From: barnabyfinch@pe.net (Barnaby Finch) Subject: Re: Rubik's cube Date: Thu, 13 Jan 2000 21:37:51 GMT Newsgroups: sci.math Summary: [missing] In article <85imsi$921$1@wanadoo.fr>, "Keyser Soze" wrote: > Hello everybody!!I'm a french studient, and i'm studying the most famous > puzzle in the world: the Rubik's cube. > I found some articles who were talking about groups, and number of > solutions, optimization, matrix, etc... a lot of maths, and i would like to > find more about it, i'd like to make a really good study... please help me > find some results from scientists, so that i learn many many things. is > there anyone who can help me? send me your answers to: > bob.le.manouche@wanadoo.fr > thanks to everyone try: http://web.usna.navy.mil/~wdj/rubik_nts.htm http://web.idirect.com/~cubeman/index.html or, peut etre, the old, unimpeachable source: Notes on Rubik's Cube by David Singmaster c'est tres magnifique! Barnaby ============================================================================== From: ishmnn@cap.bekkoame.or.jp (Ishihama Yoshiaki) Subject: Re: Rubik's cube designs Date: Sat, 15 Jan 2000 01:06:00 +0900 Newsgroups: rec.puzzles,alt.math,sci.math,alt.math.recreational,alt.brain.teasers,misc.writing,cz.soc.mensa Summary: [missing] In article <387DD6C1.24CC@ameritech.net>, hbizek@ameritech.net wrote: > Hello, all, > some of you will know me from previous postings. My quest for > 3-dimensional Rubik's cobe designers is still a dismal zero. There is a > real danger that I am the first to have come up with this. Please, if > you know of anyone who does something similar to what I have done, let > me know. The page to look at is http://cube.misto.cz. Please go down to > the Appendices and click on "Thre-dimensional designs of Dr. Hana M. > Bizek." Thank you. 3D Rubik cube is out of date, too old. Forget that. Check my 4D rubik Cube applet please. I also made 5D Rubik Cube simulations for Mac. http://www.bekkoame.ne.jp/~ishmnn/java/java.html -- Ishihama Yoshiaki E-mail: ishmnn@cap.bekkoame.ne.jp URL: http://www.asahi-net.or.jp/~hq8y-ishm/ ============================================================================== From: jmb184@frontiernet.net (John Bailey) Subject: Re: Rubik's tour. Date: Sat, 22 Jan 2000 13:14:55 GMT Newsgroups: rec.puzzles,alt.math,sci.math,alt.math.recreational,alt.brain.teasers,misc.writing,cz.soc.mensa Summary: [missing] On Fri, 21 Jan 2000 23:39:24 GMT, "Androcles" wrote: >There is a well-known little puzzle known as the "Knight's Tour". >The object of the puzzle is to have the (chess) knight visit all 64 squares >on the chessboard (snip) >Suppose we have Rubik's cube, and suggest a tour such that all possible >outcomes of the various configurations are presented. We begin with the >identity. >Question three, analogous to the knight's tour. >How many configurations are there, each to be visited once and once only? >Question four. >Is this possible? >Question five: >How many moves does it take to return to the identity? There may be other ways to interpret *tour* in the context of a Rubik cube but this one is a lot of fun. Using a Rubiks cube simulator with macro capability such as http://www.mud.ca/cube/cube.html enter a sequence of moves. How many repetitions of these identical moves will return the cube to its original state? What sequence requires the most repetitions to restore? John ============================================================================== From: jmb184@frontiernet.net (John Bailey) Subject: Re: Rubik's cube group Date: Sat, 12 Aug 2000 12:11:17 GMT Newsgroups: sci.math Summary: [missing] On Sat, 12 Aug 2000 07:00:06 GMT, kingjupiter@my-deja.com wrote: >Has anyone looked into the group of permutations induced by the Rubik's >cube (modulo the symetries of the cube.) http://web.usna.navy.mil/~wdj/rubik_nts.htm (quoting Dan Hoey) Lecture notes on the mathematics of the Rubik's cube Introduction chapter 0 : Logic chapter 1 : Functions on sets chapter 2 : Permutations chapter 3 : Permutation puzzles part 1 part 2 part 3, chapter 4 : Some solution strategies chapter 5 : Groups, I chapter 6 : Orbits, actions and cosets chapter 7 : Cayley graphs and God's algorithm chapter 8 : Symmetry groups of the Platonic solids chapter 9 : Groups, II chapter 10 : Structure of the Rubik's cube group chapter 11 : Rubika esoterica chapter 12 : Realizing PGL(2,F5) inside the Rubik's cube group References See also the Cube Lover's Archive, do a search within the document using the key word group. http://www.math.rwth-aachen.de/~Martin.Schoenert/Cube-Lovers/Index_by_Subject.html John ============================================================================== From: kingjupiter@my-deja.com Subject: Re: Rubik's cube group Date: Mon, 14 Aug 2000 02:29:06 GMT Newsgroups: sci.math Summary: [missing] In article <8n7l3f$1e7$1@nnrp1.deja.com>, kingjupiter@my-deja.com wrote: > In article , > Fred W. Helenius wrote: > > kingjupiter@my-deja.com wrote: > > > > >In article <8n4j3e$7q$1@nntp.Stanford.EDU>, > > > theodore hwa wrote: > > >> kingjupiter@my-deja.com wrote: > > > > >> : (fr)^63=1 > > > > >> I believe it should be 105, not 63. (write out the cycle structure of > > >> the permutation, or try it on an actual cube if you're really bored ;) > > > > >I did it twice. Both times I got 63. > > > > Are you sure you're not doing fr' or f'r (i.e., one of the turns > > clockwise and the other counterclockwise)? Those motions have > > period 63; fr (both turns clockwise) has period 105. > > > > Yes, most likely, this is what I am doing...let me check... > > Yes, I am turning one clockwise and the other counterclockwise... > > Does anybody know what the order of this group is off the top of their > heads? Nevermind, I found it... http://web.usna.navy.mil/~wdj/sm485_11.txt The above link has lots of cool info about this group. Thanks everyone for the info. I wonder if the Rubiks cube would be a good teaching device for an basic group theory class? Or maybe the "baby" Rubiks cube? [multiple sigs deleted --djr] ============================================================================== From: MattCAnderson1@juno.com Subject: Re: Rubik's cube group Date: Tue, 15 Aug 2000 06:57:00 GMT Newsgroups: sci.math In article <8n2sll$umt$1@nnrp1.deja.com>, kingjupiter@my-deja.com wrote: > Has anyone looked into the group of permutations induced by the Rubik's > cube (modulo the symetries of the cube.) > > It seems to have 6 generators > > f (front) > b (back) > l (left) > r (right) > u (upper) > d (downside) (I didn't want to use b or l again.) > > and relations > > fb=bf (this three relations come from turning non-incident faces) > lr=rl > ud=du > (fr)^63=1 > (and 11 more relations of this form for each pair of incident faces.) > > What other relations do I need in order to pin down the Rubik's cube > group? How many elements are in this group? > > THanks for any info. > > Sent via Deja.com http://www.deja.com/ > Before you buy. > Hi, I have a copy of 'Notes on Rubik's Magic Cube' by David Singmaster. I will quote some things from it: The number of different patterns is: N=(2^27)*(3^14)*(5^3)*(7^2)*11 N is about 4.3 * 10^19 a little notation: L-1 means move L face the other direction L2 means move L face twice. It is possible to generate the entire group with only 5 of the 6 moves. One way to do this is: Let A = RL-1F2B2RL-1 then AUA = D. So you can get the effect of moving the downside, without actually doing so. "Frank Barnes observes that the group of the cube is generated by two moves: alpha = L2BRD-1L-1 beta = UFRUR-1U-1F-1 Observe that alpha^7 is an 11-cycle of edges and alpha^11 is a 7-cycle of corners" It is a nice little book and has lots of results about Rubik's Cube. Matt Sent via Deja.com http://www.deja.com/ Before you buy. ============================================================================== From: ajw01@uow.edu.au (Andrew John Walker) Subject: Re: looking for "Cube Solver" Windows program Date: 14 Aug 2000 16:14:32 +1000 Newsgroups: sci.math Summary: [missing] midi-man writes: >Before I reformatted my harddrive, I had a Windows program called >"Cube Solver" written by a man in Germany for solving the Rubik's. >Does anyone have the URL for his page. It was a great little program, >and it could search for patterns too. Thanks. http://home.t-online.de/home/Kociemba/cube.htm Andrew ============================================================================== From: daniel_mcl@hotmail.com (Daniel McLaury) Subject: Re: cube solver Date: 15 Aug 2000 00:22:23 -0400 Newsgroups: sci.math This page has instructions for solving one; you can write your own program, if you know how. The directions are quite simple, in fact, and it also has directions for cubes with sides of 2, 4, and 5! http://www.unc.edu/~monroem/rubik.html ============================================================================== From: jmb184@frontiernet.net (John Bailey) Subject: Re: cube solver Date: Tue, 15 Aug 2000 11:28:57 GMT Newsgroups: sci.math On 15 Aug 2000 00:22:23 -0400, daniel_mcl@hotmail.com (Daniel McLaury) wrote: >This page has instructions for solving one; you can write your >own program, if you know how. The directions are quite simple, >in fact, and it also has directions for cubes with sides of >2, 4, and 5! > >http://www.unc.edu/~monroem/rubik.html Nice site. To be complete you could add http://www.frontiernet.net/~jmb184/interests/puzzles/4Cube/solution/ for a solution to the 2x2x2x2 (four dimensional cube) John