From alan@ai.mit.edu Sun Oct 14 20:01:36 1990 Return-Path: Received: from wheat-chex (wheat-chex.ai.mit.edu) by life.ai.mit.edu (4.1/AI-4.10) id AA28610; Sun, 14 Oct 90 20:01:36 EDT From: alan@ai.mit.edu (Alan Bawden) Received: by wheat-chex (4.1/AI-4.10) id AA02846; Sun, 14 Oct 90 20:01:37 EDT Date: Sun, 14 Oct 90 20:01:37 EDT Message-Id: <9010150001.AA02846@wheat-chex> To: cube-lovers Subject: Testing 1 2 3 This message shouldn't go anywhere except into the archive and into my own mailbox. I anyone else gets it, then it will be time to give up and go home. From alan@ai.mit.edu Sun Oct 14 20:48:51 1990 Return-Path: Received: from wheat-chex (wheat-chex.ai.mit.edu) by life.ai.mit.edu (4.1/AI-4.10) id AA29523; Sun, 14 Oct 90 20:48:51 EDT From: alan@ai.mit.edu (Alan Bawden) Received: by wheat-chex (4.1/AI-4.10) id AA03070; Sun, 14 Oct 90 20:48:52 EDT Date: Sun, 14 Oct 90 20:48:52 EDT Message-Id: <9010150048.AA03070@wheat-chex> To: cube-lovers Subject: [alan@ai.mit.edu: Surprise!] Now that the archive is fixed again, here is the message that I sent to resurrect the list: From: alan@ai.mit.edu (Alan Bawden) Date: Fri, 12 Oct 90 16:03:05 EDT To: cube-lovers Subject: Surprise! That's right. Cube-Lovers has returned from the dead. Due to various hardware, software and personal crises, Cube-Lovers has been down since sometime last spring. I'm sure that many of you didn't even notice, given what a low-volume list this has become. Our "official" addresses remain Cube-Lovers@AI.AI.MIT.EDU for submissions and Cube-Lovers-Request@AI.AI.MIT.EDU for administrivia. (Actually, you will find that using simply "...@AI.MIT.EDU" will work just as well.) Since this is the first message to this list after moving it to a new machine with a different mailer, I expect that many addresses on the list have ceased to function. If I were you, I wouldn't send any mail here for about a week -- just to give me a chance to process all the bounces I'm about to get. The archives are currently unavailable, but I hope to have them available for FTP soon. From alan@ai.mit.edu Mon Oct 15 03:11:33 1990 Return-Path: Received: from wheat-chex (wheat-chex.ai.mit.edu) by life.ai.mit.edu (4.1/AI-4.10) id AA05272; Mon, 15 Oct 90 03:11:33 EDT From: alan@ai.mit.edu (Alan Bawden) Received: by wheat-chex (4.1/AI-4.10) id AA05063; Mon, 15 Oct 90 03:11:35 EDT Date: Mon, 15 Oct 90 03:11:35 EDT Message-Id: <9010150711.AA05063@wheat-chex> To: cube-lovers Subject: Second Announcement OK, I think I've cleaned up Cube-Lovers enough that it's safe for anyone to use it. (For some of you this message is the first indication that Cube-Lovers is back -- many copies of my first announcement bounced back to me.) Those of you who keep asking for the archives will be pleased to know that they are again available for anonymous FTP: Connect to AI.MIT.EDU, login as "anonymous" (any password), and in the directory "/pub/alan" you will find the seven (compressed) files "cube-mail-0.Z" through "cube-mail-6.Z". Archive vital statistics: File From To Size (bytes) ---- ---- -- ------------ cube-mail-0 12 Jul 80 23 Oct 80 185037 cube-mail-1 3 Nov 80 9 Jan 81 135719 cube-mail-2 10 Jan 81 3 Aug 81 138566 cube-mail-3 3 Aug 81 3 May 82 137753 cube-mail-4 4 May 81 11 Dec 82 139660 cube-mail-5 11 Dec 82 6 Jan 87 173364 cube-mail-6 10 Jan 87 13 Apr 90 216733 (Unfortunately, due to the way mail works here at the AI Lab, it is not possible to have the current active archive accumulate anywhere where anonymous FTP can pick it up.) As you can see, things really slacked off after 1982, and we were really quiet during the middle of the decade. For those of you who missed my first message, let me repeat that our "official" addresses remain Cube-Lovers@AI.AI.MIT.EDU for submissions and Cube-Lovers-Request@AI.AI.MIT.EDU for administrivia. - Alan From pbeck@pica.army.mil Mon Oct 15 08:13:57 1990 Return-Path: Received: from FSAC1.PICA.ARMY.MIL by life.ai.mit.edu (4.1/AI-4.10) id AA07903; Mon, 15 Oct 90 08:13:57 EDT Date: Mon, 15 Oct 90 8:08:48 EDT From: Peter Beck (LCWSL) To: cube-lovers@life.ai.mit.edu Cc: pbeck@pica.army.mil Subject: [To: cube-lovers-incoming%csl.: algorithm] Message-Id: <9010150808.aa22705@FSAC1.PICA.ARMY.MIL> welcome back ----- Forwarded message # 1: Date: Fri, 1 Jun 90 12:00:37 EDT From: Peter Beck (LCWSL) To: cube-lovers-incoming%csl.ti.com@relay.cs.net cc: pbeck@PICA.ARMY.MIL Subject: algorithm Message-ID: <9006011200.aa13780@FSAC1.PICA.ARMY.MIL> Date: Tue, 27 Mar 90 22:23:00 EST From: adobe!uunet!canremote!nigel.allen@labrea.stanford.edu Subject: PROGRAMMING NEWSLETTER A.K. Dewdney, Computer Recreations columnist with Scientific American magazine, has launched a personal programming newsletter, Algorithm. The new publication is aimed at amateur and professional programmers alike. It extends the Computer Recreations tradition of recreational and educational programming projects: the Mandelbrot set, cellular automata, chaos and dynamics, weird machines, stellar simulation, puzzles and many other topics. The new publication carries seven features and will expand to include more columns. Currently, it includes Algoletter, advice from professionals; Easy Pieces, fascinating projects for beginning programmers by Michael Ecker of Creative Computing fame; Personal Programs, exercises for more advanced programmers by Cliff Pickover, IBM's computer graphics wizard; Algopuzzles, computer mind-benders by Dennis Shasha, author of The Puzzling Adventures of Dr. Ecco; Algofact and Algofiction, invited articles and stories from well-known scientists and authors. A Bulletin Board advertises hosts of recreational products by individuals and small companies. Algorithm puts the "personal" back in "personal computing" by encouraging you to develop your programming skills while pursuing high adventure on the frontiers of science and computing. Order a free examination copy by writing Algorithm at P.O. Box 29237, Westmount Postal Outlet, 785 Wonderland Road, London, Ontario, Canada N6K 1M6. --- MaS Relayer v1.00.00 Message gatewayed by MaS Network Software and Consulting/HST Internet: nigel.allen@canremote.uucp UUCP: ...tmsoft!masnet!canremote!nigel.allen ------- from infomac ----- ----- End of forwarded messages From alan@ai.mit.edu Thu Oct 18 17:06:55 1990 Return-Path: Received: from wheat-chex (wheat-chex.ai.mit.edu) by life.ai.mit.edu (4.1/AI-4.10) id AA02418; Thu, 18 Oct 90 17:06:55 EDT From: alan@ai.mit.edu (Alan Bawden) Received: by wheat-chex (4.1/AI-4.10) id AA03710; Thu, 18 Oct 90 17:06:51 EDT Date: Thu, 18 Oct 90 17:06:51 EDT Message-Id: <9010182106.AA03710@wheat-chex> To: cube-lovers Subject: Archives again I hate to bother you folks again so soon, but naturally the AI Lab chose today to reorganize how anonymous FTP access worked. Here are the updated instructions for accessing the Cube-Lovers archives: Connect to TRIX.AI.MIT.EDU, login as "anonymous" (any password), and in the directory "pub/cube-lovers" you will find the seven (compressed) files "cube-mail-0.Z" through "cube-mail-6.Z". Archive vital statistics (when uncompressed): File From To Size (bytes) ---- ---- -- ------------ cube-mail-0 12 Jul 80 23 Oct 80 185037 cube-mail-1 3 Nov 80 9 Jan 81 135719 cube-mail-2 10 Jan 81 3 Aug 81 138566 cube-mail-3 3 Aug 81 3 May 82 137753 cube-mail-4 4 May 81 11 Dec 82 139660 cube-mail-5 11 Dec 82 6 Jan 87 173364 cube-mail-6 10 Jan 87 13 Apr 90 216733 (Unfortunately, due to the way mail works here at the AI Lab, it is not possible to have the current active archive accumulate anywhere where anonymous FTP can pick it up.) From pbeck@pica.army.mil Wed Oct 24 13:47:23 1990 Return-Path: Received: from FSAC1.PICA.ARMY.MIL by life.ai.mit.edu (4.1/AI-4.10) id AA21425; Wed, 24 Oct 90 13:47:23 EDT Date: Wed, 24 Oct 90 13:34:45 EDT From: Peter Beck (LCWSL) To: cube-lovers@life.ai.mit.edu Subject: puzzling events Message-Id: <9010241334.aa15999@FSAC1.PICA.ARMY.MIL> CUBING/PUZZLING EVENTS rev 10/24/90 <--> DUTCH CUBE DAY IS: ---- 8 dec 1990 ---- Prof Willem van der Poel's new residence ---- in the netherlands <--> International puzzle collector's party (I think it is #11) ---- 3/31/91 Easter Sunday ---- culver city, ca *** Admission by invitation only!!! Contact Mr. jerry slocum, 257 south palm drive, beverly hills, ca 90212 for an invitation. From pbeck@pica.army.mil Thu Oct 25 15:26:10 1990 Return-Path: Received: from FSAC1.PICA.ARMY.MIL by life.ai.mit.edu (4.1/AI-4.10) id AA24321; Thu, 25 Oct 90 15:26:10 EDT Date: Thu, 25 Oct 90 15:17:59 EDT From: Peter Beck (LCWSL) To: cube-lovers@life.ai.mit.edu Subject: puzzling newsletters Message-Id: <9010251518.aa13527@FSAC1.PICA.ARMY.MIL> PUZZLING NEWSLETTERS -- Oct 90 .......................................................... "Cubism For Fun" The newsletter of the "Dutch Cubists Club"; in english starting with issue #14. Back issues are available. The club has over 100 active members, notable new addition Martin Gardner. Membership for 1990 is US$8. A photocopied set of the newsletters, issues 1-13, written in DUTCH (in the future selected back articles will be available in english) is also available for US$7. To order either of these send an 'INTERNATIONAL" POSTAL MONEY ORDER (cost $3 at post office) to: Paul Sijben, Witbreuksweg 397-304, NL-7522 ZA Enschede, The Netherlands. .......................................................... WORLD GAME REVIEW Michael Keller publishes a newsletter that explores the mathematical aspects of games & puzzles. 4 issues for US$11, published erratically. Back issues are available. MICHAEL KELLER, 3367-1, NORTH CHATAM ROAD, ELLICOTT CITY, MD 21043, USA .......................................................... 'PUZZLETOPIA" NOB YOSHIGAHARA has just mailed out a new issue (after 3 yrs) of his newsletter 'PUZZLETOPIA". With it came a 1990 promotional calendar from PUZZLE CITY (a subsidary of Toyo Glass) a puzzle city catalog and a catalog from PUZZLAND HIKIMI PUZZLE COLLECTION. If you want the whole package write Nob (its free outside of Japan). NOB YOSHIGAHARA, 4-10-1-408 IIDABASHI, TOKYO 102 JAPAN. .......................................................... ARM Bulletin (ACADEMY of RECREATIONAL MATHEMATICS), JAPAN This is a monthly 40-80 page newsletter of the Japanese puzzle hobbiests club. Dues Y8,000. PUZZLE KONWAKAI C/O S. TAKAGI, 1-2-4 MATSUBARA, SE TAGAYAKU, TOKYO 156 JAPAN .......................................................... From pbeck@pica.army.mil Thu Oct 25 15:26:06 1990 Return-Path: Received: from FSAC1.PICA.ARMY.MIL by life.ai.mit.edu (4.1/AI-4.10) id AA24312; Thu, 25 Oct 90 15:26:06 EDT Date: Thu, 25 Oct 90 15:16:29 EDT From: Peter Beck (LCWSL) To: cube-lovers@life.ai.mit.edu Subject: oxford press books Message-Id: <9010251516.aa12361@FSAC1.PICA.ARMY.MIL> Oxford University Press publishes a series of books called Recreations in Mathematics. The series editor is David Singmaster of Rubik's Cube fame. They are priced at about $28 each. As of Oct 90 the series contains the following: #1 "Mathematical Byways ...", by Hugh ApSimon. #2: "Ins and Outs of Peg Solitaire", by John Beasley. #3: "Rubik's Cubic Compendium", by Rubik, et al. #4 "Sliding Piece Puzzles", by L.E. Hordern. #5 "The Mathematics of Games", by John Beasley. #6 "The Puzzling World of Polyhedral Dissections", by Stewart Coffin. #7 "More Mathematical Byways", by Hugh ApSimon. TO ORDER: Send check or credit card info (MASTERCARD OR VISA) to: SCIENCE & MEDICAL MARKETTING DIRECTOR, OXFORD UNIVERSITY PRESS 200 MADISON AVE, NEW YORK, NY 10016 - -- > ADD $1.50 for shipping From pbeck@pica.army.mil Fri Oct 26 20:05:37 1990 Return-Path: Received: from FSAC1.PICA.ARMY.MIL by life.ai.mit.edu (4.1/AI-4.10) id AA19290; Fri, 26 Oct 90 20:05:37 EDT Date: Fri, 26 Oct 90 15:25:41 EDT From: Peter Beck (LCWSL) To: cube-lovers@life.ai.mit.edu Subject: puzzling events expanded Message-Id: <9010261525.aa18619@FSAC1.PICA.ARMY.MIL> CUBING/PUZZLING EVENTS rev 10/26/90 ............................................................... <--> The 10th DUTCH CUBE DAY <--> ............................................................... WHEN ---- 8 dec 1990 WHERE ---- Prof Willem van der Poel's new residence, DUBLINSTRAAAT 143, ZOETERMEER, THE NETHERLANDS TIME ---- 10:00 AM INVITITATIONS: Prof van der Poel, tel # 079-211912 or Anneke Treep, tel# 074-501181 AGENDA: .. LECTURES - A NEW CUBE SOLVING ALGORITHM BY HANS KLOOSTERMAN, POLYLINKS BY NANCO BORDEWIJK, WIRREL-WARREL CUBES BY JAN DE GEUS, POLYSPHERES BY BERNARD WIEZORKE .. EXHIBITIONS - PUZZLE COLLECTION OF Willem van der Poel, TRACO PUZZLES BY GERARD TRAABACH, NEW PUZZLES BY OSCAR VAN DEVENTER AND WILL STRIJBOS, POLYHEDRAL DISSECTIONS BY JOACHIM KRAUSE AND ANTON HANEGRAF .. PRIZE CONTESTS - RUBIKS CUBE COMPETIYION, EKKEHARD KUNZELL'S GAME RESERVAT .. VIDEO SHOWS - EALIER CUBE DAYS, FAST CUBE SOLVING ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ............................................................... <--> 11th International puzzle collector's party and fair <--> ............................................................... WHEN ---- 3/31/91 Easter Sunday WHERE ---- PACIIFICA HOTEL, 6161 CENTINELA AVE, culver city, ca, 90231-2200 USA, TEL # 213/649-1776. This is near Los Angeles Airport and a hotel courtesy bus will take travelers from airport to hotel. INVITATIONS *** Admission by invitation only!!! Contact Mr. jerry slocum, 257 south palm drive, beverly hills, ca 90212 for an invitation. AGENDA: .. PUZZLE PARTY .. SALES /EXHIBITS table rental available .. Saturday evening (3/30) dinner and magic show, estimated cost $40 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ From pbeck@pica.army.mil Fri Nov 9 11:09:19 1990 Return-Path: Received: from FSAC1.PICA.ARMY.MIL by life.ai.mit.edu (4.1/AI-4.10) id AA10686; Fri, 9 Nov 90 11:09:19 EST Date: Fri, 9 Nov 90 8:41:23 EST From: Peter Beck (LCWSL) To: Cube-Lovers@life.ai.mit.edu Subject: [To: cube-lovers: CFF #24] Message-Id: <9011090841.aa19903@FSAC1.PICA.ARMY.MIL> ----- Forwarded message # 1: Date: Wed, 7 Nov 90 8:56:58 EST From: Peter Beck (LCWSL) To: cube-lovers@ai.ai.mit.edu cc: pbeck@PICA.ARMY.MIL Subject: CFF #24 Message-ID: <9011070856.aa07569@FSAC1.PICA.ARMY.MIL> SEND TO: CUBE-LOVERS@AI.AI.MIT.EDU SUBJECT : Review of "Cubism For Fun" newsletter issue #24, July 90; the newsletter of the "Dutch Cubists Club"; in english starting with issue #14 1.. The table of contents for issue # 24, july 90 follows: TENTH CUBE DAY announcement by the secretary GRAND PRIX editors announcement of the results of the "HIKIMI WOODEN PUZZLE COMPETITION 1990" PENTAKUBEN CONTEST ANNOUNCEMENT BY EKKEHARD KUNZELL SQUA-RING by Nanco Bordewijk BLOCKED SLIDING by Wim Zwaan LOGICAL LABYBRINTHS PART 2 by Anneke Treep THE RHYTM OF MIX-BOX by Anton Hanegraaf PRETTY CUBIC PATTERNS by Anneke Treep A STRING FOLDING PROBLEM by Oskar van Deventer KEY THROUGH KEY by Oskar van Deventer MEMEBRSHIP FEE TOP SPIN PROCESSES by Bernhard Wiezorke and Anton Hanegraaf "SEVEN" PUZZLES by Dieter Gebhardt and Anton Hanegraaf THE CASCADE PYRAMID PROBLEM by joachim Krause THE DUTCH DRAUGHTBOARD PUZZLE by Wil Strijbos CRACKING THE (MAGIC) CROSS BY Ronald Fletterman WIRREL-WARREL SUPER CUBE by Paul Sijben A HEXOMINO PROBLEM by Pieter Torbijn NEWS AND LETTERS TO THE EDITOR - INTERNATIONAL PUZZLE PARTY ANNOUNCEMENT BY JERRY SLOCUM BACK ISSUES announcement CHANGES IN THE LIST OF MEMBERS - 120 active members and growing * Also an ad from STRIJBOS offering to sell his bolt puzzle (US$28 ppd) and a COCA-COLA BOTTLE puzzle (US$12 ppd) 2. Membership for 1990 is US$8. A photocopied set of the newsletters, issues 1-13, written in DUTCH (in the future selected back articles will be available in english) is also available for US$7. To order either of these send an 'INTERNATIONAL" POSTAL MONEY ORDER (cost $3 at post office) to: Paul Sijben, Witbreuksweg 397-304, NL-7522 ZA Enschede, The Netherlands. 3. If anybody would like further details please ask! CUBING IS FOREVER PETER BECK ----- End of forwarded messages From hoey@aic.nrl.navy.mil Fri Nov 9 15:01:52 1990 Received: from Sun0.AIC.NRL.Navy.Mil by life.ai.mit.edu (4.1/AI-4.10) id AA16350; Fri, 9 Nov 90 15:01:52 EST Received: from sun13.aic.nrl.navy.mil by Sun0.AIC.NRL.Navy.Mil (4.1/SMI-4.0) id AA24929; Fri, 9 Nov 90 14:57:26 EST Return-Path: Received: by sun13.aic.nrl.navy.mil; Fri, 9 Nov 90 15:02:48 EST Date: Fri, 9 Nov 90 15:02:48 EST From: hoey@aic.nrl.navy.mil Message-Id: <9011092002.AA00993@sun13.aic.nrl.navy.mil> To: Cube-Lovers@life.ai.mit.edu Subject: Rubik's Cube reassembly problem and solution References: <3924@idunno.Princeton.EDU> <1990Nov8.182534.18625@agate.berkeley.edu> Reply-To: Hoey@aic.nrl.navy.mil (Dan Hoey) In rec.puzzles article <1990Nov8.182534.18625@agate.berkeley.edu>, greg@math.berkeley.edu (Greg Kuperberg) writes: >Consider a standard Rubik's cube. Disassemble it and put it back >together at random. Find, with proof, the probability that it can be >solved. It depends on how you take it apart. If you just pull out the corner and edge pieces then put them back in without respect to color, the probability is one in 12 that you will put it back into the right orbit. I won't bore you with yet another proof of this; if you spent the last decade in a box see the archives, Singmaster's NOTES ON RUBIK'S MAGIC CUBE, J. A. Eidswick's article in the March 1986 Math Monthly, or even Hofstadter's METAMAGICAL THEMAS. Now if you take the face centers off and scramble them, then there is only one chance in 60 of getting it right. Of the 720 permutations of the six face centers, only 24 can be generated by rigid motions of the cube. But half of these 24 permutations are odd, and leaving the cube in an unsolvable orbit. If you put the face centers on in the ``standard'' configuration with opposite faces ``differing by yellow'' (i.e., white opposite yellow, red opposite orange, and blue opposite green), your chances go up to one in four--half the time you will get an odd permutation, and half the time you will get a mirror-reversed configuration. But wait, if you took the face centers off you probably noticed that the corners and edges don't stay on very well. So, say you scrambled all three kinds of pieces. You will be able to solve the resulting cube if you could solve the corner/edge permutation and the face- center permutation. But if the only thing keeping you from solving the corner/edge permutation and the face-center permutation is that both permutation parities were odd, then you will be able to solve the two of them together. Therefore your chances of success are one in 360 (= (1/12)*(1/60)*2), or one in 24 if you preserved opposite pairs of face centers. Now suppose you peeled off the 54 colored stickers and stuck them back on at random (carefully keeping them out of the reach of children, as there are rumors the paint contains lead, especially on the cheap Taiwanese knockoffs), what is the probability of getting a solvable cube? This question was posed years ago (in Singmaster?) but I believe it is still open. Dan Hoey Hoey@AIC.NRL.Navy.Mil From hirsh@cs.rutgers.edu Sat Nov 10 18:50:06 1990 Return-Path: Received: from pei.rutgers.edu by life.ai.mit.edu (4.1/AI-4.10) id AA11436; Sat, 10 Nov 90 18:50:06 EST Received: by pei.rutgers.edu (5.59/SMI4.0/RU1.2/3.05) id AA16007; Sat, 10 Nov 90 18:49:51 EST Sender: Haym Hirsh Date: Sat, 10 Nov 90 18:49:48 EST From: Haym Hirsh Reply-To: Haym Hirsh To: Hoey@aic.nrl.navy.mil (Dan Hoey), Cube-Lovers@life.ai.mit.edu Subject: Re: Rubik's Cube reassembly problem and solution In-Reply-To: Your message of Fri, 9 Nov 90 15:02:48 EST Cc: Haym Hirsh Message-Id: > Now suppose you peeled off the 54 colored stickers and stuck them back > on at random (carefully keeping them out of the reach of children, as > there are rumors the paint contains lead, especially on the cheap > Taiwanese knockoffs), what is the probability of getting a solvable > cube? This question was posed years ago (in Singmaster?) but I > believe it is still open. > > Dan Hoey > Hoey@AIC.NRL.Navy.Mil This seems easy, so I've probably messed up on something. Can anyone catch a mistake? Assume each of the stickers is given a number from 1 to 54. Then there are 54! different labelings, ignoring rotation of stickers (we'll ignore this throughout, so we'll never need to consider it). Thus there are 54! = 230843697339241380472092742683027581083278564571807941132288000000000000 = 2.3*10^71 ways to randomly resticker the cube. We want to know what proportion of these are legal (i.e., the cube can be solved). There are 8!*12!*8^3*2^12/12 = 43252003274489856000 = 4.3*10^19 legal cube states. Thus there are this many legal stickerings, if each sticker must go back to where it was. Since they need not (just the color must match), there are really an additional (9!)^6 for each of these, or 98760760257294265888495040331277846607560704000000000 = 9.9*10^52 legal stickerings. Thus the proportion of randomly restickered cubes that can be solved, and hence the probability that a randomly restickered cube can be solved, is 98760760257294265888495040331277846607560704000000000 ------------------------------------------------------------------------ 230843697339241380472092742683027581083278564571807941132288000000000000 = 9.9*10^52/2.3*10^71 = 4.3*10^-19 From dik@cwi.nl Sat Nov 10 20:17:16 1990 Return-Path: Received: from charon.cwi.nl by life.ai.mit.edu (4.1/AI-4.10) id AA12248; Sat, 10 Nov 90 20:17:16 EST Received: by charon.cwi.nl with SMTP; Sun, 11 Nov 90 02:17:08 +0100 Received: by paring.cwi.nl via EUnet; Sun, 11 Nov 90 02:17:02 +0100 Date: Sun, 11 Nov 90 02:17:02 +0100 From: dik@cwi.nl Message-Id: <9011110117.AA27431@paring.cwi.nl> To: Cube-Lovers@life.ai.mit.edu Subject: Re: Rubik's Cube reassembly problem and solution Aside from the disassembly/assembly problem there was another problem that I have not yet seen answered satisfactory. The question is: what is the maximum number of stickers that can bee peeled of such that there is still an unique solution for the cube (i.e. the remaining stickers must match in color on a face). The only solution I have seen was along the lines (this is from memory, but I do not think there are any mistakes): 1. The total rotation of the corner cubes is 0, so there is one corner cube that can have all its stickers removed; the remaining corner cubes need at least one sticker. Suppose this is the FUR cube. (3 stickers.) 2. You can remove two stickers (F, R and/or U) from each of FRD, BRU, FLU; they still remain distinguishable. (6 stickers.) 3. Of the remaining corner cubes (DBL, DRB, ULB, DLF) you cannot *now* (emphasis mine) remove two stickers because the cube will become indistinguishable from one of the cubes handled in step 2. You can remove sticker R, U and F from DRB, ULB and DLF respectively. No other stickers can be removed. (3 stickers.) 4. Because of flip parity you can remove two stickers from (say) FU. (2 stickers.) 5. You can remove the F sticker from all of FR, FL and FD. (3 stickers.) 6. Now, because of the product parity of corner cubes permutation and edge cube permutation you can make either two corner cubes identical or two edge cubes. You must nevertheless still be able to observe both the corner twist parity and the edge flip parity. This means you may a. Remove a single sticker from any edge cube that still has two stickers. b. Remove a single sticker from the DLB cube. (You can not remove two stickers from the DLB cube. Say you remove the L and B sticker. Let us denote removed sticker by lower case letters. In that case Dlb is indistinguishable from Dfr, which is not a problem. But the DLf cube can now be put in the Dlb position, leading to a 3-cycle.) (1 sticker.) 7. You can remove the sticker from the front center cube. (1 sticker.) This leads to a total of 19 removable stickers. This is not maximal. There are, for instance, other ways to do corner cubes: 1. Remove all F stickers. (4 stickers.) 2. From all Fxy cubes, remove the y sticker. (4 stickers.) 3. Also from all Bxy cubes, remove the y sticker. (4 stickers.) 4. From one Bxy cube remove also an x sticker. (1 sticker.) 5. From one Fxy cube remove also an x sticker. (1 sticker.) (Fxy and Bxy named clockwise.) This leads to 14 stickers for the corners and a total of 21. Are there other ways leading to more? Are there better ways that we can remove more center stickers? -- dik t. winter, cwi, amsterdam, nederland dik@cwi.nl From hirsh@cs.rutgers.edu Sun Nov 11 15:34:28 1990 Return-Path: Received: from pei.rutgers.edu by life.ai.mit.edu (4.1/AI-4.10) id AA23245; Sun, 11 Nov 90 15:34:28 EST Received: by pei.rutgers.edu (5.59/SMI4.0/RU1.2/3.05) id AA00310; Sun, 11 Nov 90 15:34:25 EST Sender: Haym Hirsh Date: Sun, 11 Nov 90 15:34:23 EST From: Haym Hirsh Reply-To: Haym Hirsh To: Cube-Lovers@life.ai.mit.edu Subject: Re: Rubik's Cube reassembly problem and solution In-Reply-To: Your message of Sat, 10 Nov 90 18:49:48 EST Cc: Haym Hirsh Message-Id: I just caught a bug in my reasoning. The restickering need not yield something equivalent to the original undestickered cube, but rather just one that can be solved to obtain solid colors on each face. Since there are 5*3*2 different distinguishable cubes (i.e., 30 different ways to label a die with the numbers 1-6) (6! labelings, but rotational symmetry removes 24 -- six faces can be brought to the top, and for each it can be rotated around the axis perpendicular to that face in one of 4 ways), the numerator should be multiplied by 30, and hence the probability is actually 2962822807718827976654851209938335398226821120000000000 ------------------------------------------------------------------------ 230843697339241380472092742683027581083278564571807941132288000000000000 = 3.0*10^54/2.3*10^71 = 1.3*10^-17 Haym From RGC915@uacsc2.albany.edu Mon Nov 12 01:24:08 1990 Return-Path: Received: from UACSC2.ALBANY.EDU by life.ai.mit.edu (4.1/AI-4.10) id AA28724; Mon, 12 Nov 90 01:24:08 EST Message-Id: <9011120624.AA28724@life.ai.mit.edu> Received: from uacsc2.albany.edu by UACSC2.ALBANY.EDU (IBM VM SMTP R1.2.2MX) with BSMTP id 2636; Sun, 11 Nov 90 22:09:52 EST Received: from ALBNYVM1.BITNET (RGC915) by uacsc2.albany.edu (Mailer R2.07B) with BSMTP id 0600; Sun, 11 Nov 90 22:09:51 EST Date: Sun, 11 Nov 90 22:01:08 EST From: Robert Clark Subject: Rubik's Cube Variants? To: cube-lovers@life.ai.mit.edu Does anyone know where I can find all those variations on the Rubik's theme that popped up after the Cube came out? I mean puzzles like the Pyraminx, Impossiball, etc. I haven't seen any place that sells them in the area where I live, New york state. I would even be willing to send for them from overseas if the price is reasonable. Robert Clark From @mitvma.mit.edu:RCC2@VAXB.YORK.AC.UK Mon Nov 12 09:45:25 1990 Return-Path: <@mitvma.mit.edu:RCC2@VAXB.YORK.AC.UK> Received: from mitvma.mit.edu by life.ai.mit.edu (4.1/AI-4.10) id AA02330; Mon, 12 Nov 90 09:45:25 EST Message-Id: <9011121445.AA02330@life.ai.mit.edu> Received: from MITVMA.MIT.EDU by mitvma.mit.edu (IBM VM SMTP R1.2.1MX) with BSMTP id 4628; Mon, 12 Nov 90 09:17:42 EST Received: from UKACRL.BITNET by MITVMA.MIT.EDU (Mailer R2.05) with BSMTP id 2004; Mon, 12 Nov 90 09:17:41 EST Received: from RL.IB by UKACRL.BITNET (Mailer R2.03B) with BSMTP id 6669; Fri, 09 Nov 90 20:13:59 GMT Received: from RL.IB by UK.AC.RL.IB (Mailer R2.03B) with BSMTP id 2022; Fri, 09 Nov 90 20:13:59 GMT Via: UK.AC.YORK.VAXB; 9 NOV 90 20:13:57 GMT Date: Fri, 9 Nov 90 20:13 GMT From: RCC2%VAXB.YORK.AC.UK@mitvma.mit.edu To: CUBE-LOVERS@life.ai.mit.edu Subject: hello there Hello there, This is my first posting to the cube-lovers board, so I'm probably gonna ask a couple of really obvious questions: a) Does anyone know where I can get a copy of David Singmaster's book "Notes on Rubik's magic cube?" This was THE definitive book on the cube about 8 years ago, but I lost my copy....does anyone know if it's still in print?? ( Oh yeah, maybe I should mention that I'm in England...David Singmaster was a lecturer at one of the colleges in London I think - was this book EVER published in the states? ) b) ( This is a real obvious one... ) Does anyone have any tips or advice on solving the 4*4*4 cube that appeared a few years after the original 3*3*3 one. I got really close to getting it right a couple of years ago, but never quite made it. Thanks in advance for any help, Rod Chapman rcc2@vaxa.york.ac.uk From hirsh@cs.rutgers.edu Mon Nov 12 12:05:53 1990 Return-Path: Received: from pei.rutgers.edu by life.ai.mit.edu (4.1/AI-4.10) id AA04462; Mon, 12 Nov 90 12:05:53 EST Received: by pei.rutgers.edu (5.59/SMI4.0/RU1.2/3.05) id AA08879; Mon, 12 Nov 90 12:05:44 EST Sender: Haym Hirsh Date: Mon, 12 Nov 90 12:05:42 EST From: Haym Hirsh Reply-To: Haym Hirsh To: Robert Clark Cc: cube-lovers@life.ai.mit.edu Subject: Re: Rubik's Cube Variants? In-Reply-To: Your message of Sun, 11 Nov 90 22:01:08 EST Message-Id: Peter Beck, pbeck@pica.army.mil, has many cube spinoffs for sale. That's where I got the last few I was missing. Jerry Slocum in Calif also has some items for sale -- I got his address from old cube-lovers mailings (sent by Peter, I believe). I seem to recall a few other sources outside the US, but Peter probably can provide them if there's something Slocum and Peter don't have. Haym From rp@xn.ll.mit.edu Mon Nov 12 12:09:56 1990 Return-Path: Received: from xn.ll.mit.edu by life.ai.mit.edu (4.1/AI-4.10) id AA04551; Mon, 12 Nov 90 12:09:56 EST Message-Id: <9011121709.AA04551@life.ai.mit.edu> Received: by xn.ll.mit.edu id AA17468g; Mon, 12 Nov 90 12:07:55 EST Date: Mon, 12 Nov 90 12:07:55 EST From: Richard Pavelle To: CUBE-LOVERS@life.ai.mit.edu In-Reply-To: RCC2%VAXB.YORK.AC.UK@mitvma.mit.edu's message of Fri, 9 Nov 90 20:13 GMT <9011121445.AA02330@life.ai.mit.edu> Subject: hello there Date: Fri, 9 Nov 90 20:13 GMT From: RCC2%VAXB.YORK.AC.UK@mitvma.mit.edu Hello there, This is my first posting to the cube-lovers board, so I'm probably gonna ask a couple of really obvious questions: a) Does anyone know where I can get a copy of David Singmaster's book "Notes on Rubik's magic cube?" This was THE definitive book on the cube about 8 years ago, but I lost my copy....does anyone know if it's still in print?? ( Oh yeah, maybe I should mention that I'm in England...David Singmaster was a lecturer at one of the colleges in London I think - was this book EVER published in the states? ) b) ( This is a real obvious one... ) Does anyone have any tips or advice on solving the 4*4*4 cube that appeared a few years after the original 3*3*3 one. I got really close to getting it right a couple of years ago, but never quite made it. I have not looked at it for several years but if memory serves you need only one extra transformation which is not applicable to the 3^3. It is the single edge flip. I no longer recall it explicitly but it was kinda trivial to find. From hoey@aic.nrl.navy.mil Mon Nov 12 18:37:55 1990 Received: from Sun0.AIC.NRL.Navy.Mil by life.ai.mit.edu (4.1/AI-4.10) id AA13428; Mon, 12 Nov 90 18:37:55 EST Received: from sun13.aic.nrl.navy.mil by Sun0.AIC.NRL.Navy.Mil (4.1/SMI-4.0) id AA06668; Mon, 12 Nov 90 18:33:25 EST Return-Path: Received: by sun13.aic.nrl.navy.mil; Mon, 12 Nov 90 18:38:49 EST Date: Mon, 12 Nov 90 18:38:49 EST From: hoey@aic.nrl.navy.mil Message-Id: <9011122338.AA00219@sun13.aic.nrl.navy.mil> To: Cube-Lovers@life.ai.mit.edu Subject: Re: Rubik's Cube reassembly problem and solution This problem of counting the number of solvable restickerings seems to be a lot easier than I had thought, but a lot trickier than you might think. Haym Hirsh sent in a buggy analysis, then corrected himself, but not quite enough. The fix was to account for cases where the stickers corresponded to a cube recoloring, but he just multiplied by 30 (cube recolorings up to rotational symmetry) rather than by 720 (total cube recolorings). We are dividing by 54!, which includes positions differing only by a rotation, so when figuring how many are solvable you have to count such positions also. Another way of figuring this is 6! ways of coloring the face centers, then (8! 3^8 12! 2^12)/12 ways of coloring the rest of the cube, then 9!^6 ways of arranging stickers among identically-colored faces, out of 54! ways of arranging stickers randomly. So the probability that a random restickering will be solvable is 71107747385251871439716429038520049557443706880000000000 ------------------------------------------------------------------------ 230843697339241380472092742683027581083278564571807941132288000000000000 40122452017152 = ------------------------------ ~ 3.0803 X 10^-16. 130253249618151492335575683325 It seems odd to me that this is not the reciprocal of an integer, but I guess that's because we are dealing with color cosets rather than some cube group. Haym Hirsch also asked me how to figure out the minimum number of stickers to fix to make an unsolvable stickering solvable. Sounds hard to me. His question arises in the same way that I recall the original problem arising: trying to clean up after someone who tried to solve the cube by restickering. Since the adhesive isn't designed for moving the stickers around, this leads rapidly to Dik Winter's problem: dealing cubes that have lost some of their stickers. Dan Hoey@AIC.NRL.Navy.Mil From pbeck@pica.army.mil Wed Nov 14 09:59:24 1990 Return-Path: Received: from FSAC1.PICA.ARMY.MIL by life.ai.mit.edu (4.1/AI-4.10) id AA04731; Wed, 14 Nov 90 09:59:24 EST Received: by FSAC1.PICA.ARMY.MIL id aa28413; 14 Nov 90 9:56 EST Date: Tue, 13 Nov 90 7:48:47 EST From: Peter Beck (LCWSL) To: Robert Clark Cc: cube-lovers@life.ai.mit.edu Subject: Re: Rubik's Cube Variants? Message-Id: <9011130748.aa09243@FSAC1.PICA.ARMY.MIL> I am the best general source for rubik's cube items. If you want a list of whatr is available e-mail me your postal address. THE FUTURE IS PUZZLING, BUT CUBING IS FOREVER!!!!!!!!!!! From pbeck@pica.army.mil Fri Nov 30 07:50:59 1990 Return-Path: Received: from FSAC1.PICA.ARMY.MIL by life.ai.mit.edu (4.1/AI-4.10) id AA00762; Fri, 30 Nov 90 07:50:59 EST Date: Thu, 29 Nov 90 12:33:41 EST From: Peter Beck (LCWSL) To: cube-lovers@life.ai.mit.edu Cc: pbeck@pica.army.mil Subject: bottleneck and Message-Id: <9011291233.aa21311@FSAC1.PICA.ARMY.MIL> BOTTLENECK SOURCE: Will the designer of Bottleneck please contact MIKE GREEN 24832 144th PLACE S.E KENT WASHINGTON 98042. Mike has a puzzle business and wants to sell Bottleneck. If anybody else out there manufactures or deals in mechanical puzzles and is looking for a retail or wholesale outlet please feel free to contact Mike. Mike manufactures and sells a line of wire disentanglement puzzles called "PUZZLETTS". He has opened a retail outlet in his home (the address above). Mike also collects puzzles and has a list of puzzle suppliers and puzzle solution sheets. If anybody out there is looking for something or wants to contribute I am sure he would happy to correspond. NO E-MAIL, postal or telephone only (sorry I don't have phone number handy). PS If anybody wants to contact Mike through me please feel free. From pbeck@pica.army.mil Sat Dec 8 09:51:49 1990 Return-Path: Received: from FSAC1.PICA.ARMY.MIL by life.ai.mit.edu (4.1/AI-4.10) id AA20984; Sat, 8 Dec 90 09:51:49 EST Date: Fri, 7 Dec 90 11:41:03 EST From: Peter Beck (LCWSL) To: cube-lovers@life.ai.mit.edu Subject: rec & ed computing Message-Id: <9012071141.aa04773@FSAC1.PICA.ARMY.MIL> Anybody have an opinion on the newsletter/magazine "RECREATIONAL & EDUCATIONAL COMPUTING" edited by Dr. Michael Ecker. From cosell@bbn.com Sat Dec 8 15:48:28 1990 Return-Path: Received: from WILMA.BBN.COM by life.ai.mit.edu (4.1/AI-4.10) id AA24247; Sat, 8 Dec 90 15:48:28 EST Message-Id: <9012082048.AA24247@life.ai.mit.edu> Date: Sat, 8 Dec 90 15:42:21 EST From: Bernie Cosell To: Peter Beck Cc: cube-lovers@life.ai.mit.edu Subject: Re: rec & ed computing Sure.... - REC is VERY slanted toward high school students, and so there is very little advanced or profound stuff in there. - While there is a nod to other worlds, primarily it is all in BASIC, and generally focused on the IBM PC. - There is a fascination with mindless crunching just to print out numbers that I can't fathom. A good portion of the articles center on a numbers with some odd property or another, or finding the actual _numeric_ solution to something and usually brute force [or close to it]. The graphics hacks, such as they are, are primarily crunching-based [moire patterns and such]. No real discussion of 'puzzles', for example, nor of the kinds of techniques and such you need to partially-tame one of those awful [but real world] exponential searches, nor of representing 3D objects or manipulations of them, or search strategies, no word problems, etc. /Bernie\ From pbeck@pica.army.mil Mon Dec 10 11:35:28 1990 Return-Path: Received: from FSAC1.PICA.ARMY.MIL by life.ai.mit.edu (4.1/AI-4.10) id AA25188; Mon, 10 Dec 90 11:35:28 EST Date: Mon, 10 Dec 90 11:18:02 EST From: Peter Beck (LCWSL) To: Bernie Cosell Cc: Peter Beck , cube-lovers@life.ai.mit.edu Subject: Re: rec & ed computing Message-Id: <9012101118.aa09879@FSAC1.PICA.ARMY.MIL> thanks bernie. PS: do you have address & name of owner for games people p;lay.? From @relay.cs.net:AGIN@cgi.com Thu Dec 13 23:25:58 1990 Return-Path: <@relay.cs.net:AGIN@cgi.com> Received: from RELAY.CS.NET by life.ai.mit.edu (4.1/AI-4.10) id AA18336; Thu, 13 Dec 90 23:25:58 EST Message-Id: <9012140425.AA18336@life.ai.mit.edu> Received: from relay2.cs.net by RELAY.CS.NET id ab06193; 13 Dec 90 23:25 EST Received: from cgi.com by RELAY.CS.NET id aa27113; 13 Dec 90 23:09 EST Date: Thu, 13 Dec 90 14:26 EDT From: AGIN%cgi.com@relay.cs.net Subject: Re: construction project To: cube-lovers@life.ai.mit.edu X-Vms-To: IN%"cube-lovers@life.ai.mit.edu" I was successful in creating Peter Beck's Christmas Tree ornament. The project requires 50 modules, not 120. There are 30 outside modules and 20 inside connecting modules. The outside modules correspond to th edges of a dodecahedron. The inside modules create an interior icosahedron. I used 3M Post-It notes cut in half, each starting rectangle being 3" by 1- 1/2". I folded the adhesive to the inside on the first step, so the adhesive was not holding the project together. It probably would have been possible to use the adhesive to keep each module together. This would have required a lot of extra care in the assembly, but produced a much sturdier product. As it was, once I got the hang of it, I didn't have any major problems with modules coming apart. The finished construction required no staples or extra glue. A previous attempt using 1" x 2" rectangles cut out of graph paper kept falling apart. I've got a partially finished ornament made with dollar bills, which seem to work fine. The ideal shape for an outside module is not an equilateral triangle, but an isosceles one with an apex angle of about 42 degrees. I took care of this by allowing the outside surfaces to bow outward. To finish the assembly I left three outside modules and their common connecting module until last. The outside modules were threaded into place but not closed, with the ends of the paper pointing outward. The connecting module was placed over the nearest ends of the three outside modules, then the outside modules could be closed. From j9@icad.com Fri Dec 14 19:26:43 1990 Return-Path: Received: from BU.EDU by life.ai.mit.edu (4.1/AI-4.10) id AA01678; Fri, 14 Dec 90 19:26:43 EST Received: by BU.EDU (1.99) Fri, 14 Dec 90 13:43:49 EST Received: from MOE.ICAD.COM by icad.COM (4.1/SMI-4.0) id AA21059; Fri, 14 Dec 90 13:34:43 EST Date: Fri, 14 Dec 90 13:38 EST From: Jeannine Mosely Subject: Peter Beck's construction project To: cube-lovers@life.ai.mit.edu Message-Id: <19901214183850.8.J9@MOE.ICAD.COM> I have made something along the lines that Peter Beck describes in his "construction project", but it does not quite fit his description, so I don't know if it is the same thing. It uses only 50 modules and I can't for the life of me imagine where the other 70 should go. My object looks like this. Imagine a regular icosahedron (20 equilateral triangular faces, with 5 coming together at each vertex). Erect on each of these faces a triangular prism (20 modules). At each edge of the icosahedron, two square faces of adjacent prisms rise up from the surface of the icosahedron. Band each such pair together with a module (30 modules). The reulting form resembles the Archmidean solid most conveniently designated (3,4,5,4), which means that each vertex contains a triangle, square, pentagon, square, in that order. I say "resembles" this solid, in part, because only the squares are actually present, the triangular and pentagonal "faces" are voids. But a more compelling reason for saying "resembles" is that the geometry is only approximate. If one uses the modules you describe for the triangular prisms (that is, the height of the prism equals the edge of the triangle) then the quadrilateral faces on the outer surface connecting the triangular and pentagonal voids are not squares, but rectangles whose side are in the ratio of (sqrt 5)-1 to (sqrt 3). This discrepancy can be fudged, by allowing the squares to bulge outward slightly. On the other hand, a figure could be constructed where the outer quadrilaterals were in fact square, but this would require the prisms to be shorter, and that cannot be fudged. Better results can be achieved if you do not fudge the geometry (or at least not much). It turns out that (/ (- (sqrt 5) 1) (sqrt 3)) = 5/7 (pardon my lisp) to within one tenth of one percent. Hence I make my modules as diagrammed below. Dimensions given assume paper in the ratio of 2 to 1. This module is used to make the triangular prisms: _______________________________________________ | : : : | 5/24 |.........:.............:.............:.........| | : : : | | : : : | 7/12 | : : : | |.........:.............:.............:.........| | : : : | 5/24 |_________:_____________:_____________:_________| 1/2 1/2 1/2 1/2 This module is used to band the triangular prisms together: _______________________________________________ | : : : | 1/4 |.........:.............:.............:.........| | : : : | | : : : | 1/2 | : : : | |.........:.............:.............:.........| | : : : | 1/4 |_________:_____________:_____________:_________| 5/12 7/12 7/12 5/12 Natually, you might ask, how do I fold 5/12? There is a trick. First fold the the long edge in half, and then in quarters at one end, but don't make the second crease go all the way across--just nick one edge of the paper, as a marker (point B). Now fold point B to touch the upper left-hand corner (point A). This would make a diagonal crease across the strip, but again, don't make the crease go all the way across--just nick the lower edge (point C). The line AC is the hypoteneuse of the old 5,12,13 right triangle, and point C is at 5/12, as desired. (Pretty neat, huh?) A _______________________________________________ | : | | : | | : | 12/12 | : | | : | | : | | : | |_______:______________:_____________:__________| 5/12 C 7/12 6/12 B 6/12 A similar technique is used to make the other module. I did not need any staples. -- jeannine mosely From mindcrf!ronnie@boris.mindcraft.com Tue Mar 5 19:29:53 1991 Return-Path: Received: from ames.arc.nasa.gov by life.ai.mit.edu (4.1/AI-4.10) id AA18539; Tue, 5 Mar 91 19:29:53 EST Received: by ames.arc.nasa.gov (5.64/1.2); Tue, 5 Mar 91 16:29:48 -0800 Received: by mindcrf.mindcraft.com (AIX 2.1.2/4.03) id AA22779; Tue, 5 Mar 91 11:37:03 PST Received: by boris.mindcraft.com (AIX 1.3/4.03) id AA33973; Tue, 5 Mar 91 11:45:27 -0800 Date: Tue, 5 Mar 91 11:45:27 -0800 From: mindcrf!ronnie@boris.mindcraft.com (Ronnie Kon) Message-Id: <9103051945.AA33973@boris.mindcraft.com> To: @ames.uucp:ai.ai.mit.edu!Cube-Lovers Subject: Is Meffert still around? I am wondering if Meffert is still around, with his club to purchase new and interesting Cube products. If he is, would somebody please send me his address and what the current membership fee is. Also a price list. If he is not, would people be interested in restarting such a club? I have a hard time believing that there aren't enough people for a cube-of- the-month club (or perhaps cube-of-the-quarter) as these things are not that complex (ie., expensive) to produce. We might even be able to do runs in rolled aluminum instead of plastic. Ronnie kon@groundfog.stanford.edu From @po5.andrew.cmu.edu:dn1l+@andrew.cmu.edu Fri Mar 8 13:14:12 1991 Return-Path: <@po5.andrew.cmu.edu:dn1l+@andrew.cmu.edu> Received: from po5.andrew.cmu.edu by life.ai.mit.edu (4.1/AI-4.10) id AA27925; Fri, 8 Mar 91 13:14:12 EST Received: by po5.andrew.cmu.edu (5.54/3.15) id for Cube-Lovers@life.ai.mit.edu; Fri, 8 Mar 91 13:14:02 EST Received: via switchmail; Fri, 8 Mar 91 13:14:01 -0500 (EST) Received: from aurelia.weh.andrew.cmu.edu via qmail ID ; Fri, 8 Mar 91 13:13:53 -0500 (EST) Received: from aurelia.weh.andrew.cmu.edu via qmail ID ; Fri, 8 Mar 91 13:13:45 -0500 (EST) Received: from Messages.7.8.N.CUILIB.3.45.SNAP.NOT.LINKED.aurelia.weh.andrew.cmu.edu.pmax.3 via MS.5.6.aurelia.weh.andrew.cmu.edu.pmax_3; Fri, 8 Mar 91 13:13:44 -0500 (EST) Message-Id: Date: Fri, 8 Mar 91 13:13:44 -0500 (EST) From: "Dale I. Newfield" To: Cube-Lovers@life.ai.mit.edu Subject: 5x5x5 Cube I saw a 5x5x5 Cube (Rubik's type) in a friend's office (One of his office-mates had it.)(I left a message, but never got a response from him.) I was wondering if anybody out there has seen one of these, and could point me in a direction that would lead to one? Thank You! Dale Newfield dn1l@andrew.cmu.edu From pbeck@pica.army.mil Mon Mar 11 11:13:02 1991 Return-Path: Received: from FSAC1.PICA.ARMY.MIL by life.ai.mit.edu (4.1/AI-4.10) id AA13397; Mon, 11 Mar 91 11:13:02 EST Date: Mon, 11 Mar 91 11:10:46 EST From: Peter Beck (LCWSL) To: kon@groundfog.stanford.edu Cc: cube-lovers@life.ai.mit.edu Subject: meffert Message-Id: <9103111110.aa20787@FSAC1.PICA.ARMY.MIL> SHORT ANSWER: Meffert's puzzle club is dead! MORE: Meffert is alive and is trying to get back into the puzzle business - if you want specific information Jerry Slocum, beverly hills has been in conatct with him. PUZZLE CLUBS, ETC.: 1 - the economics of a puzzle club is that well made puzzles (both from a design and engineering perspective) cost $20 and up. 2 - people interested in being current on whats happening in puzzles should subscribe to CFF, Puzzletopia and possible ARM (all have been discussed before) I have been busy but CFF#25 (silver aniverssary; cost $18) is 5 volumes plus vendor catalogs (bandelow, constatin) and encompassses the last 10 tears of puzzling around the world. SOME RETAIL PUZZLE SOURCES: cubes: peter beck, usa bandelow, germany constatin, germany other: bits & pieces kadon jon foolery science museum shops SOME WHOLESALE SOURCES: USA, PUZZLETTES USA, ISHI PRESS - JAPANESE PUZZLES USA, TUCKER-JONES TAVERN PUZZLES (what Bush does on way to camp david) UK, pentangle French, Arjeu SOME NEWER PUZZLES: magic cross, germany masterball, swiss rotos, german new rubiks, europe square one, milton bradley - in stores soon ** INTERNATIONAL PUZZLE PARTY (200+ worldwide attendees) 3/30/91 in LA. Admittance by invitation. FURTHER DISCUSSION REQUESTED. From pbeck@pica.army.mil Mon Mar 18 12:42:18 1991 Return-Path: Received: from FSAC1.PICA.ARMY.MIL by life.ai.mit.edu (4.1/AI-4.10) id AA22344; Mon, 18 Mar 91 12:42:18 EST Date: Mon, 18 Mar 91 12:36:36 EST From: Peter Beck (LCWSL) To: cube-lovers@life.ai.mit.edu Cc: pbeck@pica.army.mil Subject: tcf 91 Message-Id: <9103181236.aa07170@FSAC1.PICA.ARMY.MIL> The TRENTON COMPUTER FESTIVAL 1991 WILL BE THE 20 & 21 OF APRIL AT the same "OLD" LOCATION --> TRENTON STATE COLLEGE on state highway 31 in Trenton NJ. THIS IS THE LARGEST AND OLDEST AMATEUR COMPUTER FESTIVAL in the country. I have a table selling puzzles in the fleamarket. my best address From pbeck@pica.army.mil Tue Mar 19 09:22:42 1991 Return-Path: Received: from FSAC1.PICA.ARMY.MIL by life.ai.mit.edu (4.1/AI-4.10) id AA18445; Tue, 19 Mar 91 09:22:42 EST Received: by FSAC1.PICA.ARMY.MIL id aa09653; 19 Mar 91 9:18 EST Date: Tue, 19 Mar 91 8:30:13 EST From: Peter Beck (LCWSL) To: rp@xn.ll.mit.edu, cube-lovers@life.ai.mit.edu Subject: more on tcf Message-Id: <9103190830.aa28520@FSAC1.PICA.ARMY.MIL> The TRENTON COMPUTER FESTIVAL 1991 WILL BE THE 20 & 21 OF APRIL AT the same "OLD" LOCATION --> TRENTON STATE COLLEGE on state highway 31 in Trenton NJ. THIS IS THE LARGEST AND OLDEST AMATEUR COMPUTER FESTIVAL in the country. I have a table selling puzzles in the fleamarket. TCF is a combination retail sales show, technical symposium and fleamarket sponsored by the amateur computer clubs in the NYC-philadelphia metro area. It has a state fai atmosphere with a PC theme. Attendees come mostly from east of the mississippi and average 10-15,000 per day. It lasts for 2 days. FLEAMARKET HOURS - it is outdoors and rain or shine, sat is ALWAYS best sat 7am - 5pm sun 9am- 4pm RETAIL COMMERCIAL SALES EXHIBITS - inside gymnasium 9-4 both days TECHNICAL LECTURES - inside this is multi track 9-4 both days USER GROUP MEETINGS - inside 9-4 both days KEYNOTE BANQUET AND LECTURE 8pm sat - notable speaker, eg, bill gates my best address From pbeck@pica.army.mil Thu Apr 11 09:21:50 1991 Return-Path: Received: from FSAC1.PICA.ARMY.MIL by life.ai.mit.edu (4.1/AI-4.10) id AA00299; Thu, 11 Apr 91 09:21:50 EDT Date: Thu, 11 Apr 91 9:17:33 EDT From: Peter Beck (LCWSL) To: cube-lovers@life.ai.mit.edu Cc: brodin@pica.army.mil Subject: tcf correction Message-Id: <9104110917.aa15850@FSAC1.PICA.ARMY.MIL> 4/11/91 version The TRENTON COMPUTER FESTIVAL 1991 WILL BE THE 20 & 21 OF APRIL "NOT" at the same "OLD" LOCATION --> ie, it is at MERCER COUNTY COMMUNITY COLLEGE not TRENTON STATE COLLEGE. Directions are below, phone 609/655-4898/4999 - SORRY for the previous misinformation. THIS IS THE LARGEST AND OLDEST AMATEUR COMPUTER FESTIVAL in the country. I have a table selling puzzles in the fleamarket. TCF is a combination retail sales show, technical symposium and fleamarket sponsored by the amateur computer clubs in the NYC-philadelphia metro area. It has a state fair atmosphere with a PC theme. Attendees come mostly from east of the mississippi and average 10-15,000 per day. It lasts for 2 days. ADMISSION - $7 FOR SAT & SUN, $5 for sun only - students $3 FLEAMARKET HOURS - it is outdoors and rain or shine, sat is ALWAYS best sat 7am - 5pm sun 9am- 4pm, 900 spots RETAIL COMMERCIAL SALES EXHIBITS - inside gymnasium 9-4 both days , exhibitors include: microsoft, HP, ashton-tate, software publ, micrografx, lotus, intel, adobe, borland, ast TECHNICAL LECTURES - inside this is multi track, over 100 KEYNOTE SPEAKER; Fred Gibbons, CEO software publishing corp 9:30 AM in the theater, "What lies ahead for the software industry" 9-4 both days USER GROUP MEETINGS - inside 9-4 both days KEYNOTE BANQUET AND LECTURE 8pm sat - notable speaker, eg, bill gates $$$$$$$$$$$$$$$$$$$$$$$$$$$ map locator --> MCCC is near the intersection of US #1 and I-295. Here's how to get to a parking space at TCF! Guaranteed parking is available at Mercer County Park, which surrounds the MCCC campus on three sides. MCP has two entrances, one on Rt 535 (Edinburg Rd. or Old Trenton Rd., depending on whether you're north or south of MCCC) and one on Hughes Drive. My advice is to turn off at a park entrance. HOWEVER, if you're early (on sat this means before 7 on sun before 9) or if you're daring, continue past the park entrance to the College entrance. If you're lucky, the gendarmes will let you on campus to look for a parking space. IF THEY REFUSE YOU ACCESS, continue to the traffic light and turn (either LEFT onto Old Trenton Rd. or RIGHT onto Hughes Drive.) and proceed to the Park entrance. FROM THE NORTH: 1) VIA U.S. 1: Go south on US 1 and take the Rt 533 South (Quakerbridge Rd.) overpass. After about two miles, turn left onto Hughes Dr. The Park entrance will be on your left in about a mile, with the College entrance about 0.5 miles further. 2) VIA N.J. TURNPIKE: Go south to Exit 8 (Hightstown) and get on Rt 33 WEST. In downtown Hightstown, turn right onto Rt 571 and follow. Near GE Astro, turn left onto Rt 535. The Park entrance is about 4 miles down the road, with the College entrance about a mile further. FROM THE SOUTH: 1) VIA U.S. 1: Go north on Rt. 1 and turn right onto Rt 546 (at Mrs. G's Appliances). Just after the overpass, turn right onto Youngs Rd. Follow to the end and turn right onto Hughes Drive. The Park entrance is about a mile away. 2) VIA I-95: I-95 NORTH becomes I-295 SOUTH (don't ask!). Take Exit 65A, Sloan Rd and follow to the end (Sloan Rd. becomes Flock Rd. at the light - also don't ask!!). Go left onto Old Trenton Rd. The Campus entrance is by a jughandle turn, about a mile up Old Trenton Rd. The Park entrance is on the left about a mile further up. 3) VIA I-295: Follow I-295 NORTH to its temporary end at Rt 130, and go north to Rt. 206 where you will follow signs to TRENTON and then to I-295 NORTH. Take Exit 65A to Sloan Ave. and follow it to the end. Go left on Old Trenton Rd. The campus entrance is by a jughandle turn, about a mile up Old Trenton Rd. The Park entrance is on the left about a mile further. 4) VIA N.J. TURNPIKE: Take Exit 7A to I-195 WEST. Take the first exit, 5B to Rt 130 NORTH. Left at the first light onto Rt. 526 Bear left and take an immediate right, still on Rt 526. At end, turn left onto Rt 535, Old Trenton Rd. The Park entrance is a bout a mile away; the College, another mile. $$$$$$$$$$$$$$$$$$ my best address From pbeck@pica.army.mil Mon Apr 22 15:35:39 1991 Return-Path: Received: from FSAC1.PICA.ARMY.MIL by life.ai.mit.edu (4.1/AI-4.10) id AA21942; Mon, 22 Apr 91 15:35:39 EDT Date: Mon, 22 Apr 91 15:20:08 EDT From: Peter Beck (LCWSL) To: cube-lovers@life.ai.mit.edu Subject: puzzle party review Message-Id: <9104221520.aa15409@FSAC1.PICA.ARMY.MIL> Review of the 11th INTERNATIONAL PUZZLE PARTY Held on March 30,31 1991 at the Pacifica Hotel Culver City, CA USA EVENTS .. Saturday daytime - puzzle exchange; admission requirement a puzzle gift for each other attendee evening - dinner party and magic show; MAGICIANS: Max Maven, Mark Setteducati, Mike Weber .. Sunday: A ballroom is set up for cash sales of puzzles. CUBING HIGHLIGHTS .. Minh Thai gave a demonstration of doing the cube (he is Guiness world record holder). His algorithm is: 1 - corners first 2 - 3 of 4 edges on each face 3 - last face .. Anneke Treep a founder of CFF was in attendance. CFF will probably host 13th party scheduled for Europe. .. A spherical SKEWB is in production. Very interesting puzzle. OTHER HIGHLIGHTS .. partial list of attendees (about 100 puzzlers attended): NOB, a prominent Japanese puzzler Ed Hordern author of Sliding Block book published by OUP Jerry Slocum, party arranger and author of Puzzles Old & New Kathy Jones, owner of Kadon Solomon Golomb, polycube inventor Jose Grant, designer of jewelry quality puzzle rings Scott Kim, inversions Christoph Bandelow, German seller of magic polyhedra and author Doug Engel, designer of circle puzzler, flexagon based puzzles James Dalgety, a founder of Pentangle .. 4 artists in attendance: one makes sculptures that assemble as puzzles, one makes pattern assembly puzzles by vacuum deposition of metals on glass squares, one makes Tiffany style lamps using tangram pieces & silhouettes for the design, the last uses puzzles primarily for inspiration. .. FUTURE PARTY SCHEDULE - 12th Tokyo Japan, Host NOB - 13th Netherlands, host CFF - 14th probably USA From mindcrf!ronnie@peabody.mindcraft.com Mon Apr 22 20:09:08 1991 Return-Path: Received: from ames.arc.nasa.gov by life.ai.mit.edu (4.1/AI-4.10) id AA00250; Mon, 22 Apr 91 20:09:08 EDT Received: by ames.arc.nasa.gov (5.64/1.2); Mon, 22 Apr 91 17:09:04 -0700 Received: by mindcrf.mindcraft.com (AIX 2.1 2/4.03) id AA01931; Mon, 22 Apr 91 16:35:45 PDT Received: by peabody.mindcraft.com (AIX 1.3/4.03) id AA22704; Mon, 22 Apr 91 16:43:31 -0700 Date: Mon, 22 Apr 91 16:43:31 -0700 From: mindcrf!ronnie@peabody.mindcraft.com (Ronnie Kon) Message-Id: <9104222343.AA22704@peabody.mindcraft.com> To: @mindcrf:ames!ai.ai.mit.edu!Cube-Lovers Subject: 5-cube in a game store!!! The GameKeeper (in the Valley Fair Mall in San Jose) actually has 5x5x5 Rubik's cubes on sale (for $37 I think). They had three in stock on Saturday. Are we seeing a renascence of cubing? This is certainly a welcome development. Ronnie ------------------------------------------------------------------------------- Ronnie B. Kon | "I don't know about your brain, but kon@groundfog.stanford.edu | mine is really bossy." ...!{decwrl,ames,hpda}!mindcrf!ronnie | -- Laurie Anderson ------------------------------------------------------------------------------- From ncramer@bbn.com Mon Apr 22 23:37:39 1991 Return-Path: Received: from LABS-N.BBN.COM by life.ai.mit.edu (4.1/AI-4.10) id AA04955; Mon, 22 Apr 91 23:37:39 EDT Message-Id: <9104230337.AA04955@life.ai.mit.edu> Date: Mon, 22 Apr 91 21:01:31 EDT From: Nichael Cramer To: Ronnie Kon Cc: Cube-Lovers@life.ai.mit.edu Subject: Re: 5-cube in a game store!!! >Date: Mon, 22 Apr 91 16:43:31 -0700 >From: Ronnie Kon >To: @BBN.COM,@mindcrf.uucp:ames!ai.ai.mit.edu!Cube-Lovers >Subject: 5-cube in a game store!!! > The GameKeeper (in the Valley Fair Mall in San Jose) actually has >5x5x5 Rubik's cubes on sale (for $37 I think). They had three in stock on >Saturday. > Ronnie (First: personal to Ronnie: THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU THANK YOU I've been looking for a 5by for _years_.) I just called. First, the cubes are at Games GALLERY (boy, you guys on the west coast sure have friendly, helpful phone operators. Also store owners: when I called the nearest GamesKeeper that the operator could find, the manager there gave the number for Games Gallery!). $27.95. They got them from Dr Christopher in Germany. And, yes, they have a couple left after taking my phone order. ;) Nichael BTW, Graham (the guy that I talked to at GG --is _everybody_ this friendly out there?) said they had about a half-dozen new Rubik's toys (i.e. "new" = post Rubik's Clock). Including something called "Rubik's 15", which Graham (note how we're on a first-name basis now) described as "like the old 15- puzzle, but *NASTY*!" Does anybody know any of these? From hirsh@cs.rutgers.edu Tue Apr 23 12:26:23 1991 Return-Path: Received: from pei.rutgers.edu by life.ai.mit.edu (4.1/AI-4.10) id AA26402; Tue, 23 Apr 91 12:26:23 EDT Received: by pei.rutgers.edu (5.59/SMI4.0/RU1.4/3.08) id AA09651; Tue, 23 Apr 91 12:26:19 EDT Sender: Haym Hirsh Date: Tue, 23 Apr 91 12:26:16 EDT From: Haym Hirsh Reply-To: Haym Hirsh To: cube-lovers@life.ai.mit.edu Subject: rubik's magic alternate coloring Cc: Haym Hirsh Message-Id: After seeing my collection of Rubik's magics in my office, a student came by yesterday with a variation I hadn't seen before. It is a 2x4 version, but the 8 "tiles" are colored differently. Each of the eight tiles has a "four-square" pattern -- the square is divided into four regions, each colored red, blue, yellow, or green. The center of each is black with Rubik's signature on it. The tiles thus look something like the following: +----+----+ |Blue|Yell| | / \ ow| +--+ +--+ | \ / | |Red |Gree| +----+----+ (with Rubik's signature in the center) Both the front and back tiles have this four-square pattern. However, on one side the order of colors on the tiles are all as in the picture above, and on the other side four have that order and the remaining four have yellow and green switched (so that blue and yellow are on opposite corners). I don't know if this description gets the idea across to those who have never seen one like this, but I'm more interested in those who have seen it. Is anyone familiar with this version, and if so, what is the goal pattern to reach? It turns out that the student worked at Bradlees (a downscale version of Kmart, if such a thing is possible) four years ago, and he got it from the returns bin, without any packaging. I've looked at it briefly, and didn't come up with an obvious goal pattern. About the only other info that may be helpful is that the copyright for this variation is 1987. The copyright for the original 2x4 is 1986, and similarly for the 2x2 I have; the 2x6 is copyright 1987. Finally, since I am on the topic of the magic, I have heard a number of times about yet another version of the magic that can be folded into a cube. Does anyone know any sources for it? (I thought for a while that the alternate-coloring version may be it, but it seems to have the same connectivity as the standard 2x4.) Thanks for any help! Haym (hirsh@cs.rutgers.edu) From latto@lucid.com Tue Apr 23 18:37:44 1991 Return-Path: Received: from lucid.com by life.ai.mit.edu (4.1/AI-4.10) id AA08232; Tue, 23 Apr 91 18:37:44 EDT Received: from boston-harbor ([192.43.175.1]) by heavens-gate.lucid.com id AA15216g; Tue, 23 Apr 91 15:37:18 PDT Received: by boston-harbor id AA02639g; Tue, 23 Apr 91 18:40:21 EDT Date: Tue, 23 Apr 91 18:40:21 EDT From: Andy Latto Message-Id: <9104232240.AA02639@boston-harbor> To: hirsh@cs.rutgers.edu Cc: cube-lovers@life.ai.mit.edu, hirsh@cs.rutgers.edu In-Reply-To: Haym Hirsh's message of Tue, 23 Apr 91 12:26:16 EDT Subject: rubik's magic alternate coloring The version your student has is the one where the object is to fold it into a cube (I have it, with the instructions. Yes, it does have the same structure as the original 2x4 one---you can fold that one into a cube (with two "flaps") too. The object is to fold it into a cube where the colors of the three faces meeting at each corner always match. Andy Latto latto@lucid.com From @po2.andrew.cmu.edu:dn1l+@andrew.cmu.edu Sat May 4 12:20:57 1991 Return-Path: <@po2.andrew.cmu.edu:dn1l+@andrew.cmu.edu> Received: from po2.andrew.cmu.edu by life.ai.mit.edu (4.1/AI-4.10) id AA01850; Sat, 4 May 91 12:20:57 EDT Received: by po2.andrew.cmu.edu (5.54/3.15) id for Cube-Lovers@life.ai.mit.edu; Sat, 4 May 91 04:59:53 EDT Received: via switchmail; Sat, 4 May 91 04:59:53 -0400 (EDT) Received: from aurelia.weh.andrew.cmu.edu via qmail ID ; Sat, 4 May 91 04:58:47 -0400 (EDT) Received: from aurelia.weh.andrew.cmu.edu via qmail ID ; Sat, 4 May 91 04:58:30 -0400 (EDT) Received: from Messages.7.8.N.CUILIB.3.45.SNAP.NOT.LINKED.aurelia.weh.andrew.cmu.edu.pmax.3 via MS.5.6.aurelia.weh.andrew.cmu.edu.pmax_3; Sat, 4 May 91 04:58:29 -0400 (EDT) Message-Id: Date: Sat, 4 May 91 04:58:29 -0400 (EDT) From: "Dale I. Newfield" To: Cube-Lovers@life.ai.mit.edu Subject: Re: 5-cube in a game store!!! Cc: Cube-Lovers@life.ai.mit.edu In-Reply-To: <9104230337.AA04955@life.ai.mit.edu> References: <9104230337.AA04955@life.ai.mit.edu> I called and ordered things from this store in California, and just recieved things over the past two days. THE 5X5X5 CUBE!!!!!!!! (I just started the 5X5X5 about 2 hours ago, and already have all but a few on the bottom. I think it will be MUCH easier than the 4X4X4. It comes with instructs on how to open it, and I took it apart to look. THIS DESIGN IS IMPRESSIVE! You can make some REALLY neat patterns with the 5x5x5.) 5x5x5 from: Dr. Christoph Bandelow Haarholzer Str. 13 4620 Bochum 1 Germany Write (Dr. Bandelow) for a free mail order catalog with many twisting puzzles and books about these puzzles. The new Rubik's things: Rubik's Dice: Rubik's Dice, unlike any other dice, has nothing to do with luck. It has spots whose color can be changed from white to red and from red to white. Rbik's Dice in fact, is a hollow cube with which has 7 plates inside it. The plates are white with red dots on them. The plates are loose but adhere to the inner sides of the cube. By shaking and turning the cube, the postition and orientation of the plates can be changed and this in turn alters the color of the spots of the dice. Object: Re-arrange the plates within the cube in such a way that the dice has white and only white spots. If red is shown anywhere on the dice even through the small controll holes -- the puzzle is not complete. The number of possible combinations is 7! x 4^7=82,575,360. There is however, ony one correct solution. Rubik's Tangle: Rubik's Tngle has 25 square tiles each tile has the very same pattern of ropes, but the color of the ropes varies. Object: Lay down the tiles into a 5X5 square in such a way that each colored rop forms it's own continuous line. 24! x 4^24 = 1746 x 10^38 ( I have a feeling it should be 25!, not 24!) 2 correct solutions. 4 different tangle puzzles. each worrks by itself (differently) and together they form a 10X10 grid that also works Rubik's Triamid Dumb, and i'm tired, so I won't explain. I'm disappointed in this one, don't buy it. Rubik's 15: 2 puzzles: one side is a magic square the other side is a fifteen puzzle but the mechanisms that manouver pieces are SICK! both can't be solved at once. Sorry, I started typing in the sheet that explained them all, but i'm falling asleep, so I just finished by explaining them a little. Dale Newfield dn1l@andrew.cmu.edu From ncramer@bbn.com Sun May 5 05:02:30 1991 Return-Path: Received: from LABS-N.BBN.COM by life.ai.mit.edu (4.1/AI-4.10) id AA19791; Sun, 5 May 91 05:02:30 EDT Message-Id: <9105050902.AA19791@life.ai.mit.edu> Date: Sat, 4 May 91 17:58:35 EDT From: Nichael Cramer To: "Dale I. Newfield" Cc: Cube-Lovers@life.ai.mit.edu, Cube-Lovers@life.ai.mit.edu Subject: Re: 5-cube in a game store!!! >Date: Sat, 4 May 91 04:58:29 -0400 (EDT) >From: "Dale I. Newfield" >To: Cube-Lovers@life.ai.mit.edu >Subject: Re: 5-cube in a game store!!! > >I called and ordered things from this store in California, and just >recieved things over the past two days. > >THE 5X5X5 CUBE!!!!!!!! Synchronicity!! I was just typing in a virtually identical message when Dale's posting came! (D: thanks for saving me all the typing. ;) >(I just started the 5X5X5 about 2 hours ago, and already have all but a >few on the bottom. I think it will be MUCH easier than the 4X4X4. It >comes with instructs on how to open it, and I took it apart to look. Yeah, I think anyone who _understands_ how to work a 3by or a 4by (as opposed to merely memorizing cookbook solutions) should have no problem with it. I'm certainly no speed whiz. The UPS man rang the doorbell at 1pm and I had scrambled and "solved" it by 3[*]. (Solved is in quotes because I had the cube completly done except that two non-central edge-cubies were flipped. It took me another 15-20 minutes to back out and fix this.) [* this includes feeding lunch to my two daughters and a few minutes of code-debugging over the phone.] >THIS DESIGN IS IMPRESSIVE! You can make some REALLY neat patterns with >the 5x5x5.) (I've got one of mine completely covered in checkerboard patterns). As Dale says, the 5by seems very solid. Probably this is because it has an odd number of cubes and so has the fixed center cubie. Certainly it moves more consistently smoothly than my 4bys. On the other hand, at least once I've felt one of the cubies start to pop out in my hand while I was turning it. Another thing: the cubies are starting to get pretty small. The whole cube is only about 1/4 longer on each side than my 4by. My only concern is _where_ do these cubes actually come from? The rest of my cubes (2X, 3X, 4X) have _all_ had the Rubik's symbol and copyright notices on them. These 5bys have neither. Could these be pirated cubes? On the other hand they seem solidly made and the colors are bright and distinct unlike most cheepy copy-cubes that I've seen. But it's curious that there are no copyright notices _anywhere_ either the cube or the enclosing box. Oh well. Something to keep my hands busy during those long compiles for the next couple of weeks. Cheers Nichael From mindcrf!roadrunner.mindcraft.com.mindcraft.com!ronnie@decwrl.dec.com Fri May 10 19:17:14 1991 Return-Path: Received: from uucp-gw-1.pa.dec.com by life.ai.mit.edu (4.1/AI-4.10) id AA24716; Fri, 10 May 91 19:17:14 EDT Received: by uucp-gw-1.pa.dec.com; id AA29312; Fri, 10 May 91 16:16:59 -0700 Received: by mindcrf.mindcraft.com (AIX 2.1 2/4.03) id AA15933; Wed, 8 May 91 13:12:19 PDT Received: by roadrunner.mindcraft.com.mindcraft.com (AIX 3.1/UCB 5.61/4.03) id AA21608; Wed, 8 May 91 13:18:15 -0700 Date: Wed, 8 May 91 13:18:15 -0700 From: mindcrf!ronnie@roadrunner.mindcraft.com.mindcraft.com (Ronnie Kon) Message-Id: <9105082018.AA21608@roadrunner.mindcraft.com.mindcraft.com> To: @mindcrf.pa.dec.com:decwrl!ai.ai.mit.edu!Cube-Lovers Subject: Patterns on the order 5 cube OK, for everybody out there with the 5-cube, this is the most difficult pattern I have come up with to implement (which is still highly ordered). Top: |A|A|A|A|A| |A|B|B|B|B| |A|B|A|A|A| |A|B|A|B|B| |A|B|A|B|A| Front: |B|C|B|C|B| |C|A|C|A|C| :thgiR |B|C|B|C|C| |A|A|C|A|C| |B|C|B|B|B| |C|C|C|A|C| |B|C|C|C|C| |A|A|A|A|C| |B|B|B|B|B| |C|C|C|C|C| Where this pattern is also present on the remaining 3 sides. (This amounts to twirling a 4-cube, a 3-cube, a 2-cube and a 1-cube around a pair of diagonally opposite corners in alternating directions. It's not difficult to do after you've done it a couple of times, but the potential for getting confused is surprising. Ronnie From mindcrf!peabody.mindcraft.com!ronnie@decwrl.dec.com Fri May 10 19:16:47 1991 Return-Path: Received: from uucp-gw-1.pa.dec.com by life.ai.mit.edu (4.1/AI-4.10) id AA24712; Fri, 10 May 91 19:16:47 EDT Received: by uucp-gw-1.pa.dec.com; id AA29291; Fri, 10 May 91 16:16:33 -0700 Received: by mindcrf.mindcraft.com (AIX 2.1 2/4.03) id AA10398; Mon, 6 May 91 11:02:49 PDT Received: by peabody.mindcraft.com (AIX 1.3/4.03) id AA22955; Mon, 6 May 91 11:14:02 -0700 Date: Mon, 6 May 91 11:14:02 -0700 From: mindcrf!ronnie@peabody.mindcraft.com (Ronnie Kon) Message-Id: <9105061814.AA22955@peabody.mindcraft.com> To: @mindcrf.pa.dec.com:decwrl!ai.ai.mit.edu!Cube-Lovers Subject: 5by cubes As far as I can tell, if you can solve the order 3 and order 4 cube, you should be able to solve the order 5 with no additional fiddling, even if you only know cookbook solutions. Spoiler follows: I solve the off-center edges first (just like in the order 4 cube-- the transformations are identical), then the corners (exactly like all other orders, from 2 through 4), then the center edges (exactly like the order 3 cube, just treat the two edge faces as attached and you have an order 3 cube). All that's left are the eight centers. Four of these can be solved exactly as in the order 4, and if you can't generalize your cookbook solution to solve the remaining 4 you have no business cubing. I suspect this is why there are (and will probably never be) cubes of orders greater than 5. I believe (though have not proved) that the 5 cube contains all the complexity that is possible. Adding more cubies would only increase the amount of time needed to solve. On the other hand, I would be willing to pay a fair amount of money for an order 21 cube. :-) Ronnie From mindcrf!peabody.mindcraft.com!ronnie@decwrl.dec.com Fri May 10 19:16:59 1991 Return-Path: Received: from uucp-gw-1.pa.dec.com by life.ai.mit.edu (4.1/AI-4.10) id AA24715; Fri, 10 May 91 19:16:59 EDT Received: by uucp-gw-1.pa.dec.com; id AA29296; Fri, 10 May 91 16:16:46 -0700 Received: by mindcrf.mindcraft.com (AIX 2.1 2/4.03) id AA13108; Tue, 7 May 91 15:06:05 PDT Received: by peabody.mindcraft.com (AIX 1.3/4.03) id AA14556; Tue, 7 May 91 15:05:29 -0700 Date: Tue, 7 May 91 15:05:29 -0700 From: mindcrf!ronnie@peabody.mindcraft.com (Ronnie Kon) Message-Id: <9105072205.AA14556@peabody.mindcraft.com> To: @mindcrf.pa.dec.com:decwrl!ai.ai.mit.edu!Cube-Lovers Subject: Rubik's tangle >>> From: "Dale I. Newfield" >>> >>> Rubik's Tangle: >>> Rubik's Tngle has 25 square tiles each tile has the very same pattern >>> of ropes, but the color of the ropes varies. >>> Object: Lay down the tiles into a 5X5 square in such a way that each >>> colored rop forms it's own continuous line. >>> 24! x 4^24 = 1746 x 10^38 ( I have a feeling it should be 25!, not 24!) No, I think the 24! is correct. Since we don't count rotations as different, the first tile can be placed any way you want without affecting the outcome. Ronnie From ncramer@bbn.com Fri May 10 21:33:52 1991 Return-Path: Received: from LABS-N.BBN.COM by life.ai.mit.edu (4.1/AI-4.10) id AA26837; Fri, 10 May 91 21:33:52 EDT Message-Id: <9105110133.AA26837@life.ai.mit.edu> Date: Fri, 10 May 91 20:45:08 EDT From: Nichael Cramer To: Ronnie Kon Cc: cube-lovers@life.ai.mit.edu Subject: Re: 5by cubes >Date: Mon, 6 May 91 11:14:02 -0700 >From: Ronnie Kon >Subject: 5by cubes > I suspect this is why there are (and will probably never be) cubes of >orders greater than 5. I believe (though have not proved) that the 5 cube >contains all the complexity that is possible. Adding more cubies would only >increase the amount of time needed to solve. On the other hand, a 5X (or any cube of odd order) will still have the constraints imposed by a fixed center. As a single example, the 4X here in my office is completely "solved" except that two opposite corners are swapped. That's not something that can happen on a cube of odd order (at least I don't think so, but I would love to be proved wrong ;). N From latto@lucid.com Fri May 10 22:55:59 1991 Return-Path: Received: from lucid.com by life.ai.mit.edu (4.1/AI-4.10) id AA28273; Fri, 10 May 91 22:55:59 EDT Received: from boston-harbor ([192.43.175.1]) by heavens-gate.lucid.com id AA03012g; Fri, 10 May 91 19:54:56 PDT Received: by boston-harbor id AA29787g; Fri, 10 May 91 22:58:29 EDT Date: Fri, 10 May 91 22:58:29 EDT From: Andy Latto Message-Id: <9105110258.AA29787@boston-harbor> To: mindcrf!ronnie@peabody.mindcraft.com Cc: Cube-Lovers@life.ai.mit.edu In-Reply-To: Ronnie Kon's message of Mon, 6 May 91 11:14:02 -0700 <9105061814.AA22955@peabody.mindcraft.com> Subject: 5by cubes > On the other hand, I would be willing to pay a fair amount of money for > an order 21 cube. :-) You can't make an order 21 cube, or any cube of order 7 or higher. When you turn the top layer of such a cube by 45 degrees, the corner cubie will not touch the other layers at all, so there's no way to keep it attached, and it will fall off. Andy Latto latto@lucid.com From @po5.andrew.cmu.edu:dn1l+@andrew.cmu.edu Sat May 11 03:37:00 1991 Return-Path: <@po5.andrew.cmu.edu:dn1l+@andrew.cmu.edu> Received: from po5.andrew.cmu.edu by life.ai.mit.edu (4.1/AI-4.10) id AA01992; Sat, 11 May 91 03:37:00 EDT Received: by po5.andrew.cmu.edu (5.54/3.15) id for Cube-Lovers@life.ai.mit.edu; Sat, 11 May 91 03:36:19 EDT Received: via switchmail; Sat, 11 May 91 03:36:19 -0400 (EDT) Received: from yen.mg.andrew.cmu.edu via qmail ID ; Sat, 11 May 91 03:35:20 -0400 (EDT) Received: from yen.mg.andrew.cmu.edu via qmail ID ; Sat, 11 May 91 03:35:13 -0400 (EDT) Received: from Messages.7.8.N.CUILIB.3.45.SNAP.NOT.LINKED.yen.mg.andrew.cmu.edu.pmax.3 via MS.5.6.yen.mg.andrew.cmu.edu.pmax_3; Sat, 11 May 91 03:35:12 -0400 (EDT) Message-Id: Date: Sat, 11 May 91 03:35:12 -0400 (EDT) From: "Dale I. Newfield" To: Cube-Lovers@life.ai.mit.edu Subject: Re: Rubik's tangle In-Reply-To: <9105072205.AA14556@peabody.mindcraft.com> References: <9105072205.AA14556@peabody.mindcraft.com> > Excerpts from internet.cube-lovers: 7-May-91 Rubik's tangle Ronnie > Kon@peabody.mindc (568) > >>> From: "Dale I. Newfield" > >>> > >>> Rubik's Tangle: > >>> Rubik's Tngle has 25 square tiles each tile has the very same > pattern > >>> of ropes, but the color of the ropes varies. > >>> Object: Lay down the tiles into a 5X5 square in such a way that each > >>> colored rop forms it's own continuous line. > >>> 24! x 4^24 = 1746 x 10^38 ( I have a feeling it should be 25!, not > 24!) > No, I think the 24! is correct. Since we don't count rotations as > different, the first tile can be placed any way you want without > affecting > the outcome. > Ronnie No, Because off the rotation, the 4^25 goes down to 4^24, but again, I still think that it should be 25!, because there are that many pieces to be arranged. Dale From @po5.andrew.cmu.edu:dn1l+@andrew.cmu.edu Sat May 11 03:48:46 1991 Return-Path: <@po5.andrew.cmu.edu:dn1l+@andrew.cmu.edu> Received: from po5.andrew.cmu.edu by life.ai.mit.edu (4.1/AI-4.10) id AA02102; Sat, 11 May 91 03:48:46 EDT Received: by po5.andrew.cmu.edu (5.54/3.15) id for Cube-Lovers@life.ai.mit.edu; Sat, 11 May 91 03:48:42 EDT Received: via switchmail; Sat, 11 May 91 03:48:42 -0400 (EDT) Received: from yen.mg.andrew.cmu.edu via qmail ID ; Sat, 11 May 91 03:47:44 -0400 (EDT) Received: from yen.mg.andrew.cmu.edu via qmail ID ; Sat, 11 May 91 03:47:40 -0400 (EDT) Received: from Messages.7.8.N.CUILIB.3.45.SNAP.NOT.LINKED.yen.mg.andrew.cmu.edu.pmax.3 via MS.5.6.yen.mg.andrew.cmu.edu.pmax_3; Sat, 11 May 91 03:47:40 -0400 (EDT) Message-Id: Date: Sat, 11 May 91 03:47:40 -0400 (EDT) From: "Dale I. Newfield" To: Cube-Lovers@life.ai.mit.edu Subject: Re: 5by cubes Cc: Cube-Lovers@life.ai.mit.edu In-Reply-To: <9105110258.AA29787@boston-harbor> References: <9105110258.AA29787@boston-harbor> I solve the cubes in a way much different than lots that people have explained: (Don't read if you don't want!) I pick a "top" side and solve it. I put the centers together(on the order 3, this was REAL easy! :-) I put the edges together that go from the top to the bottom. I solve the bottom 4 corners I solve the bottom 4 middles. depending on which cube, the 2nd and 3rd steps are switched. I am only having one problem with the 5x5x5 cube, though: X|O|X|X|X X|X|X|X|X X|X|X|X|X X|X|X|X|X X|X|X|O|X looking at the bottom of my cube, the 2 pieces marked O are swaped sometimes, so that the face is still a solid color, but the sides are swapped. I also got it to have the swapped pieces near each other: X|X|X|X|X X|X|X|X|X X|X|X|X|X O|X|X|X|X X|X|X|O|X My question is this: I can't figure out what causes the swapping. Is it the because in this face, X|X|X|X|X X|O|I|O|X X|I|X|I|X X|O|I|O|X X|X|X|X|X the I's and the O's are in the "wrong" positions, even though they are indestingiushable? Dale Newfield From ncramer@bbn.com Sun May 12 17:18:48 1991 Return-Path: Received: from LABS-N.BBN.COM by life.ai.mit.edu (4.1/AI-4.10) id AA19875; Sun, 12 May 91 17:18:48 EDT Message-Id: <9105122118.AA19875@life.ai.mit.edu> Date: Sun, 12 May 91 17:12:57 EDT From: Nichael Cramer To: "Dale I. Newfield" Cc: Cube-Lovers@life.ai.mit.edu Subject: Re: 5by cubes >Date: Sat, 11 May 91 03:47:40 -0400 (EDT) >From: "Dale I. Newfield" >To: Cube-Lovers@life.ai.mit.edu >Subject: Re: 5by cubes >Cc: Cube-Lovers@life.ai.mit.edu > >(Don't read if you don't want!) Ditto! ;) >I am only having one problem with the 5x5x5 cube, though: > >X|O|X|X|X >X|X|X|X|X >X|X|X|X|X >X|X|X|X|X >X|X|X|O|X ^ ^ 1 2 >looking at the bottom of my cube, the 2 pieces marked O are swaped >sometimes, so that the face is still a solid color, but the sides are >swapped. [ ... ] I can't figure out what causes the swapping. Dale, What is wrong is that *one* of the inner planes [marked 1 & 2 above] are a quarter turn [i.e. 90dgs] out of phase. 1] The way I solve this is to turn one of the planes a quarter turn, [to get, for example the following]: >X|O|X|o|X <--(Where "o" is the other face of the "O" above.) >X|X|X|Y|X >X|X|X|Y|X >X|X|X|Y|X >X|X|X|Y|X ^ ^ 1 2 2] Then, to keep things straight in my head, I then "mark" the new position by replacing the center cubies in the turned plane to their correct positions (being careful not to mess with anything else --particularly the edge pieces): >X|O|X|o|X >X|X|X|X|X >X|X|X|X|X >X|X|X|X|X >X|X|X|Y|X ^ ^ 1 2 There's a relatively simple operator to do this, which I leave as an exercise for the reader. ;) (It's probably better to do this to all affected four faces, but you can save this until you have solved the edges.) 3] This leaves you five inner, non-central edges to solve. But it should be straightforward, so long as you be careful not to mess up anything else. Nichael From ncramer@bbn.com Sun May 12 18:05:24 1991 Return-Path: Received: from LABS-N.BBN.COM by life.ai.mit.edu (4.1/AI-4.10) id AA20500; Sun, 12 May 91 18:05:24 EDT Message-Id: <9105122205.AA20500@life.ai.mit.edu> Date: Sun, 12 May 91 18:01:38 EDT From: Nichael Cramer To: dn1l+@andrew.cmu.edu Cc: "Dale I. Newfield" , Cube-Lovers@life.ai.mit.edu Subject: ARGGHHH!! [was: 5by cubes] >Date: Sun, 12 May 91 17:12:57 EDT >From: Nichael Cramer >To: "Dale I. Newfield" >Subject: Re: 5by cubes >>Date: Sat, 11 May 91 03:47:40 -0400 (EDT) >>From: "Dale I. Newfield" >>To: Cube-Lovers@life.ai.mit.edu >>I am only having one problem with the 5x5x5 cube, though: >>X|O|X|X|X >>X|X|X|X|X >>X|X|X|X|X >>X|X|X|X|X >>X|X|X|O|X >>looking at the bottom of my cube, the 2 pieces marked O are swaped >>sometimes, so that the face is still a solid color, but the sides are >>swapped. [ ... ] I can't figure out what causes the swapping. [I write]: >Dale, [...] #$%@!! I just realize that I answered the wrong question! My answer was to the question: "My cube is completely solved *except* that the 2 pieces marked `O' are flipped." (Sorry.) The right answer should be: The state of the cube is not: X|O|X|X|X X|A|X|C|X X|X|X|X|X X|X|X|X|X X|X|X|X|X But rather: X|X|X|X|X X|X|X|X|X X|X|X|X|X X|X|X|O|X X|X|X|B|X Where cubie "C" just "looks" like it's in the right place. You need an operator that rotates A->B->C->A. (Left as an exercise; hints available on request.) This will very likely leave an inconvenient number of edges flipped. For the answer to _this_ problem, see my last post. ;) Nichael-walks-with-the-red-face From @po5.andrew.cmu.edu:dn1l+@andrew.cmu.edu Mon May 13 00:51:55 1991 Return-Path: <@po5.andrew.cmu.edu:dn1l+@andrew.cmu.edu> Received: from po5.andrew.cmu.edu by life.ai.mit.edu (4.1/AI-4.10) id AA26112; Mon, 13 May 91 00:51:55 EDT Received: by po5.andrew.cmu.edu (5.54/3.15) id for Cube-Lovers@life.ai.mit.edu; Mon, 13 May 91 00:51:46 EDT Received: via switchmail; Mon, 13 May 91 00:51:46 -0400 (EDT) Received: from kwacha.mg.andrew.cmu.edu via qmail ID ; Mon, 13 May 91 00:49:43 -0400 (EDT) Received: from kwacha.mg.andrew.cmu.edu via qmail ID ; Mon, 13 May 91 00:49:34 -0400 (EDT) Received: from Messages.7.8.N.CUILIB.3.45.SNAP.NOT.LINKED.kwacha.mg.andrew.cmu.edu.pmax.3 via MS.5.6.kwacha.mg.andrew.cmu.edu.pmax_3; Mon, 13 May 91 00:49:34 -0400 (EDT) Message-Id: Date: Mon, 13 May 91 00:49:34 -0400 (EDT) From: "Dale I. Newfield" To: Cube-Lovers@life.ai.mit.edu Subject: Re: 5by cubes Cc: Cube-Lovers@life.ai.mit.edu In-Reply-To: <9105110258.AA29787@boston-harbor> References: <9105110258.AA29787@boston-harbor> Excerpts from internet.cube-lovers: 10-May-91 5by cubes Andy Latto@lucid.com (383) >You can't make an order 21 cube, or any cube of order 7 or higher. >When you turn the top layer of such a cube by 45 degrees, the corner >cubie will not touch the other layers at all, so there's >no way to keep it attached, and it will fall off. There is no law that says that the cubes have to be the same size. XXXX|XXX|XX|X|XX|XXX|XXXX XXXX|XXX|XX|X|XX|XXX|XXXX XXXX|XXX|XX|X|XX|XXX|XXXX XXXX|XXX|XX|X|XX|XXX|XXXX ----+---+--+-+--+---+---- XXXX|XXX|XX|X|XX|XXX|XXXX XXXX|XXX|XX|X|XX|XXX|XXXX XXXX|XXX|XX|X|XX|XXX|XXXX ----+---+--+-+--+---+---- XXXX|XXX|XX|X|XX|XXX|XXXX XXXX|XXX|XX|X|XX|XXX|XXXX ----+---+--+-+--+---+---- XXXX|XXX|XX|X|XX|XXX|XXXX ----+---+--+-+--+---+---- XXXX|XXX|XX|X|XX|XXX|XXXX XXXX|XXX|XX|X|XX|XXX|XXXX ----+---+--+-+--+---+---- XXXX|XXX|XX|X|XX|XXX|XXXX XXXX|XXX|XX|X|XX|XXX|XXXX XXXX|XXX|XX|X|XX|XXX|XXXX ----+---+--+-+--+---+---- XXXX|XXX|XX|X|XX|XXX|XXXX XXXX|XXX|XX|X|XX|XXX|XXXX XXXX|XXX|XX|X|XX|XXX|XXXX XXXX|XXX|XX|X|XX|XXX|XXXX JUST AS AN EXAMPLE. From gls@think.com Mon May 13 12:04:08 1991 Received: from mail.think.com by life.ai.mit.edu (4.1/AI-4.10) id AA05129; Mon, 13 May 91 12:04:08 EDT Return-Path: Received: from Berlin.Think.COM by mail.think.com; Mon, 13 May 91 12:03:40 -0400 Received: from Ukko.Think.COM by berlin.think.com; Mon, 13 May 91 12:04:01 -0400 From: Guy Steele Received: by ukko.think.com; Mon, 13 May 91 12:03:50 EDT Date: Mon, 13 May 91 12:03:50 EDT Message-Id: <9105131603.AA01148@ukko.think.com> To: latto@lucid.com Cc: mindcrf!ronnie@peabody.mindcraft.com, Cube-Lovers@life.ai.mit.edu In-Reply-To: Andy Latto's message of Fri, 10 May 91 22:58:29 EDT <9105110258.AA29787@boston-harbor> Subject: 5by cubes Date: Fri, 10 May 91 22:58:29 EDT From: Andy Latto > On the other hand, I would be willing to pay a fair amount of money for > an order 21 cube. :-) You can't make an order 21 cube, or any cube of order 7 or higher. When you turn the top layer of such a cube by 45 degrees, the corner cubie will not touch the other layers at all, so there's no way to keep it attached, and it will fall off. Assuming the current technology, anyway. But imagine a less passive approach. Suppose each cubie had a cheap microprocessor, and some little latches. Normally cubies hang onto their neighbors, but when they notice you are applying torque, they let go of their neighbors in just that one direction and hang on for dear life in the other two directions. The latches can also be conducting in order to convey the necessary actuating power from a centrally placed battery. --Wild and Crazy Guy From hoey@aic.nrl.navy.mil Mon May 13 14:46:09 1991 Received: from Sun0.AIC.NRL.Navy.Mil by life.ai.mit.edu (4.1/AI-4.10) id AA10029; Mon, 13 May 91 14:46:09 EDT Received: from sun13.aic.nrl.navy.mil by Sun0.AIC.NRL.Navy.Mil (4.1/SMI-4.0) id AA21231; Mon, 13 May 91 14:43:49 EDT Return-Path: Received: by sun13.aic.nrl.navy.mil; Mon, 13 May 91 14:46:06 EDT Date: Mon, 13 May 91 14:46:06 EDT From: hoey@aic.nrl.navy.mil Message-Id: <9105131846.AA12000@sun13.aic.nrl.navy.mil> To: Cube-Lovers@ai.mit.edu Subject: Very silly ways of building very large cubes (was Re: 5by cubes) Organization: Navy Center for Applied Research in AI Andy Latto wrote: >You can't make an order 21 cube, or any cube of order 7 or higher. >When you turn the top layer of such a cube by 45 degrees, the corner >cubie will not touch the other layers at all, so there's >no way to keep it attached, and it will fall off. Then "Dale I. Newfield" responded: >There is no law that says that the cubes have to be the same size. and showed that by making the outer layers thicker, we can increase the size of the cube. There is another way around Andy Latto's con- cern, and that is that we can--at least in theory--design a physical cube that lets pieces overhang, such as corners that touch only two surfaces, and yet still holds the pieces so they cannot be removed. This idea (which came up in talks with Jim Saxe about a decade ago) is to slice up the cube with a fresnel saw. A fresnel saw is used to cut a piece of glass into two fresnel lenses out of pieces of glass, and you find them in the same stores that sell plaid paint and jelly- doughnut cookie cutters. (In case you don't know what a fresnel lens (pronounced freh-NEL) is, for this note it's sufficient to think of it as a surface with small concentric circular grooves in it. Kind of like those old vinyl recordings people used to listen to, except that the grooves are circular instead of spiral, and the grooves don't wiggle back and forth.) Now if you have two surfaces with mating grooves--each one has a ridge that fits in each of the other's grooves--when you put them together you can twist one with respect to the other, but you can't slide one across the other, because the grooves are locked together. There is one thing you can do that we don't want: you can lift one slab away from the other. The solution now is to get a *very* *sharp* fresnel saw, that cuts hooked grooves that interlock with each other. You get surfaces with cross sections that look somewhat like hook-in surface _________ _______________________ _________ \ / \ / . \ / \ / | | | | | | | | | | | __ | | __ . __ | | __ | | | | \ | | \ | / | | / | | \ \___/| \ \___/| . |\___/ / |\___/ / \ | \ | | | / | / \_____/ \_____/ . \_____/ \_____/ _____ _____________________ _____ / \ / | \ / \ | ___ \ | ___ . ___ | / ___ | |/ \ \ |/ \ | / \| / / \| \__ | | \__ | axis | __/ | | __/ | | | of | | | | | | rotation | | | ___________/ \_________/ \_________/ \_____ hook-out surface except that the surfaces are closer, so the hooked grooves are engaged with each other. (Now we see why we need a fresnel saw, so that we can cut the two mating surfaces in one cut, and avoid the problem of trying to assemble two separated pieces (though we could get around that difficulty messily with glue)). So we may cut up a 2n+1 x 2n+1 x 2n+1 cube with a fresnel saw, to make a large Rubik's cube. The only really touchy point is the need to make the ``direction'' of each cut match the direction of the other cuts at that ``depth.'' Here, direction refers to whether the hook-in surface faces toward the nearest parallel side or away from that side, and ``depth'' refers to the distance from the nearest parallel side. This ensures that when we permute cubies around the directions of the groove hooks will not change, so the grooves will always mate. If n is large, then pieces of one slab will overhang at each turn, so you can see the grooves on a whole surface of a corner, or on two surfaces of an edge piece. But you can't pull the piece off, because it won't move straight with respect to the rest of the cube, only in curved trajectories. We have to keep the fresnelling small with respect to the size of the cubies, and the tolerances are pretty tight, but that's the regime we theoretical engineers are working in. (I'd like to mention that cubes made with this method also have the nice feature that there's a 2n-1 x 2n-1 x 2n-1 Rubik's cube on the inside, so you can play with the theoretical invisible group while you're at it.) Now what about cubes of even side? The fresnel saw cuts two surfaces that mate to each other but not to themselves. How can we get a surface that mates to itself? I think the answer is that we can't. But this doesn't mean we are out of luck, as there are several ways of fixing up the center cuts of these cubes. Perhaps easiest way is to embed a 2x2x2 cube in the center of the original solid cube, and use it to hold the octants together. Unfortunately, this method requires an appeal to the existence of even-sided cubes, rather than teaching us how to build them. The other ways of finessing the center cut involve the thin-center- slab approach. You know you can simulate a 2x2x2 pocket cube with the corners of a regular 3x3x3 Rubik's cube, and similarly you can simulate any even cube with a larger odd cube. Also, we can make that center slab very thin, so it becomes part of the supporting structure rather than a significant part of the cube. We also remove the cor- ners from the center slab, so it does not protrude from the cube. We may even make covers for the cubies slabs adjacent to the center, to cover up the crack where the center slab lives. We are ready to cube! Or are we? The thin-center-slab suffers from the partial-twist problem. We can see this in the simulation of the 2x2x2 by a 3x3x3. If you try to simply ignore the center slabs, you can end up with the corners being aligned with each other but with a center slab twisted by 45 degrees. This makes it impossible to turn the corners except in the plane parallel to the oblique slab. If we shrink the center slab enough that it becomes unnoticeable, we will still be unable to twist the cube except in one direction except by breaking the center slab. The first solution to the partial-twist-problem is to select one of the eight near-central cubies, a cubie that abuts the center slabs on three sides. We then glue the adjacent parts of the center slabs to that cubie. Then when we turn along the center slice(s), the glued part of the thin center slab will follow the selected cubie, and will push the rest of the thin center slab along. This is a modification of the solution that is taken inside Rubik's Revenge, as I described to this group in my Invisible Revenge article of 9 August 1982. I like this solution except for one thing. It destroys the symmetry of the cube, by selecting one specialized octant that the center slab must follow. There is one more solution, though, that keeps the cube symmetric, which is *even* *sillier* than the thin center slab itself. Let us now visualize the center slab. It has the corners removed, so it is in the shape of a disc. The disc is cut in a grid pattern by the cuts from perpendicular planes. Now suppose we cut each slab in a second grid pattern, with the grid at a 45 degree offset from the original. With such a center slab, the cube can be twisted if each slab grid is in the correct position, or if some are at a 45 degree offset from the correct position. And how shall we prevent turns of less than a 45 degrees? Gears! Embed tiny gears in each fragment of the center slab, that contact tiny toothed tracks in the adjacent slabs on both sides. This will force the center slab to turn at exactly half the angular rate of one half of the cube with respect to the other. Thus when the off-center slabs of the cube are aligned, the center slab will be at one of the positions that allows twisting. Dan Hoey Hoey@AIC.NRL.Navy.Mil From latto@lucid.com Tue May 14 16:46:39 1991 Return-Path: Received: from lucid.com by life.ai.mit.edu (4.1/AI-4.10) id AA26858; Tue, 14 May 91 16:46:39 EDT Received: from boston-harbor ([192.43.175.1]) by heavens-gate.lucid.com id AA08804g; Tue, 14 May 91 10:50:14 PDT Site: Received: by boston-harbor id AA10376g; Tue, 14 May 91 13:54:02 EDT Date: Tue, 14 May 91 13:54:02 EDT From: Andy Latto Message-Id: <9105141754.AA10376@boston-harbor> To: gls@think.com Cc: Cube-Lovers@life.ai.mit.edu In-Reply-To: Guy Steele's message of Mon, 13 May 91 12:03:50 EDT <9105131603.AA01148@ukko.think.com> Subject: 5by cubes Should you really be posting the secret proposed architecture for the CM-6 to a publicly available mailing list? :-) :-) Andy latto@lucid.com From kon@bach.stanford.edu Tue May 14 21:14:14 1991 Return-Path: Received: from bach.Stanford.EDU by life.ai.mit.edu (4.1/AI-4.10) id AA02844; Tue, 14 May 91 21:14:14 EDT Received: by bach.Stanford.EDU (4.1/inc-1.0) id AA00195; Tue, 14 May 91 18:14:11 PDT Date: Tue, 14 May 91 18:14:11 PDT From: kon@bach.stanford.edu (Ronnie Kon) Message-Id: <9105150114.AA00195@bach.Stanford.EDU> To: mindcrf!ronnie@peabody.mindcraft.com, ncramer@bbn.com Subject: Re: 5by cubes Cc: cube-lovers@life.ai.mit.edu >> I suspect this is why there are (and will probably never be) cubes of >>orders greater than 5. I believe (though have not proved) that the 5 cube >>contains all the complexity that is possible. Adding more cubies would only >>increase the amount of time needed to solve. > >On the other hand, a 5X (or any cube of odd order) will still have the >constraints imposed by a fixed center. As a single example, the 4X here in >my office is completely "solved" except that two opposite corners are >swapped. That's not something that can happen on a cube of odd order (at >least I don't think so, but I would love to be proved wrong ;). Wow! I could have sworn I have gotten to this position before, but you are very definitely correct. The state with two diagonal corners swapped is in the orbit with edge cubies exchanged. Ronnie From kon@bach.stanford.edu Tue May 14 21:31:35 1991 Return-Path: Received: from bach.Stanford.EDU by life.ai.mit.edu (4.1/AI-4.10) id AA03214; Tue, 14 May 91 21:31:35 EDT Received: by bach.Stanford.EDU (4.1/inc-1.0) id AA00208; Tue, 14 May 91 18:31:33 PDT Date: Tue, 14 May 91 18:31:33 PDT From: kon@bach.stanford.edu (Ronnie Kon) Message-Id: <9105150131.AA00208@bach.Stanford.EDU> To: dn1l+@andrew.cmu.edu, ncramer@bbn.com Subject: Re: ARGGHHH!! [was: 5by cubes] Cc: Cube-Lovers@life.ai.mit.edu > >(Sorry.) The right answer should be: > >The state of the cube is not: > >X|O|X|X|X X|A|X|C|X >X|X|X|X|X X|X|X|X|X >X|X|X|X|X But rather: X|X|X|X|X >X|X|X|X|X X|X|X|X|X >X|X|X|O|X X|X|X|B|X > >Where cubie "C" just "looks" like it's in the right place. > >You need an operator that rotates A->B->C->A. (Left as an exercise; hints >available on request.) > >This will very likely leave an inconvenient number of edges flipped. For >the answer to _this_ problem, see my last post. ;) I think you must be wrong here (but would love to be proved wrong--I'm no mathematician so group theory is very much beyond me). Proof #1: We hold the cube with the red face on top, and the yellow face in front (colors obviously don't matter, but I find it easier to discuss using them). We will assign a parity to the edge cubies, being defined by holding the cube such that the red face of the cubie is on top and the yellow in front. If the cubie is on the left as we look at it in this position it is parity 0, on the right it is parity 1. There are only two operations available which affect the cubie we are interested in: rotating the front face 90deg; and rotating the slice the cubie is in 90deg. It is easy to see that neither of these moves alters the parity (assume the cubie's frame of reference, and think of rotating the rest of the cube around it--it is clear that it will not end up on the other side). Therefore the move C->A in the above is impossible. Proof #2: Take apart the order 4 cube (my falls apart depressingly easilly) and try to reassemble it with the two edges exchanged. It will not fit, as they are mirror images of each other. Note that you get an apparant parity reversal by flipping the cubies, but this does not actually move anything. In other words, no amount of flipping and moving will allow you to end up moving A->B->C->A. That's why I solve edges first. Ronnie From ncramer@bbn.com Wed May 15 22:52:53 1991 Return-Path: Received: from LABS-N.BBN.COM by life.ai.mit.edu (4.1/AI-4.10) id AA21390; Wed, 15 May 91 22:52:53 EDT Message-Id: <9105160252.AA21390@life.ai.mit.edu> Date: Wed, 15 May 91 22:09:23 EDT From: Nichael Cramer To: Ronnie Kon Cc: dn1l+@andrew.cmu.edu, ncramer@bbn.com, Cube-Lovers@life.ai.mit.edu Subject: Re: ARGGHHH!! [was: 5by cubes] Ronnie Kon writes: >I write: >>The state of the cube is not: >> >>X|O|X|X|X X|A|X|C|X >>X|X|X|X|X X|X|X|X|X >>X|X|X|X|X But rather: X|X|X|X|X >>X|X|X|X|X X|X|X|X|X >>X|X|X|O|X X|X|X|B|X >> >>Where cubie "C" just "looks" like it's in the right place. >> >>You need an operator that rotates A->B->C->A. [...] >> >>This will very likely leave an inconvenient number of edges flipped. For >>the answer to _this_ problem, see my last post. ;) > >I think you must be wrong here (but would love to be proved wrong--I'm no >mathematician so group theory is very much beyond me). > > [Proofs deleted.] Hi. I think we're in complete agreement, at least up to here. (I particularly enjoyed your "proof by hardware ;). I didn't mean to imply that the A->B->C->A operator preserved flipped-ness of the Non-Central-Edge[NCE] Cubies. Moreover, I was being imprecise where I said "a NCE cubie is simply flipped"; rather "the cubie *appears* as if it were in the right place (i.e. judged by its colors) and flipped". As you point out, *really* means that it is in the slot of its "twin". To recap more succinctly, what I was proposing was a rather pedestrian, two-step solution to the original problem. Starting from the initial state in FIG1 (where the cube is completely "solved" except that the cubies marked "O" are swapped. Also they are swapped in such a way that the visible face is all a single color). FIG1: X|O|X|X|X FIG2: X|Q|X|Q|X X|X|X|X|X X|X|X|X|X X|X|X|X|X A->B->C->A gives: X|X|X|X|X X|X|X|X|X X|X|X|X|X X|X|X|O|X X|X|X|X|X STEP1] If we then apply the A->B->C->A operator, we end up with the state in FIG2, where the cube is completely "solved" except that the cubies marked "Q" "appear" to be "simply" flipped. STEP2] We can then solve this problem, which (imo) is easier. For example see the method that I described in an earlier post; this involves turning the non-central plane (containing the flipped cubie) through a quarter turn. Of course, now that I say it, it seems that the correct course would be to *start* with the quarter turn of the non-central plane. This would leave five NCE cubies out of place, but the cube would be in the right orbit. From there the solution should be straightforward (e.g. two intersecting 3-cycles). Finally, it seems clear that this entire problem --and all the subsequent discussion-- maps directly onto a virtually identical problem on the 4by cube (i.e. simply be removing the center planes). >Note that you get an apparant parity reversal by flipping the cubies, but >this does not actually move anything. In other words, no amount of >flipping and moving will allow you to end up moving A->B->C->A. That's >why I solve edges first. Again, perhaps I'm missing the point, but if you don't care about how the flipping comes out, the A->B->C->A 3-cycle is certainly doable: For example: [WARNING: EVEN MORE BORING STUFF AHEAD!! ;] (I have no idea how to show this notationally, so I'll try pictorially.) | 1] 2] V 3] X|A|X|C|X X|Y|X|C|X ->Z|Z|Z|Z|Z X|X|X|X|X X|Y|X|X|X X|Y|X|X|X X|X|X|X|X X|Y|X|X|X X|Y|X|X|X X|X|X|X|X X|Y|X|X|X X|Y|X|X|X X|X|X|B|X X|A|X|B|X X|A|X|B|X 4] 5] 6] Z|A|Z|Z|Z X|B|X|X|X X|B|X|X|X X|X|X|X|X X|X|X|X|X X|X|X|X|X X|X|X|X|X X|X|X|X|X X|X|X|X|X X|X|X|X|X X|X|X|X|X X|X|X|X|X X|X|X|B|X Z|Z|Z|A|Z ->?|?|?|?|? ^ | [Rotate Face one-half turn] >--- 7] \ 8] 9] X|B|X|X|X \ X|B|X|X|X Z|C|Z|Z|Z X|X|X|X|X | X|X|X|X|X X|X|X|X|X X|X|X|X|X | X|X|X|X|X X|X|X|X|X X|X|X|X|X V X|X|X|X|X X|X|X|X|X ?|?|?|?|? Z|Z|Z|C|Z<- X|X|X|B|X [Rotate next- [Rotate Face to-bottom one-half turn] plane 1/4 Turn] <---- 10] 11] \ 12] Z|C|Z|Z|Z Z|C|Z|Z|Z \ Z|C|Z|Z|Z X|X|X|X|X X|X|X|X|X | X|X|X|X|X X|X|X|X|X X|X|X|X|X | X|X|X|X|X X|X|X|X|X X|X|X|X|X ^ X|X|X|X|X ->?|?|?|?|? ?|?|?|?|? X|X|X|A|X<- [Rotate next- to-bottom plane 1/4 turn] | 13] V 14] 15] Z|Z|Z|Z|Z X|Y|X|B|X<- X|C|X|B|X X|Y|X|X|X X|Y|X|X|X X|X|X|X|X X|Y|X|X|X X|Y|X|X|X X|X|X|X|X X|Y|X|X|X X|Y|X|X|X X|X|X|X|X X|C|X|A|X X|C|X|A|X X|X|X|A|X ^ | Cub.E.D From pbeck@pica.army.mil Tue May 21 11:10:45 1991 Return-Path: Received: from FSAC1.PICA.ARMY.MIL by life.ai.mit.edu (4.1/AI-4.10) id AA22456; Tue, 21 May 91 11:10:45 EDT Date: Tue, 21 May 91 11:03:02 EDT From: Peter Beck (LCWSL) To: cube-lovers@life.ai.mit.edu Subject: bilinski rhombicdodecahedron Message-Id: <9105211103.aa16846@FSAC1.PICA.ARMY.MIL> I would like help on finding info on the "BILINSKI" rhombic dodecahedron. BACKGROUND: The common rhombic dodecahedron is the KEPLER and its diagonals are in the ratio of 1:sqr rt of 2. The Bilinski has its diagonals in the ratio of 1:tau (ie, the golden section ~ 1.618). The only reference I have been able to find so far is on page 31 of Coxeter's "Regular Polytopes". AREAS OF INTEREST .. Is there a proof of why there are only 2 rhombic dodecahedrons? .. are there any interesting features of how the Bilinski fills space? Any interesting relationships with other polygons, eg, triacontahedron? .. Has anybody studied the dissections of the bilinski? Is there any significance that it takes both obtuse and acute rhomboids to construct a bilinski while a kepler only requires an obtuse? .. Is there a crystal or some other real world object that corresponds to the bilinski? .. Any ideas on fixturing/jigging to make bilinski's from wood? Thanks for any help. Pete Beck From gdparker@nike.calpoly.edu Wed May 22 04:25:46 1991 Return-Path: Received: from nike.calpoly.edu (morpheus.CalPoly.EDU) by life.ai.mit.edu (4.1/AI-4.10) id AA14318; Wed, 22 May 91 04:25:46 EDT Received: by nike.calpoly.edu (5.61-AIX-1.2/1.0) id AA837751 (for cube-lovers@life.ai.mit.edu, from gdparker/gdparker@nike.calpoly.edu); Wed, 22 May 91 01:25:48 -0700 Date: Wed, 22 May 91 01:25:48 -0700 From: gdparker@nike.calpoly.edu (Gene Dillon Parker) Message-Id: <9105220825.AA837751@nike.calpoly.edu> To: cube-lovers@life.ai.mit.edu Subject: mailing list Hi there, Im an Aero/CSC major at Cal Poly and would like to be added to your dail y mailing list. login: gdparker where: polyslo.calpoly.edu Please include me in the list or E-mail me the info need ed to do so. Thanks! Gene Parker gdparker Cc: From pbeck@pica.army.mil Wed May 22 10:23:37 1991 Return-Path: Received: from FSAC1.PICA.ARMY.MIL by life.ai.mit.edu (4.1/AI-4.10) id AA03468; Wed, 22 May 91 10:23:37 EDT Date: Wed, 22 May 91 10:16:47 EDT From: Peter Beck (LCWSL) To: cube-lovers@life.ai.mit.edu Subject: slide Message-Id: <9105221016.aa14580@FSAC1.PICA.ARMY.MIL> ANNONCEMENT OF "SLIDE" - A Sliding Block Puzzle Simulation Program DESCRIPTION: "SLIDE" is a Sliding Block Puzzle Simulation Program based on the book "Sliding Block Puzzles", by Ed Hordern, 1986 Oxford University Press. It comes on one 360K floppy with an instruction booklet. The booklet tells you how to install the program, how to use it (program does have help files) and how to add your own puzzles. It is in color and REQUIRES a mouse to move the pieces. It has all of hordern's puzzles including the background notes for each, eg, name, producer. The program gives you the minimum number of moves, the object of the puzzle and a randomized version to test your skill. The version I have was obtained at the 11th International Puzzle Party 3/30/91 and is mostly bug free. The author is in the process of updating it and will make updates available at cost (for now anyhow). I recommend "SLIDE" for everyone with a PC who enjoyed Hordern's book. PRICE: 50 dutch Guilders SOURCE: H.J.M. van Grol (Rik) (the author), van Hogendorpstraat 1a, 2515 NR DEN HAAG, The Netherlands COMPUTER REQUIREMENTS: MS-DOS machine with one 360K floppy minimum; can use 1.2 MB and harddisk if available. REQUIRES a mouse. Best with EGA, okay with VGA, needs user defined configuration for Herc or CGA. From phygillen@cs8700.ucg.ie Mon Jun 24 12:19:58 1991 Return-Path: Received: from mcsun.EU.net by life.ai.mit.edu (4.1/AI-4.10) id AA13541; Mon, 24 Jun 91 12:19:58 EDT Received: by mcsun.EU.net via EUnet; id AA29698 (5.65a/CWI-2.95); Mon, 24 Jun 91 18:19:53 +0200 Received: from swift by macneill.macneill.cs.tcd.ie id aa19206; 24 Jun 91 17:14 GMT Received: from cs8700.ucg.ie by cs.tcd.ie with PMDF#10597; Mon, 24 Jun 1991 17:11 +0100 Date: Mon, 24 Jun 91 17:08 GMT From: Patsy Gillen To: cube-lovers@life.ai.mit.edu Message-Id: X-Envelope-To: cube-lovers@ai.ai.mit.edu X-Vms-To: IN%"cube-lovers@ai.ai.mit.edu" SUBCRIBE Rubic's Patrick Gillen From pbeck@pica.army.mil Mon Jul 29 18:16:19 1991 Return-Path: Received: from FSAC1.PICA.ARMY.MIL by life.ai.mit.edu (4.1/AI-4.10) id AA01907; Mon, 29 Jul 91 18:16:19 EDT Date: Mon, 29 Jul 91 14:02:26 EDT From: Peter Beck (BATDD) To: cube-lovers@life.ai.mit.edu Subject: chess variants Message-Id: <9107291402.aa16288@FSAC1.PICA.ARMY.MIL> ANNOUNCEMENT OF "World Game Review special issue #10" - CHESS variations: rules & sample games, reviews, index & bibliography DESCRIPTION: This a a special edition devoted only to chess. It is 100 81/2 x 11 pages. The breadth is indicated by the front cover illustration of the 6 most popular chess variant boards (8x8, 10x10, 4x16, most common 4 handed board, xiang qi, 3 colored hexagonal) and the rear cover illustration of 7 other boards (tesche's 3 handed, petroff's 4 handed, de vasa's tricolor, rutland's, decimal oriental chess, double rettah, petty). TABLE OF CONTENTS BY HEADING & PAGE NUMBER: 1.. COLOPHON 2.. TABLE OF CONTENTS 3.. EDITORIAL & ACKNOWLEDGEMENTS 4.. GENERAL OBSERVATIONS 5.. APPEAL FOR INFORMATION , DAVID PRITCHARD IS WRITING A BOOK - ENCYCLOPEDIA OF CHESS VARIANTS & TERMS 7.. NOTATION 8.. GENERAL RULES, BEST VARIANTS 9.. CV ORGANIZATIONS 10.. GAMES NEWS 12.. BOOK & MAG REVIEWS - SHOGI WORLD, CHINESE CHESS, CHINESISCHE, SCHACH/KOREANISCHES SCHACH, CHINESE CHESS FOR BEGINNERS 14.. GAME REVIEWS - 4 WAY CHESS, FORAY, BATTLE CHESS II 15.. CV TIMELINE --- A PANORAMA OF CHESS VARIANTS 16.. MODIFICATIONS TO FORCES 30.. MODIFICATIONS TO BOARD 40.. MODIFICATIONS TO MOVEMENT 52.. MODIFICATIONS TO RULES OF CAPTURE 63.. OTHER MODS 69.. SAMPLE GAMES 72.. COMPUTERES AND ... 73.. ADDITIONAL PIECES 74.. ADDITIONAL RULES 76.. INVENTORS 78.. BIBLIOGRAPHY 82.. ADDRESSES 84.. INDEX OF VARIATIONS PRICE: US$10 SOURCE: WGR C/O MICHAEL KELLER 3367-I NORTH CHATAM ROAD ELLICOTT CITY, MD, 21042 PLEASE DON'T ASK ME ANY QUESTIONS ABOUT CHESS, I AM NOT A PLAYER AND HAVE NOT READ THE ISSUE.. IF YOU WANT ME TO LOOK SOMETHING UP BE VERY SPECIFIC AND I WILL - BEST YET IS TO ORDER YOUR OWN COPY. From pbeck@pica.army.mil Tue Jul 30 19:59:44 1991 Return-Path: Received: from FSAC1.PICA.ARMY.MIL by life.ai.mit.edu (4.1/AI-4.10) id AA04195; Tue, 30 Jul 91 19:59:44 EDT Date: Tue, 30 Jul 91 15:50:01 EDT From: Peter Beck (BATDD) To: cube-lovers@life.ai.mit.edu Cc: urban@rand.org Subject: world game review Message-Id: <9107301550.aa00806@FSAC1.PICA.ARMY.MIL> PUZZLING NEWSLETTERS -- Oct 90, revised 7/91 .......................................................... "Cubism For Fun" The newsletter of the "Dutch Cubists Club"; in english starting with issue #14. Back issues are available. The club has over 100 active members, notable new addition Martin Gardner. Membership for 1991 is 20 Belgian francs (US$10). A photocopied set of the newsletters, issues 1-13, written in DUTCH (in the future selected back articles will be available in english) is also available for US$7. To order either of these send an 'INTERNATIONAL" POSTAL MONEY ORDER (cost $3 at post office), no personal checks, to: Lucien Matthijsse, Loenpad 12, 3402 EP IJSSELSTEIN, The Netherlands. .......................................................... WORLD GAME REVIEW Michael Keller publishes a newsletter that explores the mathematical aspects of games & puzzles. 4 issues for US$11, published erratically. Back issues are available; ISSUE #10 CHESS ($10), ISSUE ON POLYOMINOES, some magic polyhedra. MICHAEL KELLER, 3367-1, NORTH CHATAM ROAD, ELLICOTT CITY, MD 21042, USA .......................................................... 'PUZZLETOPIA" NOB YOSHIGAHARA mailed out a fall 90 issue (after 3 yrs) of his newsletter 'PUZZLETOPIA". With it came a 1991 promotional calendar from PUZZLE CITY (a subsidary of Toyo Glass) a puzzle city catalog and a catalog from PUZZLAND HIKIMI PUZZLE COLLECTION. If you want the whole package write Nob (its free outside of Japan). NOB YOSHIGAHARA, 4-10-1-408 IIDABASHI, TOKYO 102 JAPAN. .......................................................... ARM Bulletin (ACADEMY of RECREATIONAL MATHEMATICS), JAPAN This is a monthly 40-80 page newsletter of the Japanese puzzle hobbiests club. Dues Y8,000. PUZZLE KONWAKAI C/O S. TAKAGI, 1-2-4 MATSUBARA, SE TAGAYAKU, TOKYO 156 JAPAN .......................................................... From pbeck@pica.army.mil Thu Aug 1 08:11:10 1991 Return-Path: Received: from FSAC1.PICA.ARMY.MIL by life.ai.mit.edu (4.1/AI-4.10) id AA19857; Thu, 1 Aug 91 08:11:10 EDT Date: Thu, 1 Aug 91 7:55:41 EDT From: Peter Beck (BATDD) To: cube-lovers@life.ai.mit.edu, sonicdruid@sctnve.sct.peachnet.edu Cc: pbeck@pica.army.mil Subject: last cube Message-Id: <9108010755.aa28998@FSAC1.PICA.ARMY.MIL> The question was "where can I obatin the last cube made" I am going to assume that last cube means "MAGIC POLYHEDRA", of which there a three families: the cube with 3 axis of rotation, the tetrhedron group with 4 axis of rotation, the dodecahedron group with 5 axis of rotation. The last original addition I have seen was a spherical SKEWB, april 1991. Jean Claude Constantine (germany) is making shape/surface variants by hand based on all three mecahanisms, eg, take a 3x3x3 and join together (make in operable) one 2x2x2 corner - you can now change those pieces shape anyway you want - by the way this type of restriction on the moves available to solve the cube are very interesting. Also, in the spring of 1991 Christoph Bandelow has reintroduced the truncated octahedron and had the Hong Kong factory complete from previously manufactured parts some 5x5x5's. In my estimation there will NEVER be a last cube. Solutions for all magic polyhedra, except the spherical skewb have been published. First source is CFF ,cubism for fun newsletter of dutch cubists club, some where also published in world game review. Puzzles popular when ideal was in business where also covered by many popular publications which are now hard to get. CFF has a library and somebody has a bibliography of solution algorithms, including Thistletwaites ??. This is a general answer if there are specific questions please ask them!! PS I sell much of this stuff and your US mail address will get you a listing of what is available from me. PPS I also collect this stuff and would like to trade and/or buy, any quantity, ie, onesies to 100s. Not only puzzles but all things a associated with the cube - books, patents, solutions, accessories, promotional items, replacement stickers, what have you. a good overview of this kind of stuff is in jerry slocum's book puzzles old and new. From Hoffman.El_Segundo@xerox.com Thu Aug 1 14:40:41 1991 Return-Path: Received: from alpha.xerox.com by life.ai.mit.edu (4.1/AI-4.10) id AA29574; Thu, 1 Aug 91 14:40:41 EDT Received: from IRCX400MS.ESSIT.Xerox.xns by alpha.xerox.com via XNS id <11576>; Thu, 1 Aug 1991 10:52:19 PDT X-Ns-Transport-Id: 0000AA002C468CAF2C57 Date: Thu, 1 Aug 1991 08:55:42 PDT From: Hoffman.El_Segundo@xerox.com Subject: New from Rubik To: cube-lovers@life.ai.mit.edu Cc: Hoffman.El_Segundo@xerox.com Message-Id: <" 1-Aug-91 8:55:42 PDT".*.Hoffman.El_Segundo@Xerox.com> This is taken (without permission) from the 31 July 1991 `Los Angeles Times.' It reads as though it's directly from a press release. I haven't seen any of these, nor have I called the listed phone number. -- Rodney Hoffman ------------------------------------------------------ RUBIK RETURNS WITH MENTAL FITNESS GAMES Remember Rubik's Cube, invented in 1977 by Hungarian professor of architecture Erno Rubik? Prof. Rubik is back with four "mental fitness" puzzles and a redesigned version of the cube. "One of the great misunderstandings surrounding Rubik's Cube was that I was somehow trying to drive people crazy," Rubik says. "In fact, the objective of these puzzles is to help bring about a more alert and active mental condition." Even if you can't solve the puzzles, according to Rubik, "the few moments you've spent fiddling around with them has helped greatly in exercising your mind and reducing everyday tensions." Rubik's Tangle (suggested retail, $5.99), his first two-dimensional puzzle, requires players to arrange 25 tiles of rope to create four continuous lines. Rubik's XV ($6.99) is two puzzles in one. The object of the first is to arrange Roman numerals I through XV in order by sliding levers on the puzzle's side. In Part 2, players must create a square, lining up numbers so each column, row and diagonal totals 15. Rubik's Dice ($8.99) offers 82,575,360 possible combinations, with only one correct answer. The puzzle is a hollow cube with seven plates inside. White plates, which include red dots, are loose and can adhere to the inner sides of the cube. By shaking and turning the dice, players solve the puzzle when no red appears through the holes. Rubik's Triamid ($8.99) may be tougher than the original cube. Players have to construct a large pyramid, with each color on its own side, using 10 smaller pyramids. Rubik says there are "hundreds of blind alleys programmed into the design." All the puzzles are available nationally at game, toy and specialty stores. In Los Angeles, you can find them at Thrifty Drugs; in Orange County, at Toy City and PlayCo stores. Or you can order them by calling (800) 236-7123. From mindcrf!peabody.mindcraft.com!ronnie@decwrl.dec.com Thu Aug 1 21:38:30 1991 Return-Path: Received: from uucp-gw-1.pa.dec.com by life.ai.mit.edu (4.1/AI-4.10) id AA10000; Thu, 1 Aug 91 21:38:30 EDT Received: by uucp-gw-1.pa.dec.com; id AA22922; Thu, 1 Aug 91 13:28:48 -0700 Received: by mindcrf.mindcraft.com (AIX 2.1 2/4.03) id AA18759; Thu, 1 Aug 91 12:21:38 PDT Received: by peabody.mindcraft.com (AIX 1.3/4.03) id AA11139; Thu, 1 Aug 91 12:23:10 -0700 Date: Thu, 1 Aug 91 12:23:10 -0700 From: mindcrf!ronnie@peabody.mindcraft.com (Ronnie Kon) Message-Id: <9108011923.AA11139@peabody.mindcraft.com> To: @mindcrf.pa.dec.com:decwrl!ai.ai.mit.edu!Cube-Lovers Subject: Re: New from Rubik Well I have the Rubik's XV and Rubik's pyramid. The XV is a pretty good puzzle (ie., I haven't solved it yet after trying for an hour or so). The pyramid is essentially a Pyraminx. The only complication beyond the Pyraminx that the Pyramid offers is that the vertex tetrahedrons can be rotated such that a useless color shows and a necessary color is hidden. The solution becomes trivial once you have solved the Pyraminx. This seems like a good place to save your money. Ronnie From @po5.andrew.cmu.edu:dn1l+@andrew.cmu.edu Thu Aug 22 20:09:31 1991 Return-Path: <@po5.andrew.cmu.edu:dn1l+@andrew.cmu.edu> Received: from po5.andrew.cmu.edu by life.ai.mit.edu (4.1/AI-4.10) id AA12063; Thu, 22 Aug 91 20:09:31 EDT Received: by po5.andrew.cmu.edu (5.54/3.15) id for Cube-Lovers@life.ai.mit.edu; Thu, 22 Aug 91 20:08:49 EDT Received: via switchmail; Thu, 22 Aug 1991 20:08:46 -0400 (EDT) Received: from avalanche.ucc.andrew.cmu.edu via qmail ID ; Thu, 22 Aug 1991 20:08:02 -0400 (EDT) Received: from avalanche.ucc.andrew.cmu.edu via qmail ID ; Thu, 22 Aug 1991 20:07:46 -0400 (EDT) Received: from Messages.7.15.N.CUILIB.3.45.SNAP.NOT.LINKED.avalanche.ucc.andrew.cmu.edu.pmax.ul4 via MS.5.6.avalanche.ucc.andrew.cmu.edu.pmax_ul4; Thu, 22 Aug 1991 20:07:45 -0400 (EDT) Message-Id: Date: Thu, 22 Aug 1991 20:07:45 -0400 (EDT) From: "Dale I. Newfield" To: Cube-Lovers@life.ai.mit.edu Subject: New "CUBE" I found a fun new cube, sorta. It is called Square 1. it rotates in WIERD ways. it is a challenge to return to the state of being a cube, much less to solve it. My friend calls it "unfriendly." the way it is set up, it is a cube, with a center band that has one split. the two faces on either side of it that are split into the normal three on a side, but the pieces meet at the center, i.e.: the side ones are wedges, and the corners are almost-squares with the point not on the outside being the center. it is fun. I was told it will be out at christmas, but I bought it in a store called Games Unlimited in Squirrel Hill, a neighborhood of Pittsburgh. Buy one from someone, and fry your brain. Enjoy. Dale From dik@cwi.nl Thu Aug 22 20:44:41 1991 Return-Path: Received: from charon.cwi.nl by life.ai.mit.edu (4.1/AI-4.10) id AA12611; Thu, 22 Aug 91 20:44:41 EDT Received: by charon.cwi.nl with SMTP; Fri, 23 Aug 1991 02:37:55 +0200 Received: by paring.cwi.nl via EUnet; Fri, 23 Aug 91 02:37:50 +0200 Date: Fri, 23 Aug 91 02:37:50 +0200 From: dik@cwi.nl Message-Id: <9108230037.AA00481@paring.cwi.nl> To: Cube-Lovers@life.ai.mit.edu, dn1l+@andrew.cmu.edu Subject: Re: New "CUBE" > I found a fun new cube, sorta. > It is called Square 1. > it rotates in WIERD ways. Yes, it is also on sale in Europe. > > it is a challenge to return to the state of being a cube, much less to > solve it. True. To solve it when it is a cube, knowledge of the magic domino is sufficient. But it might even be that restoring it to cube form is not much more dificult than the magic domino. I do not know yet. When my cube got in disorder, by some magical moves it was restored to cube form; not by me, but b