Victoria Animart - American Prices, Canadian Currency. | HIT Jedi http://www.focus-asia.com/home/animart | Use the Force, Mike! --------------------------------------------------------+----------------------- "No thanks. I'm trying to cut down." - Michael Garibaldi From cube-lovers-errors@mc.lcs.mit.edu Fri May 21 20:46:18 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id UAA09025 for ; Fri, 21 May 1999 20:46:18 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <199905211952.PAA04633@life.ai.mit.edu> From: "David Byrden" To: Subject: Rubik and XML Date: Fri, 21 May 1999 20:48:33 +0100 I want to define an XML dialect so that all Rubik-related programs can exchange data... I also want it to be useful to humans who are saving the state of their cube. I am putting my ideas together at http://byrden.com/puzzles/ and would be glad of criticism. David From cube-lovers-errors@mc.lcs.mit.edu Sun May 23 20:46:27 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil ([132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id UAA18154 for ; Sun, 23 May 1999 20:46:26 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Sun, 23 May 99 20:37:41 EDT Message-Id: <9905240037.AA26143@sun28.aic.nrl.navy.mil> From: Dan Hoey To: whuang@ugcs.caltech.edu (Wei-Hwa Huang) Cc: gej@spamalot.mfg.sgi.com, Cube-lovers@ai.mit.edu Subject: Re: Algorithm for the Antislice Group Gene Johannsen wrote: > I am having problems with this step. My cube is in a > configuration that this maneuver does not solve: And whuang@ugcs.caltech.edu (Wei-Hwa Huang) replied > As I e-mailed Gene, I do not believe his configuration is part of the > anti-slice group -- would any members care to give a quick heuristic to > determine if a cube is in the anti-slice group? Gene Johannsen sent in a reply agreeing that he had probably made a twisto in scrambling the cube. The moderator did not forward that reply to the group, hoping instead to determine a sure answer to the question. I'm sorry if the delay has cast doubt on Wei-Hwa Huang's antislice algorithm (which I have not examined in detail). The problem is actually fairly difficult if we want a definitive answer for any antislice-group position--Singmaster (p. 54) despairs of presenting Morwen B. Thistlethwaite's analysis of the antislice group, settling instead for an outline. I must admit that I have not yet found a complete answer that can be carried out by hand. However, I have a method that will recognize positions in a group four times the size of the antislice group, and that is good enough to weed out almost all of the near misses. In fact, a simpler method that will detect positions in a group 972 times the size of the antislice group is sufficient for the case in question. As in Singmaster we consider a corner-based representation. That is to say, we keep the BLD corner from moving, and perform an antislice as a half-turn of the F, T, or R face together with a quarter-turn of the adjacent center-slice. [ For newcomers, I'll mention that my use of "T" for "Top" instead of "U" for "Up" is an intentional preference; see 22 Feb 90 and 28 Oct 94 in the archives for an explanation. ] In this representation the face centers form a movable part of the cube. We could represent their position as a permutation of the six face centers, but it is more convenient to represent them as a permutation of the four major diagonals of the enclosing cube, as Jim Saxe and I did for the Tartan cube (16 February 1981). We may label the faces and diagonal-endpoints as follows: Z---X | B | Z---W---Y---X---Z | L | T | R | D | Y---X---Z---W---Y | F | Y---W The T antislice acts on the face centers as (F,L,B,R) and on the diagonals as (W,Y,Z,X). Similarly, the R antislice induces the face permutation (T,B,D,F) and the diagonal permutation (W,Z,Y,X). The F antislice induces the permutations (L,T,R,D) and (W,Y,X,Z). In the following, I will use note the diagonal permutations. In addition to the face centers, there are three orbits of edge cubies and two orbits of corner cubies (ignoring BLD). The corner orientation never changes, and reorientation of edges is applied to an entire orbit at a time. I label the edges and corners as follows: [Z]--Z3--Xp | | Z2 B Y2 | | [Z]--Z2--Wp--Y3--Y---Y2--Xp--Z3-[Z] | | | | | Z1 L X1 T Y1 R W1 D Z1 | | | | | Yp--X2--X---X3--Zp--W2--W---W3--Yp | | X2 F W2 | | Yp--W3--W The diagonals W-Wp, X-Xp, Y-Yp, and Z-Zp are labeled Wc, Xc, Yc, and Zc, respectively, for the purpose of recording the face center position. In addition I label the orientation of the edge orbits as P1, P2, and P3, where P1^2 = P2^2 = P3^2 = I. (These could be represented as permutations of 2-sets, but that seems unnecessary). So the three antislices are: Fa = (W,X)(Yp,Zp) (W1,Z1,X1,Y1) (W2,X2) (W3,X3) P1 (Wc,Yc,Xc,Zc), Ta = (X,Y)(Wp,Zp) (X1,Y1) (W2,X2,Z2,Y2) (X3,Y3) P2 (Wc,Yc,Zc,Xc), Ra = (W,Y)(Xp,Zp) (W1,Y1) (W2,Y2) (W3,X3,Y3,Z3) P3 (Wc,Zc,Yc,Xc). corner perm edge perm ori center perm It is immediately apparent that each antislice is an odd permutation of each orbit of corners, of each orbit of edges, and of the center diagonals. In addition, the number of Pi orientations is changed by one on each antislice. Thus we expect to see each of these seven parities agree in any position of the antislice group. Gene Johannsen's position (after replacing color letters with position letters) is BBB BBF <- Back face FFF LLR TDT LLR DTD LLL DTD RRR TDT <- Down face LRR TDT LRR DTD BBB BFF <- Front face FFF which is represented as (X,Y) (Wp,Zp) (W1,Y1)(X1,Z1) (X2,Y2) (W3,Y3,Z3,X3) in the corner-based representation. Here the permutations on the corner orbits and two of the edge orbits is odd. But the {W1,X1,Y1,Z1} orbit has an even permutation and the orientation and center positions are the identity, of even parity. So the position cannot be in the antislice group. I noticed that the difference could conceivably be caused by a single error, say an F-slice move: Fs = (W1,Z1,X1,Y1) (Wc,Yc,Xc,Zc) P1, and with a short program in GAP I was able to find the following single-error process for Gene's position: Fa Ta Fs Fa Ta' Fa Ra^2. Now I'll apologize to anyone whose head is reeling, and invite anyone who's game to join in a little bit of slightly tougher group theory. This will show you how far I've been able to analyze the antislice group, and the part that remains mysterious. Note that the parity constraints above allow: 6 permutations of {W,X,Y}, 24 permutations of {Wp,Xp,Yp,Zp}, 24 permutations each of {W1,X1,Y1,Z1}, {W2,X2,Y2,Z2}, and {W2,X2,Y2,Z2}, 8 subsets of {P1,P2,P3}, and 24 permutations of {Wc,Xc,Yc,Zc}, with a parity constraint on the seven components that reduces the number by 2^6, for 6 * 8 * 24^5 / 64 = 5971968 possible positions. Singmaster notes that the actual size of the antislice group is 6144 = 5971968 / 972 positions. Clearly there are more constraints at work than permutation parity. Most of them are due to life in a certain quotient group. The group S4 of permutations on four letters contains a normal subgroup consisting of the identity plus the three pairs of two-cycles: H = { (), (W,X)(Y,Z), (W,Y)(X,Z), (W,Z)(X,Y) }. The quotient S4/H then has six elements, and is isomorphic to S3. We can see this explicitly by writing down the blocks of S4/H: Block 0 Block 1 Block 2 Block 3 Block 4 Block 5 () (W,X,Y) (W,Y,X) (W,X) (W,Y) (X,Y) (W,X)(Y,Z) (W,Y,Z) (W,Z,Y) (Y,Z) (X,Z) (W,Z) (W,Y)(X,Z) (W,Z,X) (W,X,Z) (W,Y,X,Z) (W,X,Y,Z) (W,X,Z,Y) (W,Z)(X,Y) (X,Z,Y) (X,Y,Z) (W,Z,X,Y) (W,X,Y,X) (W,Y,Z,X) The top line of each block shows the element of S3=S({W,X,Y}) corresponding to the block. Note how easy it is to recognize the blocks 3, 4, and 5: If you have a four-cycles, use one two-cycle from its square; If you have a two-cycle containing Z, use the disjoint two-cycle. This procedure will yield the S3 representative from these blocks. Now remember the antislices? Fa = (W,X)(Yp,Zp) (W1,Z1,X1,Y1) (W2,X2) (W3,X3) P1 (Wc,Yc,Xc,Zc), Ta = (X,Y)(Wp,Zp) (X1,Y1) (W2,X2,Z2,Y2) (X3,Y3) P2 (Wc,Yc,Zc,Xc), Ra = (W,Y)(Xp,Zp) (W1,Y1) (W2,Y2) (W3,X3,Y3,Z3) P3 (Wc,Zc,Yc,Xc). Ignoring the orientation component, we see that the action of every component of Fa is from block 3, every component of Ta from block 4, and every component of Ra from block 5. So for every position in < Fa, Ta, Ra >, each permutation orbit will be in the same block, and the orientation component must still agree in parity. So instead dividing by 2^6, we divide by 6^5 2 = 15552, for 6 * 8 * 24^5 / 15552 = 24576 positions, which is only four times the size of the actual antislice group. The factor of four arises if we fix all but the {Wp,Xp,Yp,Zp} and {Wc,Xc,Yc,Zc} orbits. There are only four possibilities for the last two orbits, rather than the sixteen that my analysis provides. (As Singmaster notes, when the other components are the identity, the four possibilities consist of SOLVED and the four Zigzag/Laughter patterns). Unfortunately, I have not found any way to describe the correspondence between these components in general, to make the analysis exact. Dan Hoey@AIC.NRL.Navy.Mi From cube-lovers-errors@mc.lcs.mit.edu Mon May 24 16:21:39 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id QAA22125 for ; Mon, 24 May 1999 16:21:39 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <3748AFD3.DDEF4717@whitewolf.com.au> Date: Mon, 24 May 1999 11:48:03 +1000 From: Ryan Heise To: David Byrden Cc: Cube-Lovers@ai.mit.edu Subject: Re: Rubik and XML References: <199905211952.PAA04633@life.ai.mit.edu> David Byrden wrote: > I want to define an XML dialect so that all > Rubik-related programs can exchange data... > I also want it to be useful to humans who > are saving the state of their cube. > > I am putting my ideas together at > > http://byrden.com/puzzles/ > > and would be glad of criticism. Quote: "I want RubXML files to be able to hold move sequences instead of puzzle configurations. I will add this option after I study the notations currently in use." I think both ways of specifying a cube configuration are important. You can only specify a cube configuration in move sequences if you know the exact move sequence you used to mess it up. Move sequences are probably more useful for storing solutions to cube configurations. Also, Lars Petrus has a cube tutorial that shows you how to do each step by scripting a Java applet to rotate the cube according to stored sequences. (Sure, his "lightweight" applet would not want to drag in a whole XML parser, but the use is there) BTW, here is one way to specify move sequences: R'U'RU'R'U2R If you want something flexible, how about: RURU U'R'U'R where: usesequence imports another sequence orientation is a 3D coordinate (is there a better way to specify this?) direction is which direction to execute the sequence reflect is the axis over which the sequence should be reflected. It's flexible but I don't ask me if it's useful :-) -- Ryan Heise http://www.progsoc.uts.edu.au/~rheise/ From cube-lovers-errors@mc.lcs.mit.edu Tue May 25 11:17:55 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id LAA27167 for ; Tue, 25 May 1999 11:17:55 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <003401bea62b$d9660920$50c4b0c2@home> From: roger.broadie@iclweb.com (Roger Broadie) To: "Cube-Lovers" Subject: Availability of 5x5x5 and 2x2x2 in UK Date: Mon, 24 May 1999 22:24:45 +0100 Hah! For British readers, I can report that Toys 'R' Us have the Meffert 5x5x5 and the Rubik's 2x2x2 - the first time I have seen either of these sizes on sale in the UK. Roger Broadie From cube-lovers-errors@mc.lcs.mit.edu Fri Jun 4 15:47:14 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id PAA16443 for ; Fri, 4 Jun 1999 15:47:13 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <199906041117.HAA05009@life.ai.mit.edu> From: "David Byrden" To: Subject: Standard file format for Rubik's Cube is just about ready Date: Fri, 4 Jun 1999 12:14:00 +0100 Following on from my mail of the 21st May... I have defined a language for writing down the state of a standard Rubik's cube. Many people offered suggestions, and I thank them. The language now has its own website: http://byrden.com/rubxml/ which contains an online demo program to read the language and draw the corresponding cube in "unfolded" format. People who want to record their "pretty patterns" may find this a useful resource! I have one question that I want to ask now. This language needs a "default colour scheme". I understand that one way of colouring a Rubik's Cube was much more common than the others, but I don't know which one. Can anyone specify it exactly for me? David Byrden From cube-lovers-errors@mc.lcs.mit.edu Mon Jun 7 15:49:59 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id PAA24758 for ; Mon, 7 Jun 1999 15:49:59 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu To: cube-lovers@ai.mit.edu From: whuang@ugcs.caltech.edu (Wei-Hwa Huang) Subject: Re: Standard file format for Rubik's Cube is just about ready Date: 7 Jun 1999 13:48:49 GMT Organization: California Institute of Technology, Pasadena Message-Id: <7jgik1$d5d@gap.cco.caltech.edu> References: "David Byrden" writes: >I have one question that I want to ask now. This >language needs a "default colour scheme". I >understand that one way of colouring a Rubik's >Cube was much more common than the others, >but I don't know which one. Can anyone specify it >exactly for me? The most common color scheme was White opposite Blue, Green opposite Yellow, Red opposite Orange. If you hold Yellow as Front and Red as Up, then Blue is Right. Color "purists" have complained about this, preferring White opposite Yellow, Blue opposite Green, Red opposite Orange. -- note that each pair is the same color except for some "Yellow" added. -- Wei-Hwa Huang, whuang@ugcs.caltech.edu, http://www.ugcs.caltech.edu/~whuang/ --------------------------------------------------------------------------- If all my friends jumped off a cliff... what reason is there for me to live? [Moderator's note: You say white opposite blue was common, but when was that? My experience and other reports lead me to believe that what you call the "purist" color scheme was most common in 1985 (viz _Rubik's_Cubic_Compendium_) and I don't recall seeing any change since. It also is reportedly most common in the chirality you describe, which is called the BOY version because blue, orange, and yellow appear in that order clockwise around a corner. The mirror image coloring is called YOB (a Cockney term for a yokel). I don't know of any cute naming schemes for the enantiomorphs in color schemes in which the blue, orange, and yellow faces do not all meet--Dan ] From cube-lovers-errors@mc.lcs.mit.edu Tue Jun 8 17:22:07 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id RAA29939 for ; Tue, 8 Jun 1999 17:22:07 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <001201beb186$4ef27880$0401a8c0@sanyi.android.com> Reply-To: "Michaletzky_Sandor" From: michas@androsoft.com (michas@androsoft.com) To: , "Wei-Hwa Huang" Subject: Re: Standard file format for Rubik's Cube is just about ready Date: Tue, 8 Jun 1999 10:10:01 +0200 Hi, Friends! The original color schema is (designed by Erno Rubik, and it is written in Rubik's: The Magic Cube book also): blue is opposite to green, white is opposite to yellow and red is opposite to orange. The differerence between each opposite colour-pair is yellow: blue + yellow = green, red + yellow = orange and white + yellow = (guess it! :-). If blue is on the top and red is in front of you, yellow is on the right side. From cube-lovers-errors@mc.lcs.mit.edu Tue Jun 8 20:03:25 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id UAA01196 for ; Tue, 8 Jun 1999 20:03:25 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu From: whuang@ugcs.caltech.edu (Wei-Hwa Huang) Message-Id: <199906081306.GAA24838@necro.ugcs.caltech.edu> Subject: Re: Standard file format for Rubik's Cube is just about ready To: michas@androsoft.com Date: Tue, 8 Jun 1999 06:06:28 -0700 (PDT) Cc: cube-lovers@ai.mit.edu, whuang@ugcs.caltech.edu In-Reply-To: <001201beb186$4ef27880$0401a8c0@sanyi.android.com> from "michas@androsoft.com" at Jun 8, 99 10:10:01 am Reply-To: whuang@ugcs.caltech.edu > >[Moderator's note: You say white opposite blue was common, but when > > was that? My experience and other reports lead me to believe that > > what you call the "purist" color scheme was most common in 1985 (viz > > _Rubik's_Cubic_Compendium_) and I don't recall seeing any change > > since. It also is reportedly most common in the chirality you > > describe, which is called the BOY version because blue, orange, and > > yellow appear in that order clockwise around a corner. The mirror > > image coloring is called YOB (a Cockney term for a yokel). I don't > > know of any cute naming schemes for the enantiomorphs in color > > schemes in which the blue, orange, and yellow faces do not all > > meet--Dan ] I'm going by what I have observed -- which is mostly Ideal cubes. The Ideal Deluxe cube has white opposite blue, as well as their Revenge and the three normal cubes I have in my collection. I can check the orientation of the minicubes in Rubik's Race and the "deluxe-ish" cube supplied with Rubik's Game. The 5x5x5 in my collection is also white opposite blue, although it isn't Ideal (pun intended). The OddzOn cubes are also blue opposite white, so I think it's safe to say that the majority of cubes out there are blue opposite white. From http://www.rubiks.com/cubesolution_new.html : >Note: we use the color arrangement of the original Rubik's cube (i.e. >blue is opposite to green, red is opposite to orange, and yellow is >opposite to white; if the blue side is on the top, then the red is >on the left and the yellow on the right, and so on), because this >is the one Erno Rubik prefers. The new Rubik's Cubes made by OddzOn >since 1995 are colored differently (i.e. blue is opposite to white, >green is opposite to yellow, and red is opposite to orange). -- Wei-Hwa Huang, whuang@ugcs.caltech.edu, http://www.ugcs.caltech.edu/~whuang/ --------------------------------------------------------------------------- Is there a metonym in this sentence? From cube-lovers-errors@mc.lcs.mit.edu Tue Jun 29 18:12:20 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id SAA00650 for ; Tue, 29 Jun 1999 18:12:19 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: Date: Tue, 29 Jun 1999 16:26:03 -0400 To: Cube-Lovers@ai.mit.edu From: pink@cartserv.rserv.uga.edu (_pink) Subject: hello to all Hey! I just thought I'd drop a line to introduce myself since I've subscribed to your mailing list. My name is Brian Davis (my friends all call me "_pink". The underscore is silent.) I live in Athens, Georgia USA and Manage a Computer Graphics Facility at the Univ of Georgia. I have been a cube fanatic since day one... I've got a pretty good collection and several volumes of notes (as I sure most of you do) but feel there is still more out there. I have noticed many names here on the Cube Lovers List that have some wonderful www pages. Maybe I'll find some time to create a www cube presence of my own that doesn't overlap too much. (this might be hard to do as you guys have it pretty well wrapped up right now...) I have "e-talked" with Tim Browne some previously (don't blame him for me being here, he's innocent really) and when I found he was here and the list seems to still be alive I thought I might as well subscribe. I'll start out by sticking my neck out a bit and see if any one wants to hear some information I have about Square 1 moves or inner-workings (since I've crushed a few out of curiosity and could take picts to post on the web) or the mechanics of the Skewb since I've had to put it back together after an employee dropped it. At any rate, I'm glad to be here and will try not to ramble so incoherently in the future. _pink btw: anyone have a Siamese Cube that they would like to get rid of? ;) Ok, how about just answer a few questions about so I can try to construct one... 8) to see a listing of cubes I'm looking for go to: http://128.192.40.238/pink/wanted.html From cube-lovers-errors@mc.lcs.mit.edu Thu Jul 1 13:26:56 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id NAA11249 for ; Thu, 1 Jul 1999 13:26:56 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: Content-Type: text/plain; charset="us-ascii" Date: Wed, 30 Jun 1999 13:35:04 -0400 To: Cube-Lovers@ai.mit.edu From: pink@cartserv.rserv.uga.edu (_pink) Subject: replies all around Hello again, Thanks to all who sent me a welcoming note. A few notes of interest: Dale: Crazy 5 combined cubes man! I might have to try it... Did you also attach the edge cubes or just the corners? Chris (or Chris and Kori): I've been to your page(s) many times. Nice site! I've been to ebay a bit but I'm not giving out my ebay nickname... ;) I have the Pyramorphix and am not sold on the last pict of my wanted page being one in scrambled state... Jared: Thanks for the tip. I'll follow up and let you know what turns up. Bob Harris: Hey! another Georgian! Glad to see I'm not the only one. I'm sure we shall be talking a bit... Noel: If you are talking about the octagonal prism then the answer is just like the 3x3x3 but if you're talking about the Octahedron (double pyramid) then unfortunately I cannot help as I have not had the chance to hold one in my hands... Hana: Thank you for the wonderful note. I have not had a chance to visit your site but it will be first on my list when I get home. I am intrigued to see what you have been doing! Pete Beck: Did the money order I sent ever arrive? The beachball is a Skewb of 4 colors (thus the subclass) I contacted Meffert's a few weeks back and they informed me that the beachball is not in production but they are going to make more available in October! I have found info on the bandaged cube but need clearer direction as to which pairs of cubies are 'glued' together... As for Unknown #2 on my wanted page, when tracing the dissections I can only imagine a 2x2x2 with non cubed cubies... Who knows... Others inquired about my Square 1 and Skewb notes. Ok. I'll do a write up on each under two different posts as to keep things separated. Posts to follow... Thanks again to all for making me feel at home. _pink [ Moderator's note: also Wei-Hwa Huang noted that The "Unknown #1" on Pink's web page is just a taped cube. ] From cube-lovers-errors@mc.lcs.mit.edu Thu Jul 1 14:46:52 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id OAA11749 for ; Thu, 1 Jul 1999 14:46:51 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: Content-Type: text/plain; charset="us-ascii" Date: Wed, 30 Jun 1999 13:58:55 -0400 To: Cube-Lovers@ai.mit.edu From: pink@cartserv.rserv.uga.edu (_pink) Subject: Skewb notes Ok, while Meffert's site has the solution posted, there still seems to be some confusion about how this thing is actually made. Well I found out first hand when one of my employees dropped my skewb on a concrete floor. I have plans to take picts of the disassembled skewb and post it online but until I get around to it here's a description. The Skewb consists of: 6 Square center pieces that have small tabs on 2 opposite undersides. 4 Pyramid shaped corners with a triangular tab on its interior side. 1 4-armed spider mechanism with 4 corner pieces (described above) attached to the end of each arm. To understand the arrangement of the spider mech refer to the diagram below: A _____________________ /| /|B / | / | / | / | / | A / | B/____________________/ | | | | | | | | | | | x | | | | | | | |B | | | |_______________|____|A | / | / | / | / | / B| / A|/___________________|/ If you connect each corner marked "A" with the "x" (with the x being the exact center of the cube) you will have the spider mechanism. The corners marked "B" are only attached by the various tabs on each piece. Skewbs are EASY to disassemble if you know how... 1.) Rotate any dissection of your skewb 60 deg so that 2 centers are aligned edge to edge. 2.) Place a thin bladed screwdriver between the common edge of any 2 edge pieces and gently wiggle applying increasing pressure. 3.) Catch all the pieces as it crumbles in your hands. Putting it back together is interresting and certainly was when my employee dropped mine but after you do it it's kinda neat. 1.) Align the colors of 2 corners on the spider and insert the center of the corresponding color so that the tabs hold it in place. 2.) Align the corners and place 2 more center sections. Slight rotation of one corner helps at times. 3.) Insert the proper loose corners being sure to orient each correctly. 4.) Place one edge tab of the last center into position and snap into place. I have found it easiest to put the skewb on the table with the last center on top and firmly press it into place. Meffert's puzzle ball series are the same mechanism but some are supergroup puzzles because of the center orientations. The Meffert Beachball is IMO a subgroup because of only having 4 colors. I hope this has been of value for someone and isn't just a waste of bitspace for all. _pink From cube-lovers-errors@mc.lcs.mit.edu Thu Jul 1 17:31:32 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id RAA12373 for ; Thu, 1 Jul 1999 17:31:32 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Thu, 1 Jul 1999 15:37:36 -0400 (Eastern Daylight Time) From: Dale Newfield Reply-To: DNewfield@cs.virginia.edu To: Cube-Lovers@ai.mit.edu Subject: Re: Skewb notes In-Reply-To: Message-Id: On Wed, 30 Jun 1999, _pink wrote: > Meffert's puzzle ball series are the same mechanism but some are > supergroup puzzles because of the center orientations. The Meffert > Beachball is IMO a subgroup because of only having 4 colors. I find it interesting to think that the internal mechanism for the skewb and the puzzle balls are the same as for the pyraminx, but that the pieces stuffed into the gaps make it a completely different puzzle. -Dale From cube-lovers-errors@mc.lcs.mit.edu Fri Jul 2 12:15:09 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id MAA15239 for ; Fri, 2 Jul 1999 12:15:09 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu From: Douglas Zander Message-Id: <199907020153.UAA27551@solaria.sol.net> Subject: Q: fix a pyramorphix? To: cube-lovers@ai.mit.edu (cube) Date: Thu, 1 Jul 99 20:53:08 CDT Hello, I wonder if anyone can help me. I allowed a friend of mine to play with my pyramorphix and it broke in his hands. One of the inner pieces broke apart. It was the piece that sits on the dowel with four little rods sticking up. Does anyone know if any local (USA) shop fixes this particular puzzle? Does Meffert's Puzzle & Games fix them in Hong Kong? (I'd prefer a local shop) Does anyone have a broken pyramorphix they would sell me a piece to replace mine? :-) Thanks for any help. (Is Meffert the inventor of the pyramorphix?) -- Douglas Zander | dzander@solaria.sol.net | Shorewood, Wisconsin, USA | From cube-lovers-errors@mc.lcs.mit.edu Fri Jul 2 13:23:14 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id NAA15540 for ; Fri, 2 Jul 1999 13:23:13 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Reply-To: From: "Noel Dillabough" To: "Cube Lovers List (E-mail)" Subject: Solution for the size 2 octahedron Date: Thu, 1 Jul 1999 17:48:12 -0400 Message-Id: <000001bec441$c8879680$29f5ddce@laptop> After playing with the size 2 corner moves based octahedron, I found that the solution for most of the edges is trivial, just a matter of putting them into place using standard puzzle moves. The only part of the puzzle that needs a special move is the final step that you may be left with a pair of faces that need to be switched: The following represent a tip of the octahedron, and sides A and B must be switched R-> | _____|______ | A | B The following move accomplishes this: Down Rotate Counterclockwise Up Rotate Twice Down Rotate Twice Up Rotate Twice Down Rotate Clockwise The "Up" and "Down" moves refer to the right half of the octahedron, cut through the middle of the tip and leaving the left half steady. The Rotate moves refer to rotating the tip in place. Anyone with a good notation for this and the size 3 corners based octahedron, or the side based size 2 or 3 octrahedra let me know. [Moderator's note: Isn't a corners-based octahedron just a face-based cube with the corners flattened and the faces made pointy? I think BFTDLR or BFUDLR would work for notation. --Dan] From cube-lovers-errors@mc.lcs.mit.edu Tue Jul 6 15:19:25 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id PAA05579 for ; Tue, 6 Jul 1999 15:19:25 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Mail-from: From cube-lovers-request@life.ai.mit.edu Fri Jul 2 11:55:25 1999 Message-Id: Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Date: Fri, 2 Jul 1999 11:57:33 -0400 To: Cube-Lovers@ai.mit.edu From: pink@cartserv.rserv.uga.edu (_pink) Subject: cube picts / Square 1 picts Hello Cube Lover's Thanks to all who have provided information that should help me to track down some of the items on my wanted list. I have had several requests for pictures of cubes I have and picts of disassembled cubes. Well good news! I purchased a digital camera yesterday and will be taking picts of all requested items this weekend (time permitting) and I will post them online. A good weekend to all. _pink It's quick and dirty but... http://128.192.40.238/pink/sq1asmbly.html feel free to email with any questions. _pink From cube-lovers-errors@mc.lcs.mit.edu Tue Jul 6 18:54:46 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id SAA07213 for ; Tue, 6 Jul 1999 18:54:46 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Reply-To: From: "Noel Dillabough" To: "Cube Lovers List (E-mail)" Subject: Re: Solution to a size 2 Octahedron Date: Fri, 2 Jul 1999 19:17:23 -0400 Message-Id: <000601bec4e1$19d7a080$0ef5ddce@laptop> [Moderator's note: Isn't a corners-based octahedron just a face-based cube with the corners flattened and the faces made pointy? I think BFTDLR or BFUDLR would work for notation. --Dan] Actually this notation works perfectly, here is the move in this fashion: R' F' R F2 R' F2 R F2 R' F From cube-lovers-errors@mc.lcs.mit.edu Tue Jul 6 19:03:51 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id TAA07257 for ; Tue, 6 Jul 1999 19:03:51 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <377E55CC.3C4F@ameritech.net> Date: Sat, 03 Jul 1999 13:26:20 -0500 From: Hana Bizek Reply-To: hbizek@ameritech.net To: cube-lovers@ai.mit.edu Subject: New web page References: <377E509B.39A5@ameritech.net> To my fellow cube-lovers: Josef Jelinek and I have made a web page devoted to the cube. He contributed cube solution algorithms, accompanied by graphics and I contributed 12 of my 3-dimensional designs, many of them recent. That means they were constructed after my book was published in 1997. I also sketch another problem resulting from these designs, that of fractals. You may find all this in our URL: http://cube.misto.cz. Any comments, criticism, etc would be appreciated. I still did not get my question answered, either by you or by the search engines. It is this: Is there anyone, on or off the web, who has created something similar to what I have done? I know about the people at Wunderland, and have seen thir work; however, what I have done is different. Thank you very much for any input you can provide. Hana M. Bizek From cube-lovers-errors@mc.lcs.mit.edu Wed Jul 7 19:25:18 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id TAA10609 for ; Wed, 7 Jul 1999 19:25:17 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Sun, 4 Jul 1999 14:45:12 -0700 (PDT) From: Tim Browne To: Cube-lovers@ai.mit.edu Subject: Puzzletts? In-Reply-To: Message-Id: Has anyone been able to get through to Puzzletts at all? I've been trying to get through to their site for the past month or so, but it's always "down, overloaded, or unreachable" (surely they could narrow it down a bit better than that!). Does anyone know what's going on? Has it crashed and burned for good? L8r. -- From cube-lovers-errors@mc.lcs.mit.edu Mon Jul 12 14:25:00 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id OAA26629 for ; Mon, 12 Jul 1999 14:24:59 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <377A4984.5167C958@nadn.navy.mil> Date: Wed, 30 Jun 1999 12:44:52 -0400 From: David Joyner Reply-To: wdj@nadn.navy.mil Organization: Math Dept, USNA To: cubelovers Subject: puzzle collectors web page has moved Hello Cube Lovers: The Directory of Mechanical Puzzle Collectors web page has moved to http://anduin.eldar.org/~problemi/joyner/slocum.html Please update any links. - David Joyner -- David Joyner, Assoc Prof of Math Math Dept, 572C Holloway Dr US Naval Academy, Annapolis, MD 21402 office: 410-293-6738, fax: 410-293-4883 wdj@nadn.navy.mil, wdj@gwmail.usna.edu http://web.usna.navy.mil/~wdj/homepage.html [Moderator's note: This note was delayed because I generally give web page announcements lower priority than discussion. Also, I usually drop announcements of changes to web pages that have been previously announced, since interested people can learn about the changes from the web page itself. In the last 18 months or so, change notices for the following pages have been suppressed in this way: http://www.snipercade.com/cubeman http://www.asahi-net.or.jp/~hq8y-ishm/ http://www.rubiks.com/ http://www.ue.net/mefferts-puzzles/ http://home1.gte.net/davebarr/Cube/ http://128.192.40.238/pink/ I'm willing to accept suggestions from the list membership about these policies; direct them to cube-lovers-request@ai.mit.edu. -- Dan ] From cube-lovers-errors@mc.lcs.mit.edu Mon Jul 12 15:38:04 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id PAA27200 for ; Mon, 12 Jul 1999 15:38:03 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: Date: Mon, 12 Jul 1999 14:09:58 -0400 To: Cube-Lovers@ai.mit.edu From: pink@cartserv.rserv.uga.edu (_pink) Subject: Square 1 Notes Greetings to all, Ok, I've been extreeeeeemely busy as of late but I did find a few mins at lunch today to throw together some of my notes on the Square 1 puzzle. First my standard disclaimers: 1.) The web page design and layout for getting the Square 1 back to cube shape have been stolen directly from Christian Eggermont. My notes were very similar but I liked his presentation much better than mine. The only thing I have done to his notes was to rearrange the classification of shapes as to their 'distance' from cube shape. To see his original work please refer to: http://web.inter.nl.net/C.Eggermont/ 2.) I expanded on Andrew Arensburger's cube preserving formulas and also adopted his piece notation system. To see his original work please refer to: http://www.cfar.umd.edu/~arensb/Square1/ 3.) Some formula were revised and expanded upon from Richard Snyder's Square 1 Solution Book. Nice book but sometimes a bit cryptic. 4.) I know that there has to be some errors in my notes. If you find them please advise me so that I might make the corrections necessary. (Actually now that I think about it, I believe that in the Edge moves section there is a mistake where I say to turn the bottom 30deg in one direction but it would make an impossible Right turn... if you see this just turn the bottom the other direction... I'll try to find it and correct it asap) 5.) There are 2 or 3 pages of blank diagrams or unfinished notes that indavertantly got included. Please disregard anything that looks unusual... (hopefully that won't be every page you look at...) ;) Ok, so if you're not asleep by now you can hit http://128.192.40.238/pink/SquareList.html for the shapes list as to get from where you are now back to cube shape. There is a link at the bottom of that page to 3 PDF files. One to manipulate Corners, one for Edges and one for my initial thoughts on 2x2x2 cycling of Square 1 quadrants. I hope there is some info of use for somebody. And as always... feedback is very welcome. later all, _pink From cube-lovers-errors@mc.lcs.mit.edu Thu Jul 22 13:23:38 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id NAA28308 for ; Thu, 22 Jul 1999 13:23:37 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <006001bed45e$d4429420$1b4b43cf@compaq> From: "Paul Hanna" Reply-To: phanna@gbonline.com To: Subject: cube computer solutions using procedural languages Date: Thu, 22 Jul 1999 11:24:45 -0500 Have any of you done any work on solving the cube with computer programs using procedural languages such as C? I've seen books on the manual methods of solving the cube (with the cube in your hand) such as David Singmaster's texts but haven't seen any publications regarding computer solutions using procedural languages. Do you have any suggestions you can pass my way? I am a good programmer but not a cube solution expert. I am just a novice at best when it comes to cube algorithms and efficient cube solutions. I am attempting to work on a project involving solving the cube programmatically and also planning on doing analysis/comparisons of various algorithms to solve it. Any help, suggested methods, advice, tables, algorithms, etc. that you may be able to provide me would be very greatly appreciated. I can think of a number of ways to approach this task but would also like some of your folks expertise as well. I am having trouble getting going in the right direction. Also what is the theoretical least number of plane movements that are required to solve the cube no matter what its configuration and why? You can reply directly to me. Thanks in advance, Paul Hanna Green Bay, WI phanna@gbonline.com [Moderator's note: There's certainly a lot in the archives (ftp://ftp.ai.mit.edu/pub/cube-lovers/) on the topics of efficient and optimal programmatic solutions and upper and lower bounds. Unfortunately, it's not indexed. --Dan] From cube-lovers-errors@mc.lcs.mit.edu Tue Jul 27 18:50:00 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id SAA19974 for ; Tue, 27 Jul 1999 18:50:00 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu From: "Chris Pelley" To: "Cube-Lovers" Subject: Rubik's Cube Perpetual Calendar Date: Thu, 22 Jul 1999 21:43:52 -0400 Message-Id: I recently saw one of the original Ideal Perpetual Calendar cubes sell on EBAY for over $100 US dollars! I decided it would be cheaper and more fun to try and make my own. Based on photos I have collected, I've tried to reconstruct the original sticker scheme. This turned out to be quite a fun puzzle by itself, since there are only a few ways it can be done. For example, by a lucky coincidence, there just happen to be exactly the right number of sides for the middle letters of the months (P, O, C, A, E, and U). I did a quick scan of the cube-lovers archives to see if anyone had posted the sticker scheme before. I found nothing. I was wondering if anyone who still has their calendar cube could post either a detailed description, or even photos from a few different angles. My own homemade version can be seen here: http://www.chrisandkori.com/calendarcube.htm I just printed out the stickers I needed on paper, then cut and scotch-taped them to a "blank" cube. I plan to make a somewhat higher-quality version with real stickers once I nail down the original Ideal sticker configuration. Thanks to anyone who can help! Chris Pelley ck1@home.com From cube-lovers-errors@mc.lcs.mit.edu Thu Aug 5 17:39:56 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id RAA25389 for ; Thu, 5 Aug 1999 17:39:56 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Fri, 23 Jul 1999 14:32:38 +0200 From: "Walter van Iterson (EMN)" Subject: Solving cube with robot arm To: Cube-Lovers@ai.mit.edu Message-Id: <3173B642ECF3D111B3FB0008C724B5609527BC@enleent100.ericsson.se> Hi all, Has anybody even built (or throught about building) a device which physically solves a cube? Something like a combination of a vision system to recognize the colors, a 'robot arm' which can perform the rotations and a computer to solve the mathematics and to operate the robot arm. I'm currently thinking about making such a system, so I'm interested if anybody else has done something similar. Greetings, Walter van Iterson walter.van.iterson@hta.nl [ Moderator's note: I'm sure there are some mentions of such efforts in the archives. I seem to recall one such project at the University of Maryland. --Dan ] From cube-lovers-errors@mc.lcs.mit.edu Thu Aug 5 18:10:24 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id SAA25493 for ; Thu, 5 Aug 1999 18:10:24 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <3799A6A3.9A46C38D@doc.ic.ac.uk> Date: Sat, 24 Jul 1999 12:42:27 +0100 From: Colin Waters To: phanna@gbonline.com Cc: Cube-Lovers@ai.mit.edu Subject: Re: cube computer solutions using procedural languages References: <006001bed45e$d4429420$1b4b43cf@compaq> Hi, I'm currently working on my MSc dissertation on this topic. I'm working in Java to build a Cube to which I can then apply algorithms in Singmaster Notation. The approach I'm taking is to use an incremental breadth first search to generate a library of "interesting" macro moves (Richard Korf did some work on this a few years ago). I would then like to use a heuristic approach with the macro moves to head towards the solution. Currently I am thinking of using a version of the Manhattan distance but I would be grateful for any other heuristic suggestions. I would also be interested in a reply to Paul's question about the least number of theoretical plane moves. Best Regards, Colin Waters, Department of Computing Imperial College, London. [Moderator's note: What is a "plane" move? All cube metrics count a quarter-turn of a face as a single move. Some also include a half-turn of a face. Some also include a quarter-turn of a center slice, or perhaps also a half-turn of a center slice. I've not seen anyone count an antislice move as a single move, though it seems fairly reasonable to me, since it's fairly easy to do with one motion of the wrist. In fact, we might even include moves such as "F^2 B" under the rubric of "plane moves", so that there would be 45 generators. My recollection is that you may find fairly good bounds in the archives for the first two metrics--say a ratio of 3:2 or less--but not for the others. --Dan ] From cube-lovers-errors@mc.lcs.mit.edu Thu Aug 5 18:57:05 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id SAA26373 for ; Thu, 5 Aug 1999 18:57:04 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Tue, 27 Jul 1999 22:41:37 -0400 Message-Id: <003B08AD.C22092@scudder.com> From: Jacob_Davenport@scudder.com (Jacob Davenport) Subject: Re: Rubik's Cube Perpetual Calendar To: "Cube-Lovers" Chris, You may want to look at www.wunderland.com/WTS/Kristin/CustomCubes.html for some more information about making a custom cube. Kristin also owns a French calendar cube, if I remember correctly, but I imagine that if you have successfully made a calendar cube that you don't really need to know how hers works. -Jacob From cube-lovers-errors@mc.lcs.mit.edu Thu Aug 5 19:42:04 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id TAA26449 for ; Thu, 5 Aug 1999 19:42:03 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <4.1.19990728163706.0096d9d0@gumby145.mail.iastate.edu> Date: Wed, 28 Jul 1999 17:11:48 -0500 To: "Cube-Lovers" From: Corey Folkerts Subject: Re: Rubik's Cube Perpetual Calendar In response to Chris Pelley's message about a Rubik's Calender Cube, I would like to say that I made one, although it may not be identical to the one that Rubik manufactured. (I thought up the idea before I knew one had been made commercially) I just mapped the letters and numbers out on paper and then printed out all the characters I'd need with my printer and affixed them to a blank cube. I really lucked out because the scotch tape I had was exactly the same width as the width of one cubie! I also used an exacto knife so I could affix multiple characters at once, then cut between the cubies with the knife. An example of how the date reads is: J U L 2 8 19 9 9 The 19 (and 20 once we get there) are on one cubie. I've attached a jpg of how I arranged all the characters. I make no guarantees that is works, but I'm pretty sure it does. Sorry to those of you who can't receive files. I would have made the drawing ASCII, but I can't make upside or sideways characters =( In the drawing there may be some discrepancy between O the letter and zero. The 'thinner' one is zero. As you can see, my cube is still on Jul 27. I haven't changed it yet since yesterday. -Corey Folkerts [Moderator's note: I don't send binary attachments out on this list. However, I was able to decode Corey's picture, and here's a diagram. The characters ^ > v and < denote symbols that are rotated 0, 90, 180, or 270 degrees clockwise, respectively. N^ .. .. O< 1v 0< Nv Ev 0< R< C^ V^ D^ A^ 1< 6^ 6^ 19v 20> .. B^ 6v 3< .. .. .. 0^ 6v 2v .. .. 0> 9^ A< 1> T> Pv 2> G> Lv Uv Jv F< 5> Sv C< 8< Y^ 3v .. P> O< 4> Mv I believe the corner marked 0< should be 0^. The cube only goes through 2001, though the addition of 2< on the blank corner would add another year. Sorry for the delay in sending this message out. --Dan ] From cube-lovers-errors@mc.lcs.mit.edu Thu Aug 5 20:28:33 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id UAA26582 for ; Thu, 5 Aug 1999 20:28:33 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <006501beda1b$4cf43ec0$4dc4b0c2@home> From: roger.broadie@iclweb.com (Roger Broadie) To: "Cube-Lovers" Cc: "Chris Pelley" Subject: Re: Rubik's Cube Perpetual Calendar Date: Fri, 30 Jul 1999 00:35:35 +0100 Chris Pelley wrote (23 July 1999) >I was wondering if anyone who still has their calendar cube could >post either a detailed description, or even photos from a few >different angles. This is what my Rubik's Calendar looks like (use a non-proportional typeface). The date is as I took it out of the box, from which I deduce I last played with it in 1982, since I certainly haven't touched it this decade. Curiously enough, it will be correct again this year. The digits in the lower right corners of the cells indicate the orientation in quarter turns from the vertical as shown in the diagram. But the orientations can be worked out anyway for all except the centre pieces, because of the requirement to be the right way up on the face showing the date. Roger FRONT (Up) ------------------------- | | | | | SUN|DAY | | | | | | ------------------------- | | | | | A | U | G | | | | | ------------------------- | | | | | | | 8 | | | | | ------------------------- RIGHT (Up) ------------------------- | | | | | 5 | 1 | 1 | | 2 | 2 | 3 | ------------------------- | | | | | N | C | | | | 2 | | ------------------------- | | | | | 2 | D | | | 1 | 3 | | ------------------------- BACK (Up) ------------------------- | | | | | 7 | B | | | 2 | 3 | | ------------------------- | | | | | C | E | T | | 2 | | | ------------------------- | | | | | SATUR| J | | | 3 | 3 | | ------------------------- LEFT (Up) ------------------------- | | | | | 0 | P | | | 2 | 3 | | ------------------------- | | | | | S | O | L | | | | | ------------------------- | | | | | WEDNES| F | MON| | 3 | 3 | 2 | ------------------------- TOP (Back) ------------------------- | | | | | 6 | Y | 3 | | 2 | 3 | 3 | ------------------------- | | | | | O | P | 3 | | | | 3 | ------------------------- | | | | | THURS| | 9 | | 3 | | | ------------------------- BOTTOM (Back) ------------------------- | | | | | TUES| R | | | | 3 | | ------------------------- | | | | | V | A | M | | 2 | 2 | 2 | ------------------------- | | | | | 4 | 2 | FRI| | 1 | | 2 | ------------------------- [Moderator's note: A picture of the cube by Corey Folkerts that I described in the last message can be found at http://www.public.iastate.edu/~gumby145/cubes_gallery.html --Dan ] From cube-lovers-errors@mc.lcs.mit.edu Thu Aug 5 21:04:33 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id VAA26830 for ; Thu, 5 Aug 1999 21:04:32 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <37A19059.40026399@frontiernet.net> Date: Fri, 30 Jul 1999 07:45:30 -0400 From: John Bailey To: phanna@gbonline.com Cc: Cube-Lovers@ai.mit.edu Subject: Re: cube computer solutions using procedural languages References: <006001bed45e$d4429420$1b4b43cf@compaq> Paul Hanna wrote: > Have any of you done any work on solving the cube with computer programs > using procedural languages such as C? > > Do you have any suggestions you can pass my way? I am a good programmer but > not a cube solution expert. I am just a novice at best when it comes to cube > algorithms and efficient cube solutions. You wouldn't believe how long ago it was that I attempted a computer based cube solution. At the time, I had become adept at assembly languague for the chip in the Apple II and I worked in that. Today I would typically use C++.At the time, I had not found Singmasters book ( the time was roughly 25 years ago) and when I did, I realized that what I was attempting was doomed, so I quit. I was attempting to apply the tree search techniques used for Chess programs to look far ahead and by applying a heuristic scoring method, find likely paths to solution, which would in turn be iterated. In the process, I worked ways to encode the orientation of each cubelet, its postion, and transformation rules for moves etc. As soon as I read Singmaster, I realized how deep the iterations would have to go to reach a convergent solution. That's when I dropped the problem. Some of the recent work which the moderator referenced have moved the state of the art further, but not yet so far as to search and find solutions in a general sense. (If that statement is false, it will be worth the embarassment, if only the critic sends me a URL for source code.) I do have some suggestions about format and linguistic conventions. For an example,go to http://www.ggw.org/donorware/4D_Rubik/ and look at the source code. Yes, that's really all there is. If that helps or you think I should add a few comment lines, let me know. John http://www.frontiernet.net/~jmb184 http://www.ggw.org/donorware From cube-lovers-errors@mc.lcs.mit.edu Thu Aug 5 21:35:14 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id VAA26880 for ; Thu, 5 Aug 1999 21:34:58 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Reply-To: From: "Noel Dillabough" To: "Cube Lovers List \(E-mail\)" Subject: JPuzzler Date: Sat, 31 Jul 1999 11:06:34 -0400 Message-Id: <000001bedb68$878eb170$020a0a0a@NOEL> I have finished the last touches on JPuzzler, the Java port for Puzzler for Windows. Many people with other operating systems asked if I was going to port the program and well, this is it. Speed is an issue. The program runs very well on a PPro200 or better, but I believe the video card that is used makes the biggest difference because on a PII-300 with a basic video card the program ran slower. JPuzzler was written in 100% pure Java so it should work on any Java compatible browser but for now it has only been tested on Netscape 4.5+ and Internet Explorer 4+. I don't have access to other hardware, so I am particularly interested in hearing from players with Macintosh computers, or any flavour of XWindows. All 17 puzzles from Puzzler are implemented and I will probably add more in the future; suggestions and criticism are welcome. http://www.mud.ca/puzzler/JPuzzler/JPuzzler.html -Noel From cube-lovers-errors@mc.lcs.mit.edu Fri Aug 6 11:10:06 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id LAA28883 for ; Fri, 6 Aug 1999 11:10:05 -0400 (EDT) Message-Id: <199908061510.LAA28883@mc.lcs.mit.edu> Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Tue, 3 Aug 1999 02:11:45 -0700 (PDT) From: Tim Browne To: Cube-Lovers@ai.mit.edu Subject: Notes on the Bandaged Cube... combinations and other musings. In-Reply-To: I just picked up a bandaged cube the other day, and I get the feeling that this might be one of the few puzzles which would beat even the Square-1 for solving difficulty. For those of you who haven't seen this nightmare of a cube, Hendrik Haak has a picture of it in the museum section of his Puzzle Shop (he calls it a "Bicube"). After playing around with it for a bit, I figured I'd try and work out the number of possible combinations. The cube is constructed from a standard Rubik's Cube mechanism, so all the standard Rubik's Cube restrictions apply here. The cube is made up of 13 pieces. One of them is created by fusing an edge piece between 2 centres, effectively turning it into a 2x2 piece. Because of this piece, 2 axes of motion are effectively cut off permanently, making a maximum of 4 axes of rotation. There are 4 pieces which are made up by fusing an edge to a centre, 7 pieces are a corner/edge fusion, leaving us with one standard corner piece. These fusions make the puzzle much more difficult than it first appears, as the contortions of all of these 1x2 pieces effectively block axes of rotation which were easily accessible only a quarter turn ago, sometimes getting so bad as to make the only available axis the one you just turned, in some extreme cases even forcing you to back out following exactly the same path you used to enter the current state. Needless to say, this makes solving the puzzle very frustrating indeed. Anyhoo, back to the combinations... Two of the centres are effectively locked into place for all time, leaving us with 4 edge/centre fusions which can be rotated one of 4 ways, giving us a factor of 4^4 combinations. Piece rotations in place are impossible. The first potential restriction would be creating more than one area where only the corner cube could fit, but the 2x2 piece makes this an impossibility. The second would be potential collisions between pieces. There are 5 pairs of adjacent sides where you have a 1:16 chance of a conflict, and 2 ways of creating a double conflict, so we reduce this amount by 5*256/16-2=82, leaving us with 174 possible arrangements of the edge/centre fusions. The edge/corner fusions and the lone corner piece will be handled together. The corner piece can be placed into any one of 8 corner slots, while the edge/corner fusions fit tightly into the remaining slots surrounding it, giving us a factor of 8!=40,320 combinations. Now for the restrictions... let's start with a simple swap first. Let's take an example side. Like numbers in the table are bandaged together. 112 345 345 Would it be possible to swap piece 1 and piece 3? Given the restrictions carried over from the Rubik's Cube, the only way you can swap a pair of edges or a pair of corners is if you also swap either a second pair of the same type, or a pair of its opposite. To see this latter case, rotate a slice of a solved cube 90 degrees either way and then "reconstruct" it using your favourite patterns. God's Algorithm in this case is expressly prohibited. Since the corners and edges are fused, a swap of one expressly implies a swap of the other, so this is OK. How about swapping pieces 3 and 5? This one's a bit more difficult. Not only are you swapping the pieces, but you're rotating them as well. When you swap these 2, both edge pieces are inverted, maintaining the even parity, so that's OK... the corner half of piece 3 is given a positive rotation, while the corner half of piece 5 is given a negative rotation. Modulo 3 parity is maintained, so this is also OK, meaning the whole swap is OK. Swapping any 2 edge/corner fusions on the cube can be broken down into a compound movement of either of these, so any of these pieces can be swapped with any other similar piece without restriction. The second potential restriction happens with edge/centre fusions. In certain special cases, the centres can rotate in such a way they they box in a 1x1x1 area, limiting it to 1 possible place. This can happen in one of two possible ways, bringing our combinations from 174x40,320 down to 172x40,320 + 2x5,040. The final possible restriction happens when we swap an edge/centre fusion with an edge/corner fusion. What happpens when we swap pieces 4 and 5? So you don't have to scroll back, here it is again... 122 122 345 --> 344 ? 345 355 There are 3 problems with this: 1) you're swapping a single pair of edge pieces, 2) you're flipping a single edge piece, and 3) You're rotating a single corner in place, *all* of which are definite no-no's on the Rubik's Cube, either solo or in any combination, so you definitely can't do it here. The corner rotation can be accounted for easily enough by rotating the 1x1x1 piece in place to compensate, which you've probably noticed that I conveniently left out of all calculations to this point, to save multiplying and dividing by 3 unnecessarily. ALL of these problems can be compensated for by either simply not doing it, or by doing the same thing with another set, giving us 2 pairs of swapped edges and 2 edges flipped, compensating for the corner rotation again with the 1x1x1. This effectively slashes the potential combinations in half, bringing us down to 86x40,320 + 1x5,040 = (86x8+1)x5,040 = 689 x 5,040 = 5040 689 ---- 45360 403200 3024000 -------- 3472560 possible combinations. Most puzzles of this type are difficult because of the sheer number of combinations. This is perhaps the only one of this type which is so difficult because of its limits. If you want to take it apart and put it back together randomly, you've got a 1 in 6 1/1920th chance of doing so correctly, perhaps this puzzle's one advantage over the cube. However, if you want to tough it out and devise a pattern for it, then you'll need to work out 172x8+2 = 1,378 patterns to get it back to its default shape, followed by at least 6 more patterns to restore the edge/corner fusions to their proper positions, making at least 1,384 patterns to work out for a general solution. I've graciously decided to leave this as an exercise for the reader. ;-) L8r. From cube-lovers-errors@mc.lcs.mit.edu Fri Aug 6 14:45:54 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id OAA29499 for ; Fri, 6 Aug 1999 14:45:53 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <37A88ED4.B35BA92F@u.washington.edu> Date: Wed, 04 Aug 1999 12:04:52 -0700 From: David Barr To: cube-lovers@ai.mit.edu Subject: Meffert's Assembly Cube I saw on the http://www.mefferts-puzzles.com/ web site that he has a new 3x3x3 cube design. Has anyone gotten their hands on one yet? David From cube-lovers-errors@mc.lcs.mit.edu Fri Aug 6 16:15:54 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id QAA29813 for ; Fri, 6 Aug 1999 16:15:54 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu From: WaVeReBeL@webtv.net Date: Thu, 5 Aug 1999 16:46:13 -0700 (PDT) To: Walter.van.Iterson@emn.ericsson.se Cc: Cube-Lovers@ai.mit.edu Subject: Re: Solving cube with robot arm Message-Id: <17117-37AA2245-5060@postoffice-123.bryant.webtv.net> In-Reply-To: "Walter van Iterson (EMN)"'s message of Fri, 23 Jul 1999 14:32:38 +0200 Hi Walter, Have you visited the web page below? I think this is exactly what you're talking about. http://www2.active.ch/~jbyland/english.html -ALEX- From cube-lovers-errors@mc.lcs.mit.edu Fri Aug 6 17:22:52 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id RAA00162 for ; Fri, 6 Aug 1999 17:22:52 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu From: GJB1332@aol.com Message-Id: <5b03f8b9.24dc5396@aol.com> Date: Fri, 6 Aug 1999 11:04:54 EDT Subject: 5x5x5 To: Cube-Lovers@ai.mit.edu My new 5x5x5 cube arrived a few days ago [took it 8 weeks to be delivered 'cos I was too cheap to get air-mail], and I have a couple of questions pertaining to it: Does anyone know a [reasonably] simple move to swap two edge pieces [the ones on the very edge, not the center and not the corner] around? Also, does anyone know of an equivalent to the Cube Explorer or anything like it that can do 5x5x5 cubes? Thank-you very much, Gary (-; From cube-lovers-errors@mc.lcs.mit.edu Fri Aug 6 17:52:20 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id RAA00242 for ; Fri, 6 Aug 1999 17:52:04 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <379F9979.E9CD2EBD@telegram.infi.net> Date: Wed, 28 Jul 1999 19:59:53 -0400 From: Howard Organization: The Drake Family To: Cube-Lovers Subject: Puzzle Shop, was Rubik's Cube Perpetual Calendar References: Thanks to Chris's post, and his web page, I found a new shop in Germany for twist-to-solve puzzles. It is Hendrik Haak's Puzzle Shop http://www.puzzle-shop.de/ Has anyone in the group ordered from this shop and what have been your results? I especially like the looks of the dogic, octagon, mozaika, and octaedercube puzzles. Has anyone tried these, and does anyone have pictures of them in mid-twist, on their web pages? Thanks for any info. Howard Drake From cube-lovers-errors@mc.lcs.mit.edu Fri Aug 6 18:37:44 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id SAA00506 for ; Fri, 6 Aug 1999 18:37:44 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <37AB5804.6956@sgi.com> Date: Fri, 06 Aug 1999 14:47:48 -0700 From: Derek Bosch Organization: SGI To: Cube-Lovers@ai.mit.edu Subject: scrambling puzzle anyone know the "shortest" sequence of moves to "scramble" a cube... By scramble, my definition is: all six colors on each face (except for 2x2x2), no 2 adjacent tiles of the same color, and no "dominating" color on a face (ie for a 3x3x3 cube, no more than 2 of a single color on a face, for 4x4x4, no more than 3 of a given color on a face). D -- Derek Bosch "A little nonsense now and then (650) 933-2115 is relished by the wisest men"... W.Wonka bosch@sgi.com http://reality.sgi.com/bosch_engr/ From cube-lovers-errors@mc.lcs.mit.edu Fri Aug 6 19:13:19 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id TAA00614 for ; Fri, 6 Aug 1999 19:13:09 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Fri, 6 Aug 1999 18:22:01 -0400 (EDT) From: Nicholas Bodley To: David Barr Cc: cube-lovers@ai.mit.edu Subject: Re: Meffert's Assembly Cube In-Reply-To: <37A88ED4.B35BA92F@u.washington.edu> Message-Id: On Wed, 4 Aug 1999, David Barr wrote: }I saw on the http://www.mefferts-puzzles.com/ web site that he has a new }3x3x3 cube design. Has anyone gotten their hands on one yet? Being a legacy-software addict, I use Lynx (2.8.2dev22) with a shell account, so I haven't seen the images yet, but this seems to be even more desirable than the very-nice, discontinued Ideal DeLuxe Cube. Let's hope that it self-aligns as well as, or better than, the Ideal I mentioned. |* Nicholas Bodley *|* Autodidact & Polymath * Electronic Tech. (ret.) |* Waltham, Mass. *|* ----------------------------------------------- |* nbodley@tiac.net *|* Before 1960 or so: $100. Later: 100$ |* Amateur musician *|* Before 1990 or so: 100%. Later: %100 -------------------------------------------------------------------------- From cube-lovers-errors@mc.lcs.mit.edu Mon Aug 9 14:41:59 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id OAA08180 for ; Mon, 9 Aug 1999 14:41:59 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Fri, 6 Aug 1999 18:18:42 -0400 Message-Id: <003D9A41.C22092@scudder.com> From: Jacob_Davenport@scudder.com (Jacob Davenport) Subject: Re: 5x5x5 To: Cube-Lovers@ai.mit.edu Sure. You can find my full solution to the 5x5x5 at http://www.wunderland.com/WTS/Jake/5x5x5.html. You will want to skip ahead to section on solving the "Wings" as I've been calling them, namely the Sixth Step--Wings to Edges. Let us know when you get to Step Eight. -Jacob Davenport From cube-lovers-errors@mc.lcs.mit.edu Mon Aug 9 15:23:00 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id PAA08335 for ; Mon, 9 Aug 1999 15:22:59 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Sat, 7 Aug 1999 00:37:50 -0700 (PDT) From: Tim Browne To: cube-lovers@ai.mit.edu Subject: Re: Puzzle Shop, was Rubik's Cube Perpetual Calendar In-Reply-To: <379F9979.E9CD2EBD@telegram.infi.net> Message-Id: On Wed, 28 Jul 1999, Howard wrote: > Thanks to Chris's post, and his web page, I found a new shop > in Germany for twist-to-solve puzzles. It is > > Hendrik Haak's Puzzle Shop http://www.puzzle-shop.de/ Actually, that's been around for well over a year now... He has, however, just recently undergone a major change on his site, including adding a museum section with lots of really twisted puzzles. Anyone on this list who checks it out should get a plastic keyboard cover to avoid its shorting out due to the inevitable salivation. A few notables to check out are the Skewb Diamond, the Extended Cube, the Mushroom, and the Rubik's Revenge Special. If anyone can tell me how this is constructed, I'd really like to know about it. > Has anyone in the group ordered from this shop and what > have been your results? I especially like the looks of the > dogic, octagon, mozaika, and octaedercube puzzles. Is the octaeder the Magic Octohedron, or the Cuboctohedron? I placed several puzzles on order with him over a month ago, but he only shipped them out some time last week as there were several he didn't have in stock. Apparently, once they're shipped they take about 6 weeks to reach North America, unless you expedite the service. I asked him about it, but he just kept telling me "$19 for surface mail". :-/ > Has anyone > tried these, and does anyone have pictures of them in mid-twist, > on their web pages? I've placed the Dogic on order... it looks especially nightmarish, but everyone I've heard from who's tried it claimed it was really easy to solve. Given that it's a superset of the Impossiball, I'd think it would be particularly painful. I guess I'll find out once it arrives. The Mozaika I haven't seen yet, but it doesn't look all that difficult... Then again, I also thought that including a hint book with the Square-1 was an insult to the intelligence and that anyone with as much experience as I had with Rubik's Cube and similar puzzles should have no problem with it before I found out just how wrong I was (it took over a year for me to solve it once), so who's to say? For the other two... if you mean the "Octagon barrel", it's basically a Rubik's Cube subset, The Magic Octahedron can be solved as 2 Pyraminxen slammed back to back, and the Cuboctohedron, being no more than a Rubik's Cube with huge chunks sliced out of it, would be solved the same way. As for pictures showing puzzles in mid twist, the only site I'm aware of with pictures like that would be Chris and Kori's page. L8r. From cube-lovers-errors@mc.lcs.mit.edu Mon Aug 9 16:02:48 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id QAA08424 for ; Mon, 9 Aug 1999 16:02:38 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <000201bee0f0$f84cace0$295755ca@pca200series> From: "MEFFERT" To: Subject: Meffert's Puzzles News Date: Sun, 8 Aug 1999 00:17:46 +0800 Dear Gary Sorry to hear that you had to wait 8 weeks for your Prof. cube to arrive. So here is some good news for Cube Lovers. We are offering free Airmail Postage for all of our puzzles ordered during the Summer Holidays. I would also like to announce our New PUZZLER CHALLENGE of the Month competition. Starting with the 3x3x3 cube and Orbix which can be played both with mouse or SpaceOrb. The fasted time in each category, puzzle plus mouse or SpaceOrb receives a free puzzle of their choice. There will be a different Puzzle each month. See: http://www.mud.ca/puzzler/JPuzzler/challenge.html You can practice on line at: http://www.mud.ca/puzzler/JPuzzler/JPuzzler.html For all cube lovers that do not have a SpaceOrb and would like one, we have arranged a special deal with Spacetec who will ship the SpaceOrbs ordered directly by UPS, at the Special Price of US$45.00 including free delivery in the USA & Canada, add US$16.00 for all other countries, see our Puzzle Shop. I will be announcing the start of the "Mind Sports Olympiad 2000, Puzzle Championships soon. There will be great prizes, puzzles must be played both online as well as the real thing. The finals will be held August 19 - 27 the Year 2,000 in the National Hall at Olympia in London UK, which has 9,000 square meters of floor space (approx 100,000 square feet). Something very spectacular is being planned for the millennium year. We intend to smash the record for the largest number of entries at any Olympiad ever, which currently stands at 10,744 for the Olympic Games in Atlanta 1996. This will be achieved by having a number of "biggest ever" tournaments including the Puzzle Championships within the Mind Sports Olympiad. HAPPY PUZZLING TO ALL Uwe Uwe Meffert MPG, "Meffert's Puzzles & Games" 2008, Remex Centre, 42 Wong Chuk Hang Road, P.O. Box 24455, Aberdeen, Hong Kong. Email:- Meffert@mefferts.com www.mefferts.com From cube-lovers-errors@mc.lcs.mit.edu Mon Aug 9 18:30:49 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id SAA08961 for ; Mon, 9 Aug 1999 18:30:48 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu To: cube-lovers@ai.mit.edu From: whuang@ugcs.caltech.edu (Wei-Hwa Huang) Subject: Re: Rubik's Cube Perpetual Calendar Date: 7 Aug 1999 18:53:51 GMT Organization: California Institute of Technology, Pasadena Message-Id: <7ohvbv$k0t@gap.cco.caltech.edu> References: Corey Folkerts writes: >I've attached a jpg of how I arranged all the characters. I make >no guarantees that is works, but I'm pretty sure it does. >Sorry to those of you who can't receive files. I would have made the >drawing ASCII, but I can't make upside or sideways characters =( >-Corey Folkerts >[Moderator's note: I don't send binary attachments out on this list. > However, I was able to decode Corey's picture, and here's a diagram. > Sorry for the delay in sending this message out. --Dan ] For those of you who want to see the original jpg, I've put it on my website at http://www.ugcs.caltech.edu/~whuang/gp/cube/calender-cube.jpg If anyone else would like to share graphics and stuff with the rest of cube-lovers, I can provide similar services. Offer good until I get overwhelmed (not likely, I think). -- Wei-Hwa Huang, whuang@ugcs.caltech.edu, http://www.ugcs.caltech.edu/~whuang/ --------------------------------------------------------------------------- It's not sarcasm. It's reductio ad absurdum. From cube-lovers-errors@mc.lcs.mit.edu Wed Aug 11 12:02:16 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id MAA16647 for ; Wed, 11 Aug 1999 12:02:16 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <37ADC0A2.35DC8809@pressenter.com> Date: Sun, 08 Aug 1999 12:38:42 -0500 From: Joe Johnson To: Cube-Lovers@ai.mit.edu Subject: repairing broken cubes I recently broke one of the face cubies of my 4X4. I attempted to repair it by drilling a hole for a pin and gluing it together (it broke in the "ankle" that holds the "foot" to the top.) I tried several different types of glues and epoxies and nothing seemed to stick very well. I finally used some woodworkers glue and it is holding together for now. I'm being very carefull and cannot do any fast moves with it. Does anyone know of a better way to repair these types of breaks. I would not have attempted the repair at all if the cubes were still readily available, but since they are out of production I have little choice. This is the second 4X4 I've broken in this manner. Joe Johnson From cube-lovers-errors@mc.lcs.mit.edu Wed Aug 11 13:54:40 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id NAA17010 for ; Wed, 11 Aug 1999 13:54:30 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu From: gete@cheerful.com Message-Id: <007401bee3ec$7e546640$9f1c9eca@dzine> To: References: <37AB5804.6956@sgi.com> Subject: Re: scrambling puzzle Date: Wed, 11 Aug 1999 18:21:34 +0700 Derek Bosch wrote: > anyone know the "shortest" sequence of moves to "scramble" > a cube... By scramble, my definition is: > > all six colors on each face (except for 2x2x2), no 2 adjacent tiles > of the same color, and no "dominating" color on a face (ie for > a 3x3x3 cube, no more than 2 of a single color on a face, for > 4x4x4, no more than 3 of a given color on a face). I don't, but for 3x3x3, I use software: Cube Explorer by H.Kociemba http://home.t-online.de/home/kociemba/cube.htm Here are some move sequences I get: * D L2 B2 F2 R2 U' L2 . F L2 B2 R F2 D' U R2 B L2 R2 B R2 (20 moves) * U2 F' L2 B D2 B F' U2 . R' B D R' F' L R U' F' L2 R U' (20 moves) Just apply them on an already-solved cube.