Date: Sat, 10 Jan 87 02:56:40 EST
From: Alan Bawden <ALAN@AI.AI.MIT.EDU>
Subject:  The Archive & Administrivia
To: CUBE-LOVERS@AI.AI.MIT.EDU
Message-ID: <138605.870110.ALAN@AI.AI.MIT.EDU>


Those of you who look through the archives of old Cube-Lovers mail will
notice that I have split off a new section of the archive.  The mail now
lives on MIT-AI in the files:

AI:ALAN;CUBE MAIL0	;oldest mail in forward order
AI:ALAN;CUBE MAIL1	;next oldest mail in forward order
AI:ALAN;CUBE MAIL2	;more of same
AI:ALAN;CUBE MAIL3	;still more of same
AI:ALAN;CUBE MAIL4	;yet more
AI:ALAN;CUBE MAIL5	;more still
AI:ALAN;CUBE MAIL	;recent mail in reverse order

As always files can be FTP'd from MIT-AI without an account.  (And yes, the
spaces in those filenames are a significant part of our filename syntax.)

While I have everyone's attention let me remind you all that last year
Cube-Lovers moved from its original home on MIT-MC to MIT-AI.  Our new
addresses are Cube-Lovers@AI.AI.MIT.EDU for submissions and
Cube-Lovers-Request@AI.AI.MIT.EDU for administrivia.

If you have occasion to send mail to Cube-Lovers, you will generally find
that a fair number of copies of your message will be returned to you by
various mailers around the world for various reasons.  This is always a
problem with old, and fairly quiet mailing lists.  If you would like to be
helpful, you can collect these errors and forward them to
Cube-Lovers-Request (I will eventually flush anyone who is consistently
unreachable), but under no condition should you forward the error message
to Cube-Lovers itself.  Thank you.

				-Alan

Received: from MIT-MULTICS.ARPA (TCP 1200000006) by AI.AI.MIT.EDU 12 Jan 87 01:15:27 EST
Date:  Mon, 12 Jan 87 01:07 EST
From:  Paul Schauble <Schauble@MIT-MULTICS.ARPA>
Subject:  Sci. Am. reference needed
To:  Cube-Lovers@AI.AI.MIT.EDU
Message-ID:  <870112060752.852656@MIT-MULTICS.ARPA>

Perhaps someone on this list can help me locate an item that appeared in
the Mathamatical Games section of Scientific American.  If memory
serves, the primary subject of the article was Erno Rubik and the
Hungarian School of Architecture.  The particular item I am looking for
is a puzzle that waas given to entering students.  They were shown a
picture of a monument and were told to duplicate it using paper and
scissors.  The article contained the picture.  Can anyone give me the
issue that this appeared in?

And while we're at it, does any have a machine-readable copy of the
current rules for Eleusis?  If not, the issue they last appeared in.

          Thanks much,
          Paul <Schauble -at MIT-Multics>

Received: from ARDEC-LCSS.ARPA.ARPA (TCP 30003004013) by AI.AI.MIT.EDU 20 Jan 87 15:05:42 EST
Date: 20 Jan 87 14:47:00 EST
From: "CLSTR1::BECK" <beck@clstr1.decnet>
Subject: recreational math
To: "cube-lovers" <cube-lovers@mit-ai>
cc: gerritsen,mailer!<fuzzy@ardec>
Reply-To: "CLSTR1::BECK" <beck@clstr1.decnet>
BOOKS:  Singmaster is editing a series of books for Oxford University Press on
Recrreational Mathematics and is requesting input on the following:
1) " I (Singmaster) have embarked on a project to find the sources of classical
problems in recreational mathematics.  .....
    The initial object of this project was to produce a book of sources,
translated into english with annotation, for .... However, it now appears that
the first stage must be the prpearation of an annotated bibliography of the
material.  ...  draft of paper which outlines the project and some of the
material is available.  I would be delighted to hear from anyone interested in
this project, particularly anyone able to provide info."
2)  "I am also compiling a list of mathematical monuments and have a draft
article on this."

ADDRESS;  DAVID SINGMASTER, POLYTECHNIC OF THE SOUTH BANK, LONDON, SE1 OAA, UK

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
BOOKS IN SERIES SO FAR:
1)  MATHEMATICAL BYWAYS IN AYLING, BEELING, AND CEILING by Hugh ApSimon,  128
pages; 30 illus,  853201-6, $10
2) THE INS AND OUTS OF PEG SOLITAIRE by John Beasley, 300 pages; 571 illus,
853203-2,  $17
3) RUBIK'S CUBIC COMPENDIUM by Erno Rubik et al, 200 pages, 183 illus, 853202-4,
$15
CONTENTS:  Intro: the fascination of rubik's cube - david singmaster, 1. in play
-rubik, 2 the art of cubing - varga, 3. restoration methods and table of
processes - keri, 4. mathematics - keri & varga, 5. the universe of the cube -
marx, 6. my fingers remember - vekerdy, 7. afterword - singmaster, bibliography
& index.
4)  SLIDING PIECE PUZZLES by Edward Horden - in preparation.
AVAILABLE FROM:  Science and Medical Marketing Manager, OXFORD UNIVERSITY PRESS,
200 Madison ave, NY, NY 10016,  212/679-7300
ADD $1.50 for shipping
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

from  <beck@ardec-lcss>
.........................................
------

Received: from ARDEC-LCSS.ARPA.ARPA (TCP 30003004013) by AI.AI.MIT.EDU 22 Jan 87 08:39:00 EST
Date: 22 Jan 87 08:25:00 EST
From: "CLSTR1::BECK" <beck@clstr1.decnet>
Subject: magic variants
To: "cube-lovers" <cube-lovers@mit-ai>
Reply-To: "CLSTR1::BECK" <beck@clstr1.decnet>
1.  My crack puzzle team has added four squares to "MAGIC".  This puzzle has
much more variability in making planar patterns (I count doubled up squares) ,
while retaining the same flavor as the original puzzle.  Some examples:

     XXXXXX            XXXX              XXXX                     XXXX
     XXXXXX            XXXX              X    X                     XXXX
                            XXXX             X    X                     XX
                                                XXXX                     XX

Has anybody else changed the number of squares?  

2.  Has anybody speculated on Rubik's next puzzle based on this hinge mechanism?
 My puzzle team thinks a equilateral triangles instead of squares has potential.
 Any comments?

<beck@ardec-lcss>
..............................
------

Received: from PROPHET.BBN.COM (TCP 20026200117) by AI.AI.MIT.EDU 23 Jan 87 14:11:26 EST
Date:     Fri, 23 Jan 87 14:06:33 EST
From:     Bernie Cosell <cosell@prophet.bbn.com>
To:       cube-lovers@ai.ai.mit.edu
cc:       jr@prophet.bbn.com, beeler@prophet.bbn.com, alatto@prophet.bbn.com
Subject:  Postscript on the Oxford RecMath series

I just talked to Oxford and the Rubik's book is expected any moment now,
but is apparently not yet available (in the states, at least).  The
fourth in the series (sliding piece puzzles) is expected to be available
in April or May.

  /Bernie\

ps, the number for phone orders is 201-796-8000 /b

Bernie Cosell                       Internet:  cosell@bbn.com
Bolt, Beranek & Newman, Inc         USENET:    bbnccv!bpc
Cambridge, MA   02238               Telco:     (617) 497-3503

Received: from ARDEC-LCSS.ARPA.ARPA (TCP 30003004013) by AI.AI.MIT.EDU 23 Jan 87 16:06:52 EST
Date: 23 Jan 87 15:52:00 EST
From: "CLSTR1::BECK" <beck@clstr1.decnet>
Subject: MEFFERT CORRECTION
To: "cube-lovers" <cube-lovers@mit-ai>
Reply-To: "CLSTR1::BECK" <beck@clstr1.decnet>


RE:  MEFFERT  (this is a duplicate, I forgot to give his address)

I received amil from meffert yesterday, 1/22/87.  He says "he will be releasing
later this year the 'I.Q. DIE" ( which is the Skewb with Die markings on the
corner pieces), and a GAME called 'KING/ACE (which uses the Pyraminx tetrahedron
dercorated in the 4 card suits and truncated by removing the four apexes.  The
game is similar to black jack.  They are  available for US$25 each including
registered airmail postage.  He also has standard Skewbs available for US$16.

The mailing included a 2-sided glossy color flyer with pictures of various
puzzles.  The ones new to me are:  The Crystal Ball -  it looks like a
Babylonian Tower on a sphere with the capablity to move groups of balls at one
time;  Space Grenade -   a cylindrical version of the crystal ball.

PRICEWELL (FAR EAST) LIMITED

*business address* 
EXCELLENTE COMMERCIAL BLDG (15TH FLOOR)
456 JAFFE ROAD
HONG KONG

*postal address*
POB 31008 CAUSEWAY BAY,  HONG KONG

<beck@ardec-lcss>
....................................
------

Received: from ARDEC-LCSS.ARPA.ARPA (TCP 30003004013) by AI.AI.MIT.EDU 23 Jan 87 16:51:04 EST
Date: 23 Jan 87 15:42:00 EST
From: "CLSTR1::BECK" <beck@clstr1.decnet>
Subject: meffert
To: "cube-lovers" <cube-lovers@mit-ai>
Reply-To: "CLSTR1::BECK" <beck@clstr1.decnet>



RE:  MEFFERT

I received amil from meffert yesterday, 1/22/87.  He says "he will be releasing
later this year the 'I.Q. DIE" ( which is the Skewb with Die markings on the
corner pieces), and a GAME called 'KING/ACE (which uses the Pyraminx tetrahedron
dercorated in the 4 card suits and truncated by removing the four apexes.  The
game is similar to black jack.  They are  available for US$25 each including
registered airmail postage.  He also has standard Skewbs available for US$16.

The mailing included a 2-sided glossy color flyer with pictures of various
puzzles.  The ones new to me are:  The Crystal Ball -  it looks like a
Babylonian Tower on a sphere with the capablity to move groups of balls at one
time;  Space Grenade -   a cylindrical version of the crystal ball.

<beck@ardec-lcss>
....................................
------

Received: from ARDEC-LCSS.ARPA.ARPA (TCP 30003004013) by AI.AI.MIT.EDU 18 Feb 87 08:14:06 EST
Date: 18 Feb 87 07:51:00 EST
From: "CLSTR1::BECK" <beck@clstr1.decnet>
Subject: new magic version
To: "cube-lovers" <cube-lovers@mit-ai>
Reply-To: "CLSTR1::BECK" <beck@clstr1.decnet>



RE:  New versions of MAGIC

1.  The 2/14/87 edition of the "Toy & Hobby World's Show (ie, the NY Toy  Show)
Daily" announced the planned 1987 additions to the MAGIC line.  It said "Rubik's
MAgic puzzle, which debuted in October, 1986, is updated with a Masters Edition
puzzle, Unlink The Rings, featuring 12 panels and multi-color, multi-graphic
designs on a silvery Mylar-foil background.

Rubik's Magic Strategy Game features the colors of the original puzzle in a
tic-tac-toe game; the difference is that the pieces are colored black on one
side and silver on the other, and players can flip opponents' pieces before
making a move."

2.  As previously noted on this board it is fairly simple to make your own 12
piece MAGIC.   I am using MAcDraw to experiment with graphic patterns.  I have
not decided on which graphic(s) I like best yet.

3.  As an aside there are "CLONES"  of MAGIC around and Matchbox is prosecuting.
 I am not aware of exactly what is protected so using a different number of
squares or different graphics might be legal.

<beck@ardec-lcss>

............
------

Received: from ARDEC-LCSS.ARPA.ARPA (TCP 30003004013) by AI.AI.MIT.EDU 19 Feb 87 08:36:06 EST
Date: 19 Feb 87 08:18:00 EST
From: "CLSTR1::BECK" <beck@clstr1.decnet>
Subject: magic construction
To: "cube-lovers" <cube-lovers@mit-ai>
Reply-To: "CLSTR1::BECK" <beck@clstr1.decnet>



RE: CONSTRUCTION

Since I have suggested that people might want to take their MAGICs apart I have
prepared the following directions.  I would appreciate comments as to their
clarity and completeness.  

...................................
For those of you who would like to take MAGIC apart and then put it back
together here are some hints.  First get out your tools, a heavy duty paper clip
or a nut pick will do (black electrical tape is helpful for keeping the strings
in place when putting it back together) and then pull the string over the corner
of a square (strings do break, the weak point is the crimp so minimize the
pulling and stretching you do by the crimp also when you reassemble put the
crimp in the middle of a long channel).  Keep doing this until the puzzle is
completely disassembled. 

If you failed to take notes you may have missed the following.  The loops of
string (they are actually nylon fishline and they are redundant, ie, each path
is taken by two strings, with 16 strings in all) are threaded through the
channels, one set of strings takes the long path on the front face and the other
set of strings takes the short path on the front face (the opposite is true on
the back face OR adjacent square) with both sets of strings going in the same
direction on the same face.    Thus the strings on the front faces are
perpendicular to those on the back face of the same square.   NOTE:  The strings
are not really redundant.  They are placed to maximize lateral stability (twist
of the squares).  This is done by having the strings (there are two) of a given
channel routing form the same sandwiching order where they cross over to the
next square.  The string that uses the long channel and the string that uses the
short channel cross at separarte points.  Each string criss crosses itself at
this point (making 4 string segments at the cross over point) with one part of
itself in the NE channel and its other part in the NW channel.  The stability is
gained by having the NE going string sandwiched between the NW going string (or
vice versa) for both crossover points, ie , sets of strings.   Both patterns
shown below are used on the same set of three squares (THIS UNIT IS CALLED A
TRIPLET.).  

               string #1 in                    string #2 in
        SHORT channel ON TOP       LONG channel ON TOP 
             for squares 1&3              for squares 1&3
               ---- ---- ----             ---- ----  ----
              |/ \  |   / \|/ \   |            |   / \|/ \   |   / \|   TRIPLET
HAS BOTH
              |\  \ | /   /|\   \ |   AND   | /   /|\  \  | /   /|   STRING
PATTERNS
              | \  \|/   / |  \  \|            |/   / |  \  \|/   / |
              |  \ /|\ /   |   \ /|            |\ /   |   \ /|\ /   |
               ---- ---- ----             ---- ----  ----

After having made two triplets there will be two squares free.  They are used to
join the triplets.  Place one of this extra squares between the two triplets,
ie, where the "AND" is in the diagram above and thread the strings through the
channels as if this square was the middle square of a triplet (REMEMBER THAT the
STRINGS GO ONLY ONE WAY ON each face OF A SQUARE).  THEREFORE, THE ENDS OF THE
PREVIOUSLY MADE TRIPLETS WILL BE THE ENDS OF THIS NEW TRIPLET ALSO.  THIS WILL
CAUSE THESE ENDS TO HAVE TWICE AS MANY STRINGS AS THE MIDDLE SQUARES OF THE
TRIPLETS AND IN FACT IF YOU LOOK AT MAGIC YOU WILL SEE THAT THE NUMBER OF
STRINGS IN THE CHANNELS ALTERNATES FROM SINGLE DENSITY TO DOUBLE DENSITY, ie,
either 2 or 4.



CUSTOMIZATION OF MAGIC

In the disassembly process an easy thing to do is to break the circularity of
the puzzle by removing one square, leaving a chain of seven squares.  This can
be done by lifting the strings off a single density square.  The square will
come out but its strings will stil be entangled with the puzzle.  You will now
have to temporarily lift strings off the adjacent squares to disentangle them. 
This can be done easily.  You now have a chain of seven squares.  Each hinge can
be manipulated without the constraint of being connected as a loop. A basic
hinge between two squares has the following motions:
NOTE:  The flipping of the pieces changes the direction of the squares as shown
by the arrows.

       POSITION  1                  folded  A            folded  B
________  _______          _________         _________
sq 1 TOP      sq 2 top           sq 1 on bot          sq 2 on bot
  >>>>>>          >>>>>>             sq 2 on top          sq 1 on top
________  _______          _________         _________


      POSITION  2       >>>>>       A unfolded          B unfolded
                                              ________          _________
                                               SQ 1 TOP             SQ 2 TOP
                                                <<<<<<<<               <<<<<<<
                                               ________          _________
                                               ________          _________
                                                SQ 2 TOP             SQ 1 TOP
                                                  >>>>>>>                >>>>>>>
                                               ________          _________

The robustness of this hinge permits the making of all possible planar patterns
that has each square butting up to the edge of another square.


<beck@ardec-lcss>
------

Received: from ARDEC-LCSS.ARPA.ARPA (TCP 30003004013) by AI.AI.MIT.EDU 20 Feb 87 08:35:41 EST
Date: 20 Feb 87 08:08:00 EST
From: "CLSTR1::BECK" <beck@clstr1.decnet>
Subject: rubik's books
To: "cube-lovers" <cube-lovers@mit-ai>
Reply-To: "CLSTR1::BECK" <beck@clstr1.decnet>


I have been reviewing issues of the "CUBIC CIRCULAR" ,a set of which I recently
obatined form Singmaster, and would like references to  information on the
following:

1-   a book Rubik edited called  "A BUVOS KOCKA"  which was to be also done in
english by PENGUIN.

2 -  Rubik's newsletter "RUBIK'S - LOGIC AND FANTASY DIMENSIONS"

3-  "TEN BILLION BARREL" puzzle invented by Gumpei Yokoi.  Possibly a reference
to a published?? solution by Trevor Hutton.  This is supposed to be harder than
the cube and is available for about $6 at Child World in northen NJ.

4 -  "TRILLION" a flat version of 3.

<beck@ardec-lcss>
./..................
------

Received: from ARDEC-AC3.ARPA (TCP 30003004017) by AI.AI.MIT.EDU 10 Apr 87 08:28:52 EDT
Date:     Fri, 10 Apr 87 8:15:46 EST
From:     Peter Beck (LCWSL) <pbeck@ARDEC.ARPA>
To:       cube-lovers@AI.AI.MIT.EDU
Subject:  dc puzzle shops
Message-ID:  <8704100815.aa28501@ARDEC-AC3.ARDEC.ARPA>

 
I am taking a trip to Wash DC the week of April 13 and expect to have some extra
time while there to pursue puzzling.  If anybody out there knows of a good
puzzle store or possible an exhibit I would greatly appreciate the reference.
 
                    THNX
                 Pete Beck   <beck@ardec-lcss>
 
PS In FEb an article was published in TELECRAN , author Henri Leyder, titled
"610 Denkspiele im Regal"  about Marcel Gillen's puzzle collection.  The article
had several black an d white pictures of his puzzle collection.  The article is
in german, which I do not read, so I cannot paraphrase it.
 
..............

Received: from note.nsf.gov (TCP 1202200024) by AI.AI.MIT.EDU 27 Apr 87 16:08:22 EDT
To: cube-lovers@AI.AI.MIT.EDU
Subject: Rubik's Cube
Date: Mon, 27 Apr 87 16:07:17 -0400
From:  "Aaron R. Coles" <acoles@nsf.arpa>
Message-ID:  <8704271607.aa27081@note.note.nsf.gov>

Maybe this is not the approriate place to ask this question, but does anyone
out there know where I can purchase a Rubik's Cube Revenge from?  I would
appreciate any help.

Thanks


Received: from nrl-aic.ARPA (TCP 3200200010) by AI.AI.MIT.EDU 27 Apr 87 16:53:27 EDT
Return-Path: <hoey@nrl-aic.ARPA>
Received: Mon, 27 Apr 87 16:50:36 edt by nrl-aic.ARPA id AA20059
Date: 27 Apr 1987 16:47:22 EDT (Mon)
From: Dan Hoey <hoey@nrl-aic.ARPA>
Subject: Rubik's Cube
To: "Aaron R. Coles" <acoles@nsf.arpa>
Cc: Cube-Lovers@ai.ai.mit.edu
Message-Id: <546554843/hoey@nrl-aic>

If you happen by the Boston area, you can get Rubik's Revenge at Games
People Play in Cambridge.

A harder problem is to get an ordinary magic cube.  I haven't seen one
for sale in years.

Dan

Received: from BFLY-VAX.BBN.COM (TCP 20026200235) by AI.AI.MIT.EDU 27 Apr 87 17:56:43 EDT
To: Dan Hoey <hoey@nrl-aic.ARPA>
cc: "Aaron R. Coles" <acoles@note.nsf.gov>, Cube-Lovers@ai.ai.mit.edu, 
    dm@bfly-vax.bbn.com
Subject: Re: Rubik's Cube
In-reply-to: Your message of 27 Apr 1987 16:47:22 EDT (Mon).
	     <546554843/hoey@nrl-aic>
Date: 27 Apr 87 17:55:18 EDT (Mon)
From: dm@bfly-vax.bbn.com


> A harder problem is to get an ordinary magic cube.  I haven't seen one
> for sale in years.

Yard sales.  Even if you don't find one for sale at the sale, you can
probably ask the person running the sale if they have one they
wouldn't mind selling.

Received: from ARDEC-LCSS.ARPA.ARPA (TCP 30003004013) by AI.AI.MIT.EDU 28 Apr 87 08:10:41 EDT
Date: 28 Apr 87 08:06:00 EST
From: "CLSTR1::BECK" <beck@clstr1.decnet>
Subject: 
To: "cube-lovers" <cube-lovers@mit-ai>
Reply-To: "CLSTR1::BECK" <beck@clstr1.decnet>
From:	CLSTR1::SYSTEM       27-APR-1987 15:30
To:	CLSTR1::BECK
Subj:	Undeliverable mail

 ----Transcript of session follows----
"mit.ai" is an unrecognized hostname/address

 ----Unsent message follows----
Date: 27 Apr 87 15:18:00 EST
From: "CLSTR1::BECK" <beck@clstr1.decnet>
Subject: rubiks square
To: "cube-lovers" <cube-lovers@mit.ai>
Reply-To: "CLSTR1::BECK" <beck@clstr1.decnet>


HI CUBE-LOVERS, 

I understand that the "Puzzle Exhibition" tour has been changed and that it
won't be coming to MIT until the fall.  Does anybody have more information.  

One of my co-workers advised me that she saw a puzzle called "Rubik's SQUARE",
not magic, in the San Jose airport gift shop.  Does anybody know what this is
and where it can be obtained or even a picture seen.

I have been working on alternate designs for the 8 square magic with some
success.  If anybody out there is also doing the same I would like to talk, swap
designs, etc.   If anybody has suggestions for alternate designs I would
appreciate receiving them.

The Future is Puzzling and Cubing is Forever,

Pete beck                  <BECK@ARDEC-LCSS>
..................................

------
------

Received: from ARDEC-LCSS.ARPA.ARPA (TCP 30003004013) by AI.AI.MIT.EDU 28 Apr 87 08:30:40 EDT
Date: 28 Apr 87 08:28:00 EST
From: "CLSTR1::BECK" <beck@clstr1.decnet>
Subject: availability of cubes
To: "cube-lovers" <cube-lovers@mit-ai>
Reply-To: "CLSTR1::BECK" <beck@clstr1.decnet>


RE:  SEARCH FOR CUBES

1.  The large chains are slowly clearing out the surplus stocks of cubes.  The
best for a revenge is "THRIFT DRUG" probably around $5, also try KAYBEE.  If
this fails send me your address and I will send you one a competitive price.

2.  As I have previously posted I am also trying to buy up surplus cubes and
make them available to cube collectors.  If anybody would like a list send me
your name and address and I will mail it to you.  If you are looking for a
particular cube ask for it I will tell you where to get it.  I correspond with
Singmaster, Gillen, Helm, Bandelow, Hess, Cecil Smith, Wally Webster about
cubes.

3.  If anybody knows of a good source of cubes a wholesale prices I would
appreciate the reference.

................................................................
>>>>>>  The Future is Puzzling and Cubing is Forever,  <<<<<<<<

Pete beck                  <BECK@ARDEC-LCSS>
..................................

------

Received: from ARDEC-LCSS.ARPA.ARPA (TCP 30003004013) by AI.AI.MIT.EDU 28 Apr 87 14:50:45 EDT
Date: 28 Apr 87 14:32:00 EST
From: "CLSTR1::BECK" <beck@clstr1.decnet>
Subject: RUBIK'S "SQUARE"
To: "cube-lovers" <cube-lovers@mit-ai>
Reply-To: "CLSTR1::BECK" <beck@clstr1.decnet>


THIS MAYBE A DUPLICATE - I AM HAVING TROUBLE WITH MY MAILER

HI CUBE-LOVERS, 

I understand that the "Puzzle Exhibition" tour has been changed and that it
won't be coming to MIT until the fall.  Does anybody have more information.  

One of my co-workers advised me that she saw a puzzle called "Rubik's SQUARE",
not magic, in the San Jose airport gift shop.  Does anybody know what this is
and where it can be obtained or even a picture seen.

I have been working on alternate designs for the 8 square magic with some
success.  If anybody out there is also doing the same I would like to talk, swap
designs, etc.   If anybody has suggestions for alternate designs I would
appreciate receiving them.

The Future is Puzzling and Cubing is Forever,

Pete beck                  <BECK@ARDEC-LCSS>
..................................

------

Date: Tue,  5 May 87 17:19:21 EDT
From: Alan Bawden <ALAN@AI.AI.MIT.EDU>
Subject:  TOC Seminar -- Akos Seress -- Thursday May 28, 1987
To: CUBE-LOVERS@AI.AI.MIT.EDU
Message-ID: <195855.870505.ALAN@AI.AI.MIT.EDU>

Mathematically inclined Cube Hackers in the Boston area might find the
following seminar interesting.  All I know about this is what I read here
in the abstract.  (I'll bet its been a while since anyone on this list did
any serious thinking about the Cube as a permutation group...)


			DATE: Thursday, May 28, 1987
			 TIME: Refreshments: 3:45PM
			      LECTURE:  4:00PM
			      PLACE: NE43-512A

			  PERMUTATION GROUPS IN NC

				 AKOS SERESS
			Mathematical Institute of the
			Hungarian Academy of Sciences

Given a permutation group G on an n-element set A by a list of generators, we
present NC-algorithms (parallel algorithms using (log n)^c time and
n^c processors) for basic permutation group manipulation (membership
testing, order).  These problems have been suggested by Cook and McKenzie to
be LOGSPACE-complete for P and therefore not in NC unless NC=P.
    We shall outline previous work by Luks on the subject and focus on the
key problems left open by Luks' 1986 FOCS paper.  In particular, we shall
discuss in detail, how to construct in NC any permutation from a given set of
generators of the symmetric group.
    The presentation will be elementary, although the analysis of the
algorithms depends in several ways on consequences of the classification of
finite simple groups.
    Our methods have sequential consequences as well.  We obtain algorithms
for basic permutation group management with O(n^4(log n)^c) running
time, improving one order of magnitude from the best prevously known results
(Knuth, Babai, and Jerrum).
    This is joint work with Laszlo Babai and Eugene M. Luks.

Host:  Professor David Shmoys

Received: from EDDIE.MIT.EDU by AI.AI.MIT.EDU via Chaosnet; 5 MAY 87  21:09:07 EDT
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Date: Tue, 5 May 87 17:56:58 PDT
From: long@oliveb.atc.olivetti.com (Tom Long)
Message-Id: <8705060056.AA29561@oliveb.ATC.OLIVETTI.COM>
To: ALAN@ai.ai.mit.edu, CUBE-LOVERS@ai.ai.mit.edu
Subject: Re:  TOC Seminar -- Akos Seress -- Thursday May 28, 1987


       Akos,
Ez egy baratomnaatk a gepjen dolgozom.  Metg vagyokgg vagyok lepodve hogy mas
magyar is itten ir.  Te honan irs? En Californiaban vagyaok.
iIde irhatc viszasza.  A rubik kockarol beszeltel? aA z iskolaban omost
tanulok a permutation-okrol. Nagyon erdekesnek hallatcik.
				irIrjal Vissza,
					Jeno

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Date: Tue, 5 May 87 22:23:43 edt
From: Bernard S. Greenberg <bsg@scrc-pegasus>
To: cube-lovers%ai.ai.mit.edu@stony
Subject: A magyar kocka

    Date: Tue, 5 May 87 17:56:58 PDT
    From: long@oliveb.atc.olivetti.com (Tom Long)
    Message-Id: <8705060056.AA29561@oliveb.ATC.OLIVETTI.COM>
    To: ALAN@ai.ai.mit.edu, CUBE-LOVERS@ai.ai.mit.edu
    Subject: Re:  TOC Seminar -- Akos Seress -- Thursday May 28, 1987


       	   Akos,
    Ez egy baratomnaatk a gepjen dolgozom.  Metg vagyokgg vagyok lepodve hogy mas
    magyar is itten ir.  Te honan irs? En Californiaban vagyaok.
    iIde irhatc viszasza.  A rubik kockarol beszeltel? aA z iskolaban omost
    tanulok a permutation-okrol. Nagyon erdekesnek hallatcik.
				    irIrjal Vissza,
					    Jeno


1. I refuse to deal with something so full of overstrikes and corrections.
   How do you expect anyone to make sense out of it?

2. "That way, mate.  Two blocks down and to the left."


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Date: Wed, 6 May 87 14:54:29 PDT
From: long@oliveb.atc.olivetti.com (Tom Long)
Message-Id: <8705062154.AA15491@oliveb.ATC.OLIVETTI.COM>
To: ACW@waikato.s4cc.symbolics.com, ALAN@ai.ai.mit.edu,
        CUBE-LOVERS@ai.ai.mit.edu, long@oliveb.atc.olivetti.com
Subject: Re:  TOC Seminar -- Akos Seress -- Thursday May 28, 1987

Your progtranslation of dthe the message is comendable.  Yoyu did fair;luy well.
Did Adoskos write from your machine, or is there a link to Hungary?
The later I doubt.  I am a nat6itive speaker th,thougyh bortn here.

tThe reason for the simple language is that I did not know
the vocabularythere wasw no need to 
use anything more complex.  IWhile I wasw not looking for a pen-pal,
I was intderested that there was an other Hungarian on the system,
having never seen it befor.





Thanks for your repy.


Date: Thu, 14 May 87 18:24:57 EDT
From: Alan Bawden <ALAN@AI.AI.MIT.EDU>
Subject:  TOC Seminar--Adi Shamir--Friday, May 22, 2:00PM
To: CUBE-LOVERS@AI.AI.MIT.EDU
Message-ID: <200230.870514.ALAN@AI.AI.MIT.EDU>

This one is even better than the last seminar announcement I forwarded to
this list!  (And -this- time, REMEMBER:  replying to this message will
-not- send mail that Shamir will get; it will only send everyone on
Cube-Lovers a piece of junk mail.)


		       DATE: Friday, May 22, 1987
                       TIME: Refreshments: 1:45PM
                             Lecture:      2:00PM
		      PLACE: NE43-512A

			    HOW TO SOLVE THE CUBE

				 Adi Shamir
				Applied Math
		       The Weizmann Institute, Israel

   Given k generators for a permutation group G, it is easy to verify that a
permutation belongs to G but NP-complete to find a short representation of
the permutation as a product of the generators.  In this talk we describe a
new algorithm for computing the shortest representation which significantly
improves the time/space complexities of previous algorithms.  The new
algorithm is particularly interesting in the context of Rubik's cube since it
makes it possible to solve previously intractable problems such as finding
the shortest sequence of moves which fixes a given state or the optimal
subroutine for permuting certain subcubes, in just 2^40 time and 2^20 space,
compared to 2^80 time in previous algorithms.

Host:  Prof. Ron Rivest

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Date: Wed, 20 May 87 10:05:20 CDT
From: jknox@ngp.utexas.edu (John W. Knox)
Posted-Date: Wed, 20 May 87 10:05:20 CDT
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Subject: Re:  TOC Seminar--Adi Shamir--Friday, May 22, 2:00PM



Date: Wed, 27 May 87 16:34:04 EDT
From: Alan Bawden <ALAN@AI.AI.MIT.EDU>
Subject:  Shamir's talk really was about how to solve the cube!
To: CUBE-LOVERS@AI.AI.MIT.EDU
Message-ID: <205924.870527.ALAN@AI.AI.MIT.EDU>

Here is a rough sketch of Shamir's algorithm, as he presented it at the
talk last Friday.  The fact that I have typed this in does not
-necessarily- indicate a willingness on my part to supply any further
details.  Nor do I guarantee that my description will enable you to
correctly reconstruct the algorithm, although I tried to make it
comprehensible.

I think Shamir gave credits for a couple of graduate students of his for
some of this, but I didn't make a note of their names.  It is always nice
to give people proper credit...

You are given a scrambling of the cube, and you want to know if the cube
can be restored in 4*N quarter twists.  (Shamir is a half-twister, but I in
this message I will rephrase everything in quarter-twist terms.  It makes
little difference, the algorithm applies equally well to any set of
generators.)

Represent a permutation as a vector that simply lists the values of the
permutation.  That is, if the permutation sends 0 to 7, 1 to 2, 2 to 4, 3
to 1, etc., then the vector [7, 2, 4, 1, ...] represents it.

We will be ordering permutations in "dictionary order".  That is, a
permutation sigma is less than a permutation tau just in case there exists
an i such that

          sigma(i) < tau(i) and for all j < i, sigma(j) = tau(j).


We start by generating a list of all permutations generated by N quarter
twists.  The algorithm requires space to store several datastructures
proportional to the size of this list.  (If N=5, this list has 93840
elements.  Its size is about 10^N for the cube group in quarter twists.
For an arbitrary group and generators it will be exponential in N.)

Now what we would like to do is generate -and- -sort- the list of all
permutations generated by 2*N quarter twists.  We could do this by simply
multiplying all possible pairs of elements from our list, and then sorting
again, but this generates an absurdly large list, that it takes an absurd
amount of effort to sort.

The trick is to generate this list of products both incrementally and
already sorted!  This gives us the ability to ask for the -next- element of
the list, which is exactly what we need:  Given two such permutation-list
generators we can easily scan through both lists to see if any element
occurs in both lists (using an algorithm that the reader can easily
reconstruct).  Thus we can build one generator for the list of all
positions 2*N twists away from solved, and another for positions 2*N twists
away from the given one, and if we find an element on both lists, then we
have a 4*N twist solution.

OK, so how do we construct this magic generator?

First we take the list of length N permutations and make it into a tree.
There will be one leaf for each permutation in the list.  All permutations
that share a common prefix will share a common internal node in the tree.
For example, given the permutations:

                              [0, 1, 2, 3, 4]
                              [0, 1, 3, 2, 4]
                              [1, 0, 3, 4, 2]
                              [1, 3, 0, 4, 2]
                              [2, 3, 1, 4, 0]

we get the tree:

                                      [0, 1, 2, 3, 4]
                                     /
                                    /2
                         [0]--[0, 1]
                        /   1       \3
                       /             \
                      /               [0, 1, 3, 2, 4]
                     /
                    /0        [1, 0, 3, 4, 2]
                   /         /
                  /         /0
                []-------[1]
                  \  1      \3
                   \         \
                    \2        [1, 3, 0, 4, 2]
                     \
                      \
                       \
                        \
                         [2, 3, 1, 4, 0]

Now consider one element of the original list, say 

                         sigma = [2, 3, 1, 4, 0].

We want to find the permutation tau, such that sigma * tau is smallest in
dictionary order.  So, what is the first entry of sigma * tau?  That is,
what is sigma(tau(0))?  Well, looking at sigma we can see that -if-
tau(0) = 4, then sigma(tau(0)) = 0.  Unfortunately their are no
permutations in our list that start with 4, but we can get
sigma(tau(0)) = 1 if tau(0) = 2.  Now there is only one such permutation on
our list, so that must be it:

              tau = [2, 3, 1, 4, 0] (= sigma as it happens).

What about the tau such that sigma * tau is -second- smallest?  We have
exhausted permutations with tau(0) = 2, what should we consider next?  Well,
if tau(0) = 0, then sigma(tau(0)) = 2, so we should next consider
permutations that start with 0.  After that, we should do those that start
with 1, followed by those that start with 3.

The exact same argument applies to tau(1).  That is, to minimize the
product, first consider permutations such that tau(1) = 4, followed by
tau(1) = 2, then tau(1) = 0, then tau(1) = 1, and finally tau(1) = 3.

Thus you can see that to generate the sigma * tau products in order, we can
just take tau to be successive leaf nodes in the above tree, where we order
the inferiors of any internal node in the order 4, 2, 0, 1, 3.  It is easy
to generate this ordering given sigma.

Now for -each- permutation sigma in our original list we will be taking a
different walk through the tree using a different ordering of inferiors.
So we maintain a queue of pairs <sigma, tau>, sorted according to
sigma * tau.  When called upon to generate the next element of the
list-of-products, we take the head of the queue (smallest) and return it.
Then we advance to the next tau for the given sigma, and insert the new
pair <sigma, tau'> back into the queue.

Modifying this construction to generate permutations of the scrambled
position, rather than solved is easily accomplished by first composing the
inverse of the scrambling permutation with each element of the list of
length N permutations.  Now we combine each element of this list with each
element of the same tree as above.

Analysis of space and time requirements left to the reader.

Received: from ARDEC-LCSS.ARPA.ARPA (TCP 30003004013) by AI.AI.MIT.EDU  2 Jun 87 09:48:40 EDT
Date: 2 Jun 87 09:45:00 EST
From: "CLSTR1::BECK" <beck@clstr1.decnet>
Subject: PUZZLE TOUR EXHIBITION SCHEDULE UPDATE
To: "cube-lovers" <cube-lovers@mit-ai>
cc: beck
Reply-To: "CLSTR1::BECK" <beck@clstr1.decnet>


>>>  UPDATE <<<<  to  " PUZZLES OLD AND NEW"  exhibition tour SCHEDULE
    source  Jerry Slocum,  5/87

 LOCATION:
    Craft and Folk Art Museum, LA   Nov. 26, '86 - Feb. 22, 1987
         Hudson River Museum             July 26 - Sept. 27, 1987
             Yonkers, NY    914/963-4550
         MIT Museum                            OCT 22 - JAN 3 1988
             Cambridge, MA   617/253-4444
         Ontario Science Center          Jan. 25 - March 13, 1988
             Toronto, Canada  416/429-4100
         JAPAN TOUR                           APR 28 - SEPT 1988
            (TOKYO, OSAKA, KYOTO, NAGOTA)

RE:   Rodney Hoffman's review posted in the spring.

<BECK@ARDEC-LCSS>
..........................................................


------

Received: from ARDEC-LCSS.ARPA.ARPA (TCP 30003004013) by AI.AI.MIT.EDU  3 Jun 87 12:01:50 EDT
Date: 3 Jun 87 11:45:00 EST
From: "CLSTR1::BECK" <beck@clstr1.decnet>
Subject: request for puzzles sources
To: "cube-lovers" <cube-lovers@mit-ai>
cc: beck
Reply-To: "CLSTR1::BECK" <beck@clstr1.decnet>

I am interested in obtaining the following puzzles ( references are from
"Sliding Pieces Puzzles" by Ed Horden,  Oxford Univ Press, 1986):
  1 -  Change the Seasons, plate IX
  2 -  Inversion, plate IX
  3 -  Great Gears, plate X

I would like to trade for them, if possible.   A source where they can be
purchased would also be appreciated.   Thanks for any and all help.

The Future is Puzzling but Cubing is Forever,

Pete beck                  <BECK@ARDEC-LCSS>
..................................
------

Received: from ARDEC-LCSS.ARPA.ARPA (TCP 30003004013) by AI.AI.MIT.EDU  4 Jun 87 08:25:49 EDT
Date: 4 Jun 87 08:17:00 EST
From: "CLSTR1::BECK" <beck@clstr1.decnet>
Subject: MAZES
To: "cube-lovers" <cube-lovers@mit-ai>
cc: beck
Reply-To: "CLSTR1::BECK" <beck@clstr1.decnet>


I would like to hear from anybody who has visited a "MAZE" amusement center or
read an article, hopefully with pictures on same.   

I understand that there are 20 such centers in Japan and that the "MAZE PRODUCTS
COMPANY" (a NOB enterprise) is going to bring it to the USA.  

Nob's centers have mazes designed by a New Zealander, Stuart Landsborough and
puzzle shops that sell Nob's puzzles.  There was also an article in the dec 86
Sci Amer, pg140 on Labryinths which referenced a book called "Celebration of
Mazes" available from Minotaur Designs, 247 Montgomery st, Jersey City, NJ 07302
for $9.  Has anybody read this?  Are these phenomina the same?  Are the MAZES
coming !!!

Pete beck                  <BECK@ARDEC-LCSS>
..................................

------

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Date: 4 Jun 87 16:35:54 GMT
From: fluke!ssc-vax!cxsea!blm@beaver.cs.washington.edu  (Brian Matthews)
Organization: Computer X Inc.
Subject: Look for two books by Dmitri Borgmann
Message-Id: <2100@cxsea.UUCP>
Sender: cube-lovers-request@ai.ai.mit.edu
To: cube-lovers@ai.ai.mit.edu

I'm looking for information about the books _Beyond Language_ and
_Language on Vacation_ by Dmitri Borgmann.  I can't find them in any
of the various Books in Print, so they're either no longer in print,
or from a small publisher.  In any event, I would appreciate it if
someone could send me the following information:

  1. The correct spelling of the titles and the author's name (if I
     don't have them correct above).

  2. The publisher, and the publisher's address if it's available in
     either of the books.

  3. The ISBN.

Thanx for any information anyone can provide!

-- 
                                                +---------+
Brian L. Matthews                               | P L A N |
...{mnetor,uw-beaver!ssc-vax}!cxsea!blm         | A H E A |
+1 206 251 6811                                 +--------D+
Computer X Inc. - a division of Motorola New Enterprises

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	id AA20441; Mon, 8 Jun 87 11:51:27 EDT
From: <eric@ATHENA.MIT.EDU>
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Message-Id: <8706081551.AA19656@THESEUS.MIT.EDU>
To: cube-lovers@ai.ai.mit.edu
Reply-To: eric@athena.mit.edu
Subject: Info on Dmitri Borgmann books
Date: Mon, 08 Jun 87 11:51:05 EDT

Brian Matthews asked for information about Dmitri Borgmann books.  Here it is.
Dmitri Borgmann published three books:

	Language On Vacation (An Olio of Orthographical Oddities)
		Copyright 1965.  Published by Charles Scribner's Sons

	Beyond Language (Adventures in Word and Thought)
		Copyright 1967.  Published by Charles Scribner's Sons

	Curious Crosswords (edited and annotated by Borgmann)
		Copyright 1970.  Published by Charles Scribner's Sons

_Language on Vacation_ is a paperback.  _Beyond Language_ is a hardcover.
_Curious Crosswords_ is a large format paperback.  So far as I know, all three
have been out of print for years and it's unlikely they'll be reprinted.
But, there's good news -- you can get them all as follows:

_Curious Crosswords_ and _Language on Vacation_ are available for $7.00 each
from

	National Library Publications
	Box 73
	Brooklyn, NY 11234

Don't forget to add 10 percent for postage and handling.  I got my copies
from this place and had no trouble with them.  _Beyond Language_ can only
be found by combing used book stores, which I did for several years.  Then
I found two of them!  If you promise to love the book, I'll send you one of
them for $10.00.  Please note that it is missing its cover, but is otherwise
in perfect condition.

If you are a maniac about the peculiarities of language, all three of these
are must-buys.  You should also consider subscribing to the journal "Word
Ways" for $15.00 a year.  It's a quarterly 64-page journal devoted to the
kind of stuff Dmitri Borgmann writes about (weird spellings, words with
greatest number of vowels, pangrams, dictionaries, etc., etc.).  You can
order a subscription from Faith W. Eckler, Spring Valley Road, Morristown,
New Jersey 07960.

By the way, Dmitri Borgmann died last year of a heart attack.  It was a
great blow to logologists everywhere.  "Word Ways" has been running
memorial issues filled with unpublished articles by him.

Hope this helps!

Eric Albert (eric@athena.mit.edu)
12 Abbott Street
Medford, MA 02155
(617) 396-2424




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Date: 21 May 87 01:24:05 GMT
From: philabs!micomvax!musocs!mcgill-vision!mouse@nyu.arpa  (der Mouse)
Organization: McGill University, Montreal
Subject: Re: Repeated words answer
Message-Id: <777@mcgill-vision.UUCP>
References: <1036@theory.cs.cmu.edu>
Sender: cube-lovers-request@ai.ai.mit.edu
To: cube-lovers@ai.ai.mit.edu

In article <1036@theory.cs.cmu.edu>, dld@theory.cs.cmu.edu (David Detlefs) writes:
> [about repeated word sentences]
>	Police!
>	Police police.
....
>	Police police police police police.

> Etc....I have to stop now.  "Police" is becoming a meaningless text
> string...

Indeed.  I find this will happen with any word, if you examine it
enough.  My favorite example is "sock".

					der Mouse

				(mouse@mcgill-vision.uucp)

Received: from ARDEC-LCSS.ARPA.ARPA (TCP 30003004013) by AI.AI.MIT.EDU 11 Jun 87 08:52:17 EDT
Date: 11 Jun 87 08:37:00 EST
From: "CLSTR1::BECK" <beck@clstr1.decnet>
Subject: INFO RQST ON DOMINOES
To: "cube-lovers" <cube-lovers@mit-ai>
cc: beck
Reply-To: "CLSTR1::BECK" <beck@clstr1.decnet>


I picked up the following on AI-LIST.  

<beck@ardec-lcss>
.......................
Date: 8 Jun 87 19:46:16 GMT
From: ai!gautier@rsch.wisc.edu  (Jorge Gautier)
Subject: WANTED: references on the game of dominoes
 
I am looking for references on computer implementations of the game of
dominoes.  I suspect there are many variations on the rules for this game,
but any pointers to papers, commercial products, Ph.D. theses :-), etc.
would be much appreciated.  Please reply by mail.
 
Jorge Gautier
gautier@ai.wisc.edu
 
 
.............
------

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Date: 15 Jun 87 15:20:00 EST
From: "CLSTR1::BECK" <beck@clstr1.decnet>
Subject: DUTCH CLUB
To: "cube-lovers" <cube-lovers@mit-ai>
cc: beck
Reply-To: "CLSTR1::BECK" <beck@clstr1.decnet>



SUBJECT :  Review of "Cubism For Fun" newsletter; the newsletter of the "Dutch
Cubists Club"


1.   The dutch cubists club is alive and well.   It is probably the only
organized group of people still collecting and distributing information about
Rubik's cube and related combinatorial and geometrical puzzles.  

2.  This spring in order to improve contacts between cubists they started
publishing their newsletter in english (issue #14 dated 3/87).  The newsleter is
distributed free to members of the club.   Membership for 1987 is  US$5.   A
photocopied set of the newsletters, issues 1-13, written in DUTCH is also
available for  US$7.    To order either of these send a POSTAL MONEY ORDER to: 
Anton Hanegraaf,  Heemskerkstraat,  6662 AL ELST,  The Netherlands.

3.  The table of contents from issue #14 follows (it is 14 double sided folded 8
1/2 x 11 sheets, making a 28 page newsletter):

INTRODUCTION
LETTER FROM THE PRESIDENT - KLAAS STEENHUIS
SECRETATIAL REPORT - GUUS RAZOUX SCHULTZ
DUTCH CUBISTS DAY - ANTON HANEGRAAF
CALL FOR PAPERS
MORE ABOUT RUBIK'S MAGIC - GUUS RAZOUX SCHULTZ
THE ALGORITHM USED BY MARC WATERMAN - ANNEKE TREEP & MARC                       
WATERMAN
COMPUTERS IN SRVICE OF THE CUBE-KNOWLEDGE - KLAAS STEENHUIS
UPPER-TABLE BY HOME COMPUTER - BEN JOS WALBEEHM
SHORT HISTORY OF THE UPPER TABLE - ANTON HANEGRAAF
IMPROVEMENTS TO THE UPPER TABLE
LETTERS TO THE EDITOR
LIST OF MEMBERS

4.  If anybody would like further details please ask!

CUBING IS FOREVER      PETER BECK

<BECK@ARDEC-LCSS>  OR  <PBECK@ARDEC>
....................
------

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Date: 16 Jun 87 13:15:52 GMT
From: umnd-cs!umn-cs!dayton!ems!srcsip!notch@rsch.wisc.edu  (Michael k Notch)
Organization: Honeywell, Inc. Systems & Research Center, Camden, MN
Subject: Give or Take
Message-Id: <148@altura.srcsip.UUCP>
Sender: cube-lovers-request@ai.ai.mit.edu
To: cube-lovers@ai.ai.mit.edu


Have I got an interesting puzzle to at least look at:


           GIVE or TAKE

You can take 45 from 45 and have
a remainder of 45. A trick, yes, but it
can be done.
           Give it a try
             It's fun


There is an obvious answer - You take 45 eggs from 45 chickens and you still
                             have 45 chickens left.
Can you find the other answer?
GOOD LUCK!

-- 
 "Go with the flow, Have a plan, Go with the grain, And ...
    never never let the VAX see you sweat."
					   -G Saunders  07/14/86

USENET:  {ihnp4,mmm,philabs,umn-cs}!srcsip!notch        Michael k Notch
MailSt:	 Honeywell S&RC/SIP/MVT  MN65-2300
         3660 Technology Drive
         Minneapolis, Mn 55418
--

Received: from ucbvax.Berkeley.EDU (TCP 1200400116) by AI.AI.MIT.EDU 18 Jun 87 12:24:47 EDT
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	(contact usenet@ucbvax.Berkeley.EDU if you have questions)
Date: 17 Jun 87 13:47:50 GMT
From: ihnp4!homxb!houxm!homxc!halle@ucbvax.Berkeley.EDU  (J.HALLE)
Organization: AT&T Bell Laboratories, Holmdel
Subject: Re: Give or Take
Message-Id: <515@homxc.UUCP>
References: <148@altura.srcsip.UUCP>
Sender: cube-lovers-request@ai.ai.mit.edu
To: cube-lovers@ai.ai.mit.edu

In article <148@altura.srcsip.UUCP>, notch@srcsip.UUCP (Michael k Notch) writes:
> 
> Have I got an interesting puzzle to at least look at:
> 
> 
>            GIVE or TAKE
> 
> You can take 45 from 45 and have
> a remainder of 45. A trick, yes, but it
> can be done.
>            Give it a try
>              It's fun
Just get together two score and five gunslingers, only one of whom has two
guns, and take away one of the guns (assuming you survive :-) ).

Received: from ucbvax.Berkeley.EDU (TCP 1200400116) by AI.AI.MIT.EDU 19 Jun 87 06:03:20 EDT
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	(contact usenet@ucbvax.Berkeley.EDU if you have questions)
Date: 19 Jun 87 03:18:06 GMT
From: duke!mps@mcnc.org  (Michael P. Smith)
Organization: Duke University, Durham NC
Subject: Palindromes
Message-Id: <9794@duke.cs.duke.edu>
Sender: cube-lovers-request@ai.ai.mit.edu
To: cube-lovers@ai.ai.mit.edu


I was waiting for someone in the recent discussion on palindromes to
refer to this book but no one did ...
	PALINDROMES & ANAGRAMS  Howard W. Bergerson, Dover 1973.
It has hundreds of palindromic sentences longer than those posted, as
well as palindromic poetry, etc.  No section on palindromes
constructed of palindromic letters, though.
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

Michael P. Smith		"Ungate me, vi, I've met a gnu!"
mps@duke.cs.duke.edu
 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

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Date: 18 Jun 87 22:45:19 GMT
From: tektronix!tekgen!tektools!gvgpsa!friday!kirkg@ucbvax.Berkeley.EDU  (Kirk M Gramcko)
Organization: Grass Valley Group Professional Video Div, Grass Valley
Subject: Re: Give or Take
Message-Id: <120@friday.UUCP>
References: <148@altura.srcsip.UUCP>
Sender: cube-lovers-request@ai.ai.mit.edu
To: cube-lovers@ai.ai.mit.edu

In article <148@altura.srcsip.UUCP> notch@srcsip.UUCP (Michael k Notch) writes:
>
>Have I got an interesting puzzle to at least look at:
>           GIVE or TAKE
>You can take 45 from 45 and have
>a remainder of 45. A trick, yes, but it
>can be done.
>There is an obvious answer - You take 45 eggs from 45 chickens and you still
>                             have 45 chickens left.
>Can you find the other answer?

I have to disagree with your obvious answer for 2 reasons.

	1.  Using that kind of logic there are innumerable answers such as:

	You take 45 donuts from 45 bakers and you still have 45 bakers!

	2.  Your answer is not correct if you consider eggs to be chickens in
their primary stage of development.  Then you really have 90 chickens!!


Here is another puzzle to solve (perhaps a bit too easy):

	How can the following equation be correct?

	80 - 50 = 0

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	(contact usenet@ucbvax.Berkeley.EDU if you have questions)
Date: 18 Jun 87 13:12:20 GMT
From: mtune!mtgzz!mtuxo!gertler@RUTGERS.EDU  (D.GERTLER)
Organization: AT&T, Middletown NJ
Subject: Re: Give or Take
Message-Id: <36@mtuxo.UUCP>
References: <148@altura.srcsip.UUCP>
Sender: cube-lovers-request@ai.ai.mit.edu
To: cube-lovers@ai.ai.mit.edu

In article <148@altura.srcsip.UUCP>, notch@srcsip.UUCP (Michael k Notch) writes:
< Have I got an interesting puzzle to at least look at:
<            GIVE or TAKE
< You can take 45 from 45 and have
< a remainder of 45. A trick, yes, but it
< can be done.
<            Give it a try
<              It's fun
< There is an obvious answer - You take 45 eggs from 45 chickens and you still
<                              have 45 chickens left.
< Can you find the other answer?
< GOOD LUCK!
Simple!  Your friend has $45.  You TAKE his $45.  You have $45 remaining.
(Of course, you're out a friend.)  :-)

-- 

-Don Gertler		UUCP:	...!mtuxo!gertler

   "If this works, we'll eat like kings."

Date: Fri, 19 Jun 87 13:10:57 EDT
From: Alan Bawden <ALAN@AI.AI.MIT.EDU>
Subject:  recent random mail
To: CUBE-LOVERS@AI.AI.MIT.EDU
Message-ID: <216830.870619.ALAN@AI.AI.MIT.EDU>

The recent spate of messages to Cube-Lovers having to do with wordplay,
numerology, etc. was caused by an automatic feed from some usenet newsgroup
for puzzle fans.  This was set up without without asking
Cube-Lovers-Request's permission or even informing us that it had been
done.  I believe that I have now arranged for the feed to be terminated, so
there shouldn't be any more such messages.

If you were actually interested in some of the things that were sent, you
can probably arrange to subscribe to the newsgroup directly.  But please
don't ask me how to do it, I haven't even been able to get anyone to tell
me the -name- of the newsgroup in question!

Received: from MCC.COM (TCP 1200600076) by AI.AI.MIT.EDU 22 Jun 87 12:57:33 EDT
Date: Mon 22 Jun 87 11:52:32-CDT
From: Clive Dawson <AI.CLIVE@MCC.COM>
Subject: Re: Give or Take
To: mtune!mtgzz!mtuxo!gertler@RUTGERS.EDU
cc: cube-lovers@AI.AI.MIT.EDU
In-Reply-To: <36@mtuxo.UUCP>
Message-ID: <12312563719.54.AI.CLIVE@MCC.COM>

I don't know how this nonsense got started, but I'll gladly contribute. :-)

	How can you start with 4, then take away 4, and have 8 remain?

Answer in a day or two.

Clive
-------

Received: from MCC.COM (TCP 1200600076) by AI.AI.MIT.EDU 22 Jun 87 13:08:27 EDT
Date: Mon 22 Jun 87 12:02:02-CDT
From: Clive Dawson <AI.CLIVE@MCC.COM>
Subject: Re: recent random mail
To: ALAN@AI.AI.MIT.EDU
cc: cube-lovers@AI.AI.MIT.EDU
In-Reply-To: <216830.870619.ALAN@AI.AI.MIT.EDU>
Message-ID: <12312565446.54.AI.CLIVE@MCC.COM>

Oh, so those random messages were not generated by cube lovers?!
Then I guess I should modify my last puzzle to make it more
relevant to cubes (and thereby provide a hint):

	How do you start with 8, then take away 8, and have 24 remain?

Clive
-------

Received: from note.nsf.gov (TCP 1202200024) by AI.AI.MIT.EDU 22 Jun 87 16:57:39 EDT
To: Clive Dawson <AI.CLIVE@MCC.COM>
cc: mtune!mtgzz!mtuxo!gertler@RUTGERS.EDU, cube-lovers@AI.AI.MIT.EDU
Subject: Re: Give or Take 
In-reply-to: Your message of Mon, 22 Jun 87 11:52:32 -0500.
             <12312563719.54.AI.CLIVE@MCC.COM> 
Date: Mon, 22 Jun 87 16:53:22 -0400
From: Aaron Coles <acoles@note.nsf.gov>
Message-ID:  <8706221653.aa29184@note.note.nsf.gov>

In response to your question:

    How can you start with 4, then take away 4, and have 8 remain?

Here is my answer:  First you start off with 4 cows three in each row,
                    then you take 4 cows aways, and then you have
                    8 cows remaining.


Received: from nrl-aic.ARPA (TCP 3200200010) by AI.AI.MIT.EDU 24 Jun 87 03:18:32 EDT
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Received: Wed, 24 Jun 87 03:12:52 edt by nrl-aic.ARPA id AA18187
Date: 24 Jun 1987 02:40:53 EDT (Wed)
From: Dan Hoey <hoey@nrl-aic.ARPA>
Subject: Groups of the larger cubes
To: Cube-Lovers@AI.AI.MIT.EDU
Message-Id: <551515254/hoey@nrl-aic>

Last year Rodney Hoffman cited an article by J. A. Eidswick (in the
March 1986 Math Monthly) that develops a general approach to analyzing
several magic polyhedra.  Did anyone else go read this one?  Of
particular interest is Eidswick's analysis of the larger three-
dimensional cubes.  The article shows that the only constraints on
these cubes are the permutation parity constraints implicit in the
generators and the corner and edge orientation constraints we already
know about.  Eidswick shows that this even holds for the ``theoretical
invisible group'', where we imagine that the interior of the magic
N-cube is a magic (N-2)-cube that must be solved simultaneously.  The
solution method he presents is to solve the parity problems by applying
zero or one qtw at each of the floor(N/2) depths, then to work with
commutators (aka mono-ops) to solve the rest of the cube, piece by
piece.

As a supplement to that article, here are the number of positions
G[t](N) of the N^3 magic cube, where t, a subset of {s,m,i},
indicates the set of traits we find interesting:

    s (for N odd) indicates that are working in the Supergroup, and
      so take account of twists of the face centers.
    m (for N > 3) indicates that the pieces are marked so that we
      take account of the permutation of the identically-colored
      pieces on a face.
    i (for N > 3) indicates that we are working in the theoretical
      invisible group, and solve the pieces on the interior of the
      cube as well as the exterior.  I will assume that the M and S
      traits apply to the interior pieces as if they were on the
      exterior of a smaller cube.

A formula for the number of positions is

               2^A (8!/2 3^7)^B (12!/2 2^11)^C (4^6/2)^D (24!/2)^E
    G[t](N) =  ---------------------------------------------------
                                 24^F (24^6/2)^G

The following table gives the values of parameters A-G, depending on
the traits, and on whether N is even or odd.

        Parameter   Traits  (N odd)              (N even)

(Parity)        A =         (N-1)/2              N/2

(Corners)       B = i       (N-1)/2              N/2
                    ~i      1                    1

(Edge centers)  C = i       (N-1)/2              0
                    ~i      1                    0

(Face centers)  D = ~s      0                    0
                    s,i     (N-1)/2              0
                    s,~i    1                    0

(Other cubies)  E = i       (N+4)(N-1)(N-3)/24   N(N^2-4)/24
                    ~i      (N+1)(N-3)/4         N(N-2)/4

(Whole-cube)    F =         0                    1

(Color cosets)  G = m       0                    0
                    ~m,i    (N^2-1)(N-3)/24      N(N-1)(N-2)/24
                    ~m,~i   (N-1)(N-3)/4         (N-2)^2/4

In any case, the size of the group is exponential in a polynomial in N;
the polynomial is cubic if trait "i" is present and quadratic otherwise.
Here is a table of numeric approximations for cubes up to 10^3.

              Traits excluding s
 N     {}        {m}       {i}      {m,i}
 2  3.674e6   3.674e6   3.674e6   3.674e6
 3  4.325e19  4.325e19  4.325e19  4.325e19 
 4  7.401e45  7.072e53  3.263e53  3.118e61 
 5  2.829e74  2.583e90  6.117e93  5.585e109
 6  1.572e116 1.310e148 3.077e170 2.451e210
 7  1.950e160 1.484e208 2.982e253 2.072e317
 8  3.517e217 2.335e289 3.247e388 1.717e500
 9  1.417e277 8.208e372 5.283e529 2.126e689
10  8.298e349 4.007e477 4.041e738 1.032e978

              Traits including s
 N     {s}      {s,m}     {s,i}    {s,m,i}
 3  8.858e22  8.858e22  8.858e22  8.858e22 
 5  5.793e77  5.289e93  2.566e100 2.343e116
 7  3.994e163 3.039e211 2.562e263 1.780e327 
 9  2.902e280 1.681e376 9.293e542 3.740e702 

Enough, then, of what are essentially Eidswick's results.  In my next
message, I plan to produce lower bounds for solving these cubes.

Dan

Received: from nrl-aic.ARPA (TCP 3200200010) by AI.AI.MIT.EDU 24 Jun 87 09:10:18 EDT
Return-Path: <hoey@nrl-aic.ARPA>
Received: Wed, 24 Jun 87 09:04:34 edt by nrl-aic.ARPA id AA19977
Date: 24 Jun 1987 08:54:48 EDT (Wed)
From: Dan Hoey <hoey@nrl-aic.ARPA>
Subject: Lower bounds for the 3^N cubes
To: Cube-Lovers@AI.AI.MIT.EDU
Message-Id: <551537688/hoey@nrl-aic>

The ability to calculate the sizes of large cube groups prompts me to
generalize the lower-bound machinery we have for magic cubes, to see
how it behaves asymptotically.  The machinery we have uses the three
isomorphic Abelian groups A(N) generated by the three sets of parallel
generators for the N^3 cube.  Since the group of the N^3 cube is a
quotient of the free product of three copies of A(N), we can
upper-bound the number of positions close to SOLVED in the cube group
by the number of positions close to SOLVED in the free product.  This
implies a lower bound for the diameter of the cube group.

One useful tool for group diameter work is the Poincare series.  The
Poincare series of a finitely generated group is the power series p(z)
in which the coefficient of z^d is the number of group elements of
length d.  When the group is finite, the power series is a polynomial.
For our analysis, we will need the Poincare polynomial of A(N).

When N is odd, the analysis is straightforward, since A(N) is the
direct product of (N-1) cyclic groups of order 4.  Let S be the set of
generators for A(N), |S| = 2(N-1) including inverses.  Now suppose we
take a subset T of S.  We can construct a group element F(T) by
multiplying the elements of T together, *except* that when both a
generator G and its inverse G' appear in T we replace them with G^2.
It is easy to see that F is a bijection between the power set of S and
the group A(N).  The interesting thing about F is that the length of
F(T) is |T|.  So the number of length-d elements of A(N) is the number
of d-element subsets of S, and the binomial theorem gives us the
Poincare polynomial of A(N):  p(z) = (z+1)^(2(N-1)).

When N is even, we are in considerably murkier waters.  It's easy
enough in the Cutist analysis I presented on 1 June 1982:  There are
N-1 ways of cutting the cube into two pieces perpendicular to each
axis, and so 2(N-1) generators of A(N), and the analysis proceeds as
above.  But a year later I converted to Eccentric Slabism, and I
suppose I should present that analysis here.  In the Slabist
interpretation, the generators of A(N) are the 2N quarter-turns of
unit-thickness slabs.  But to avoid charging for whole-cube moves, we
must single out a particular slab S0 for which a turn is equivalent to
turning each of the other slabs {S1,S2,...,SN} in the opposite
direction.  The Poincare polynomial for A(N) is
        p(z) = ((z+1) (SUM[0<=i<N/2] C(N-1,i) z^i))^2
where C(N,r) is the binomial coefficient.  This can be shown by
constraining T to include fewer than N/2 of {S1,...,SN} and fewer than
N/2 of {S1',...,SN'} in the previous analysis.  Showing that this is a
length-preserving bijection is tricky, and I will spare you the gory
details, barring pleas to the contrary.  Does anyone know of a closed
form for that sum?

In general, the free product of three copies of A(N) has Poincare
series
    q(z) = p(z)/(3 - 2p(z))
where p(z) is the Poincare series of A(N).  The series q(z) can be
expanded term by term using the technique I sent in on 9 January 1981.
As in that message, we add up every other coefficient through that of
z^d to produce an upper bound on the number of positions of the
move-parity of d reachable in d qtw or fewer, and if this is less than
half the size of the group of the cube we have a lower-bound of d+2 qtw
to solve the cube.  I've done this for the cubes up to 10^3, and I get
the following lower bounds.  The traits are as given in my previous
message.

          LOWER BOUNDS ON GOD'S NUMBER FOR N^3 PUZZLES
      Traits
 N     {}     {m}     {i}   {m,i}     {s}   {s,m}   {s,i} {s,m,i}
 2     11
 3     21                              25
 4     37      44      43      50
 5     59      72      74      87      62      74      79      92
 6     81     102     118     145
 7    111     143     174     218     113     146     181     225
 8    138     183     246     316
 9    175     236     334     435     178     238     343     443
10    208     284     439     580

Asymptotically, the coefficients of q(z) grow by a factor approaching
R, where p(1/R) = 3/2.  This allows us to calculate the rate at which
the free product grows.  Here's a table of the smaller values.

    N    R (exact)                   R (approx)

    2    1/((3/2)^(1/2) - 1)          4.449
    3    1/((3/2)^(1/4) - 1)          9.371
    4    6/((4 + 6^(3/2))^(1/2) - 4) 18.519
    5    1/((3/2)^(1/8) - 1)         19.235
    6                                29.047
    7    1/((3/2)^(1/12) - 1)        29.098
    8                                38.960
    9    1/((3/2)^(1/16) - 1)        38.963
   11    1/((3/2)^(1/20) - 1)        48.828 (for even N>=10, use
   13    1/((3/2)^(1/24) - 1)        58.693  approximation for N+1).
   15    1/((3/2)^(1/28) - 1)        68.558
   17    1/((3/2)^(1/32) - 1)        78.423
   19    1/((3/2)^(1/36) - 1)        88.288
   21    1/((3/2)^(1/40) - 1)        98.153

Clearly R grows proportionally to N, so our asymptotic lower bound will
be somewhere around Log[N](G[t](n)), which is O(N^3/log(n)) for the
theoretical invisible groups (trait i) and O(N^2/log(n)) for the
surface groups.  This is as opposed to Eidswick's upper bounds, which
are O(N^3) and O(N^2), respectively.  So the gap increases, but not
terribly quickly.

It is interesting to compare this with the sort of behavior we see in
the 8-puzzle, 15-puzzle, ..., N^2-1-puzzles, as Jim Saxe suggested to
me many years ago.  The N^2-1-puzzle has (N^2)!/2 positions and 2 to 4
possible moves, so the lower bound based on this sort of counting
argument is O(log((N^2)!)) = O(N^2 log N).  Yet we know that we can put
O(N^2) pieces at a distance of O(N) from their home, so God's number
for the puzzle is O(N^3).  It is pleasant to see that our bounds on the
cubes are tight to within a log factor.

Dan

Received: from ARDEC-AC4.ARPA (TCP 30003004020) by AI.AI.MIT.EDU 29 Jun 87 10:22:30 EDT
Date:     Mon, 29 Jun 87 8:13:39 EDT
From:     Peter Beck (LCWSL) <pbeck@ARDEC.ARPA>
To:       cube-lovers@AI.AI.MIT.EDU
cc:       beck@ARDEC-LCSS.ARPA
Subject:  puzzle availability
Message-ID:  <8706290813.aa06155@ARDEC-AC4.ARDEC.ARPA>



HI CUBE-LOVERS, 

PUZZLE AVAILABILITY:

6/17 MACY'S RAN AN AD IN THE NY TIMES FOR 12 PIECE RUBIK'S MAGIC.  The puzzle
has 5 rings that have to be linked and was advertised for $15.

In Japan, associated with the New Zealand mazes are puzzle shops.  These shops
are creating a demand for puzzles.  A co-worker just back from Tokyo purchased
some puzzles at the "MATSUYA" department store in GINZA.  There is a line of
cast puzzles that cost about $7:  KEY, A-B-C, STAR, S&S, HORSESHOES (see slocums
book).  There is also a line of Ring disentanglement puzzles that cost about $6;
 BROKEN HEART, SWING, "U" RING, DEVIL, POT, LOOP, TRIO RING.  Both puzzle lines
are Bronze colored and come nicely gift boxed.

The Future is Puzzling and Cubing is Forever,

Pete beck                  <BECK@ARDEC-LCSS>
..................................
ps this msg has been delayed to "MAILER" problems with my host.
...........

Received: from ARDEC-LCSS.ARPA.ARPA (TCP 30003004013) by AI.AI.MIT.EDU 29 Jun 87 12:08:58 EDT
Date: 26 Jun 87 12:45:00 EST
From: "CLSTR1::BECK" <beck@clstr1.decnet>
Subject: 
To: "cube-lovers" <cube-lovers@mit-ai>
cc: mailer!<pbeck@ardec>
Reply-To: "CLSTR1::BECK" <beck@clstr1.decnet>
From:	CLSTR1::SYSTEM       26-JUN-1987 12:13
To:	BECK
Subj:	Undeliverable mail

 ----Transcript of session follows----
Mail could not be delivered in 3 days to <beck@ardec-lcss.arpa>

 ----Unsent message follows----
Date: 23 Jun 87 11:48:00 EST
From: "CLSTR1::BECK" <beck@clstr1.decnet>
Subject: 
To: "cube-lovers" <cube-lovers@mit-ai>
cc: beck
Reply-To: "CLSTR1::BECK" <beck@clstr1.decnet>
From:	CLSTR1::SYSTEM       23-JUN-1987 11:22
To:	BECK
Subj:	Undeliverable mail

 ----Transcript of session follows----
Mail could not be delivered in 3 days to <cube-lovers@mit-ai>

 ----Unsent message follows----
Date: 19 Jun 87 12:44:00 EST
From: "CLSTR1::BECK" <beck@clstr1.decnet>
Subject: puzzle avialability
To: "cube-lovers" <cube-lovers@mit-ai>
cc: beck
Reply-To: "CLSTR1::BECK" <beck@clstr1.decnet>

HI CUBE-LOVERS, 

PUZZLE AVAILABILITY:

6/17 MACY'S RAN AN AD IN THE NY TIMES FOR 12 PIECE RUBIK'S MAGIC.  The puzzle
has 5 rings that have to be linked and was advertised for $15.

In Japan, associated with the New Zealand mazes are puzzle shops.  These shops
are creating a demand for puzzles.  A co-worker just back from Tokyo purchased
some puzzles at the "MATSUYA" department store in GINZA.  There is a line of
cast puzzles that cost about $7:  KEY, A-B-C, STAR, S&S, HORSESHOES (see slocums
book).  There is also a line of Ring disentanglement puzzles that cost about $6;
 BROKEN HEART, SWING, "U" RING, DEVIL, POT, LOOP, TRIO RING.  Both puzzle lines
are Bronze colored and come nicely gift boxed.

The Future is Puzzling and Cubing is Forever,

Pete beck                  <BECK@ARDEC-LCSS>
..................................

------
------
------

Received: from Xerox.COM (TCP 1200400040) by AI.AI.MIT.EDU 27 Jul 87 18:16:37 EDT
Received: from CheninBlanc.ms by ArpaGateway.ms ; 27 JUL 87 15:06:53 PDT
Date: 27 Jul 87 15:06:45 PDT (Monday)
From: Hoffman.es@Xerox.COM
Subject: Puzzle shows
To: CUBE-LOVERS@AI.AI.MIT.EDU
Message-ID: <870727-150653-1010@Xerox>

The traveling puzzle show, "PUZZLES OLD AND NEW" is reviewed in the
Sunday, July 26 New York Times' Arts & Leisure section, page 31.  It has
opened at the Hudson River Museum.

Also of possible interest:  In the same section, page 33, is a review of
the exhibit "SAFE AND SECURE: KEYS AND LOCKS", which is at the
Cooper-Hewitt Museum.

  -- Rodney

Received: from nrl-aic.ARPA (TCP 3200200010) by AI.AI.MIT.EDU 30 Jul 87 15:51:13 EDT
Return-Path: <hoey@nrl-aic.ARPA>
Received: Thu, 30 Jul 87 15:47:50 edt by nrl-aic.ARPA id AA22816
Date: 30 Jul 1987 15:46:10 EDT (Thu)
From: Dan Hoey <hoey@nrl-aic.ARPA>
Subject: Planar positions of Rubik's Magic
To: Cube-Lovers@AI.AI.MIT.EDU
Message-Id: <554672771/hoey@nrl-aic>

    PLANAR POSITIONS OF RUBIK'S MAGIC, THE 8 SQUARE PUZZLE

    by P Beck and D Hoey,  July 1987
       <BECK@ARDEC-LCSS.ARPA> or <PBECK@ARDEC.ARPA>,
       <HOEY@NRL-AIC.ARPA>

This is a catalog of the 96 planar positions of the 8-square Rubik's
Magic puzzle.  The list is based on two rules for positioning the eight
squares.

RULE 1--Placement:  Let the pieces be numbered from 1 to 8.  Any planar
position must consist of squares in the pattern

                ``2x4''       or      ``3x3''

                A B C D                A B C
                H G F E                H E D
                                       G F

where A,B,C,D,E,F,G,H is a cyclical rearrangement of 1,2,3,4,5,6,7,8.
These patterns can also be rotated or reflected.

Both the 2x4 and the 3x3 patterns have eight rotations and reflections,
and there are eight possible assignments of the numbers 1-8 to the
letters A-H.  However, a 180-degree rotation of the 2x4 is equivalent
to a reassignment of the numbers.  So there are only 32 different 2x4
positions, while there are a full 64 of the 3x3 positions.

RULE 2--Orientation:  The pieces fit together as if the four edges
of each unrotated piece were

         +-b-+                                +-d-+
labeled  a O c  for odd-numbered pieces, and  a E c  for even-numbered
         +-d-+                                +-b-+

pieces, and the small letters must match where neighbors abut.

From rule 1, it is apparent that when neighbors abut, one of them must
be an even-numbered piece and the other odd.  From rule 2, we observe
that if a piece is rotated by 0 or 180 degrees, then its top and bottom
neighbors must be rotated the same amount and its left and right neigh-
bors must be rotated 180 degrees differently.  In this catalog, piece 1
will be placed in its unrotated orientation.  Then the orientation of
each piece is determined from its position relative to piece 1, and the
entire position is determined by the choice of pattern under rule 1.

TRANSFORMATION:  Each 2x4 position can be directly transformed into any
of four 3x3 positions, by folding out either end to either side.  Each
of the 3x3's can be directly transformed into either a vertical or a
horizontal 2x4.

SYMBOLOGY:  Plain numbers indicate an unrotated piece, while numbers
followed by an asterisk indicate pieces rotated 180 degrees.

The use of numbers seems to be the most popular alternate graphics
pattern at this time, as it most clearly shows what is happening as the
puzzle is manipulated.

ACKNOWLEDGEMENT:  Thanks to Rodney Hoffman for reviewing a preliminary
version of the catalog and the inspiration to prepare it in the first
place.

THE CATALOG:

>>>>>   16  VERTICAL  POSITIONS

+--+--+    +--+--+    +--+--+    +--+--+
|1 |8*|    |1 |2*|    |8*|1 |    |2*|1 |
+--+--+    +--+--+    +--+--+    +--+--+
|2 |7*|    |8 |3*|    |7*|2 |    |3*|8 |
+--+--+    +--+--+    +--+--+    +--+--+
|3 |6*|    |7 |4*|    |6*|3 |    |4*|7 |
+--+--+    +--+--+    +--+--+    +--+--+
|4 |5*|    |6 |5*|    |5*|4 |    |5*|6 |
+--+--+    +--+--+    +--+--+    +--+--+

+--+--+    +--+--+    +--+--+    +--+--+
|8 |7*|    |2 |3*|    |7*|8 |    |3*|2 |
+--+--+    +--+--+    +--+--+    +--+--+
|1 |6*|    |1 |4*|    |6*|1 |    |4*|1 |
+--+--+    +--+--+    +--+--+    +--+--+
|2 |5*|    |8 |5*|    |5*|2 |    |5*|8 |
+--+--+    +--+--+    +--+--+    +--+--+
|3 |4*|    |7 |6*|    |4*|3 |    |6*|7 |
+--+--+    +--+--+    +--+--+    +--+--+

+--+--+    +--+--+    +--+--+    +--+--+
|7 |6*|    |3 |4*|    |6*|7 |    |4*|3 |
+--+--+    +--+--+    +--+--+    +--+--+
|8 |5*|    |2 |5*|    |5*|8 |    |5*|2 |
+--+--+    +--+--+    +--+--+    +--+--+
|1 |4*|    |1 |6*|    |4*|1 |    |6*|1 |
+--+--+    +--+--+    +--+--+    +--+--+
|2 |3*|    |8 |7*|    |3*|2 |    |7*|8 |
+--+--+    +--+--+    +--+--+    +--+--+

+--+--+    +--+--+    +--+--+    +--+--+
|6 |5*|    |4 |5*|    |5*|6 |    |5*|4 |
+--+--+    +--+--+    +--+--+    +--+--+
|7 |4*|    |3 |6*|    |4*|7 |    |6*|3 |
+--+--+    +--+--+    +--+--+    +--+--+
|8 |3*|    |2 |7*|    |3*|8 |    |7*|2 |
+--+--+    +--+--+    +--+--+    +--+--+
|1 |2*|    |1 |8*|    |2*|1 |    |8*|1 |
+--+--+    +--+--+    +--+--+    +--+--+

>>>> 16  HORIZONTAL POSITIONS

+--+--+--+--+    +--+--+--+--+    +--+--+--+--+    +--+--+--+--+
|1 |8*|7 |6*|    |1 |2*|3 |4*|    |2 |3*|4 |5*|    |8 |7*|6 |5*|
+--+--+--+--+    +--+--+--+--+    +--+--+--+--+    +--+--+--+--+
|2 |3*|4 |5*|    |8 |7*|6 |5*|    |1 |8*|7 |6*|    |1 |2*|3 |4*|
+--+--+--+--+    +--+--+--+--+    +--+--+--+--+    +--+--+--+--+

+--+--+--+--+    +--+--+--+--+    +--+--+--+--+    +--+--+--+--+
|2*|1 |8*|7 |    |8*|1 |2*|3 |    |3*|4 |5*|6 |    |7*|6 |5*|4 |
+--+--+--+--+    +--+--+--+--+    +--+--+--+--+    +--+--+--+--+
|3*|4 |5*|6 |    |7*|6 |5*|4 |    |2*|1 |8*|7 |    |8*|1 |2*|3 |
+--+--+--+--+    +--+--+--+--+    +--+--+--+--+    +--+--+--+--+

+--+--+--+--+    +--+--+--+--+    +--+--+--+--+    +--+--+--+--+
|3 |2*|1 |8*|    |7 |8*|1 |2*|    |4 |5*|6 |7*|    |6 |5*|4 |3*|
+--+--+--+--+    +--+--+--+--+    +--+--+--+--+    +--+--+--+--+
|4 |5*|6 |7*|    |6 |5*|4 |3*|    |3 |2*|1 |8*|    |7 |8*|1 |2*|
+--+--+--+--+    +--+--+--+--+    +--+--+--+--+    +--+--+--+--+

+--+--+--+--+    +--+--+--+--+    +--+--+--+--+    +--+--+--+--+
|4*|3 |2*|1 |    |6*|7 |8*|1 |    |5*|6 |7*|8 |    |5*|4 |3*|2 |
+--+--+--+--+    +--+--+--+--+    +--+--+--+--+    +--+--+--+--+
|5*|6 |7*|8 |    |5*|4 |3*|2 |    |4*|3 |2*|1 |    |6*|7 |8*|1 |
+--+--+--+--+    +--+--+--+--+    +--+--+--+--+    +--+--+--+--+

>>>> 16 NORTHWEST POSITIONS

   +--+--+       +--+--+       +--+--+       +--+--+
   |1 |8*|       |1 |2*|       |8*|1 |       |2*|1 |
+--+--+--+    +--+--+--+    +--+--+--+    +--+--+--+
|3*|2 |7*|    |7*|8 |3*|    |6 |7*|2 |    |4 |3*|8 |
+--+--+--+    +--+--+--+    +--+--+--+    +--+--+--+
|4*|5 |6*|    |6*|5 |4*|    |5 |4*|3 |    |5 |6*|7 |
+--+--+--+    +--+--+--+    +--+--+--+    +--+--+--+

   +--+--+       +--+--+       +--+--+       +--+--+
   |7*|6 |       |3*|4 |       |2 |3*|       |8 |7*|
+--+--+--+    +--+--+--+    +--+--+--+    +--+--+--+
|1 |8*|5 |    |1 |2*|5 |    |8*|1 |4*|    |2*|1 |6*|
+--+--+--+    +--+--+--+    +--+--+--+    +--+--+--+
|2 |3*|4 |    |8 |7*|6 |    |7*|6 |5*|    |3*|4 |5*|
+--+--+--+    +--+--+--+    +--+--+--+    +--+--+--+

   +--+--+       +--+--+       +--+--+       +--+--+
   |7*|8 |       |3*|2 |       |6*|5 |       |4*|5 |
+--+--+--+    +--+--+--+    +--+--+--+    +--+--+--+
|5 |6*|1 |    |5 |4*|1 |    |8 |7*|4 |    |2 |3*|6 |
+--+--+--+    +--+--+--+    +--+--+--+    +--+--+--+
|4 |3*|2 |    |6 |7*|8 |    |1 |2*|3 |    |1 |8*|7 |
+--+--+--+    +--+--+--+    +--+--+--+    +--+--+--+

   +--+--+       +--+--+       +--+--+       +--+--+
   |5 |6*|       |5 |4*|       |6*|7 |       |4*|3 |
+--+--+--+    +--+--+--+    +--+--+--+    +--+--+--+
|3*|4 |7*|    |7*|6 |3*|    |4 |5*|8 |    |6 |5*|2 |
+--+--+--+    +--+--+--+    +--+--+--+    +--+--+--+
|2*|1 |8*|    |8*|1 |2*|    |3 |2*|1 |    |7 |8*|1 |
+--+--+--+    +--+--+--+    +--+--+--+    +--+--+--+

>>>> 16 NORTHEAST POSITIONS

+--+--+       +--+--+       +--+--+       +--+--+
|1 |8*|       |1 |2*|       |8*|1 |       |2*|1 |
+--+--+--+    +--+--+--+    +--+--+--+    +--+--+--+
|2 |7*|6 |    |8 |3*|4 |    |7*|2 |3*|    |3*|8 |7*|
+--+--+--+    +--+--+--+    +--+--+--+    +--+--+--+
|3 |4*|5 |    |7 |6*|5 |    |6*|5 |4*|    |4*|5 |6*|
+--+--+--+    +--+--+--+    +--+--+--+    +--+--+--+

+--+--+       +--+--+       +--+--+       +--+--+
|8 |7*|       |2 |3*|       |7*|8 |       |3*|2 |
+--+--+--+    +--+--+--+    +--+--+--+    +--+--+--+
|1 |6*|5 |    |1 |4*|5 |    |6*|1 |2*|    |4*|1 |8*|
+--+--+--+    +--+--+--+    +--+--+--+    +--+--+--+
|2 |3*|4 |    |8 |7*|6 |    |5*|4 |3*|    |5*|6 |7*|
+--+--+--+    +--+--+--+    +--+--+--+    +--+--+--+

+--+--+       +--+--+       +--+--+       +--+--+
|6 |7*|       |4 |3*|       |3 |4*|       |7 |6*|
+--+--+--+    +--+--+--+    +--+--+--+    +--+--+--+
|5 |8*|1 |    |5 |2*|1 |    |2 |5*|6 |    |8 |5*|4 |
+--+--+--+    +--+--+--+    +--+--+--+    +--+--+--+
|4 |3*|2 |    |6 |7*|8 |    |1 |8*|7 |    |1 |2*|3 |
+--+--+--+    +--+--+--+    +--+--+--+    +--+--+--+

+--+--+       +--+--+       +--+--+       +--+--+
|6*|5 |       |4*|5 |       |5 |6*|       |5 |4*|
+--+--+--+    +--+--+--+    +--+--+--+    +--+--+--+
|7*|4 |3*|    |3*|6 |7*|    |4 |7*|8 |    |6 |3*|2 |
+--+--+--+    +--+--+--+    +--+--+--+    +--+--+--+
|8*|1 |2*|    |2*|1 |8*|    |3 |2*|1 |    |7 |8*|1 |
+--+--+--+    +--+--+--+    +--+--+--+    +--+--+--+

>>>> 16 SOUTHWEST POSITIONS

+--+--+--+    +--+--+--+    +--+--+--+    +--+--+--+
|1 |2*|3 |    |1 |8*|7 |    |8*|1 |2*|    |2*|1 |8*|
+--+--+--+    +--+--+--+    +--+--+--+    +--+--+--+
|8 |7*|4 |    |2 |3*|6 |    |7*|6 |3*|    |3*|4 |7*|
+--+--+--+    +--+--+--+    +--+--+--+    +--+--+--+
   |6*|5 |       |4*|5 |       |5 |4*|       |5 |6*|
   +--+--+       +--+--+       +--+--+       +--+--+

+--+--+--+    +--+--+--+    +--+--+--+    +--+--+--+
|3 |2*|1 |    |7 |8*|1 |    |2 |3*|4 |    |8 |7*|6 |
+--+--+--+    +--+--+--+    +--+--+--+    +--+--+--+
|4 |5*|8 |    |6 |5*|2 |    |1 |8*|5 |    |1 |2*|5 |
+--+--+--+    +--+--+--+    +--+--+--+    +--+--+--+
   |6*|7 |       |4*|3 |       |7*|6 |       |3*|4 |
   +--+--+       +--+--+       +--+--+       +--+--+

+--+--+--+    +--+--+--+    +--+--+--+    +--+--+--+
|3*|4 |5*|    |7*|6 |5*|    |4 |3*|2 |    |6 |7*|8 |
+--+--+--+    +--+--+--+    +--+--+--+    +--+--+--+
|2*|1 |6*|    |8*|1 |4*|    |5 |6*|1 |    |5 |4*|1 |
+--+--+--+    +--+--+--+    +--+--+--+    +--+--+--+
   |8 |7*|       |2 |3*|       |7*|8 |       |3*|2 |
   +--+--+       +--+--+       +--+--+       +--+--+

+--+--+--+    +--+--+--+    +--+--+--+    +--+--+--+
|4*|5 |6*|    |6*|5 |4*|    |5 |4*|3 |    |5 |6*|7 |
+--+--+--+    +--+--+--+    +--+--+--+    +--+--+--+
|3*|2 |7*|    |7*|8 |3*|    |6 |7*|2 |    |4 |3*|8 |
+--+--+--+    +--+--+--+    +--+--+--+    +--+--+--+
   |1 |8*|       |1 |2*|       |8*|1 |       |2*|1 |
   +--+--+       +--+--+       +--+--+       +--+--+

>>>> 16 SOUTHEAST POSITIONS

+--+--+--+    +--+--+--+    +--+--+--+    +--+--+--+
|1 |2*|3 |    |1 |8*|7 |    |8*|1 |2*|    |2*|1 |8*|
+--+--+--+    +--+--+--+    +--+--+--+    +--+--+--+
|8 |5*|4 |    |2 |5*|6 |    |7*|4 |3*|    |3*|6 |7*|
+--+--+--+    +--+--+--+    +--+--+--+    +--+--+--+
|7 |6*|       |3 |4*|       |6*|5 |       |4*|5 |
+--+--+       +--+--+       +--+--+       +--+--+

+--+--+--+    +--+--+--+    +--+--+--+    +--+--+--+
|3 |2*|1 |    |7 |8*|1 |    |2 |3*|4 |    |8 |7*|6 |
+--+--+--+    +--+--+--+    +--+--+--+    +--+--+--+
|4 |7*|8 |    |6 |3*|2 |    |1 |6*|5 |    |1 |4*|5 |
+--+--+--+    +--+--+--+    +--+--+--+    +--+--+--+
|5 |6*|       |5 |4*|       |8 |7*|       |2 |3*|
+--+--+       +--+--+       +--+--+       +--+--+

+--+--+--+    +--+--+--+    +--+--+--+    +--+--+--+
|5*|4 |3*|    |5*|6 |7*|    |4 |3*|2 |    |6 |7*|8 |
+--+--+--+    +--+--+--+    +--+--+--+    +--+--+--+
|6*|1 |2*|    |4*|1 |8*|    |5 |8*|1 |    |5 |2*|1 |
+--+--+--+    +--+--+--+    +--+--+--+    +--+--+--+
|7*|8 |       |3*|2 |       |6 |7*|       |4 |3*|
+--+--+       +--+--+       +--+--+       +--+--+

+--+--+--+    +--+--+--+    +--+--+--+    +--+--+--+
|3 |4*|5 |    |7 |6*|5 |    |6*|5 |4*|    |4*|5 |6*|
+--+--+--+    +--+--+--+    +--+--+--+    +--+--+--+
|2 |7*|6 |    |8 |3*|4 |    |7*|2 |3*|    |3*|8 |7*|
+--+--+--+    +--+--+--+    +--+--+--+    +--+--+--+
|1 |8*|       |1 |2*|       |8*|1 |       |2*|1 |
+--+--+       +--+--+       +--+--+       +--+--+

>>>> END OF CATALOG

Received: from ARDEC-LCSS.ARPA.ARPA (TCP 30003004013) by AI.AI.MIT.EDU 25 Aug 87 15:14:27 EDT
Date: 25 Aug 87 14:58:00 EST
From: "CLSTR1::BECK" <beck@clstr1.decnet>
Subject: TILING BOOKS
To: "cube-lovers" <cube-lovers@mit-ai>
Reply-To: "CLSTR1::BECK" <beck@clstr1.decnet>


BOOK OF INTEREST

Tilings and Patterns  by Branko Grunbaum and G. C. Shephard
from w. h. Freeman and Co,  1987,    ISBN   0-7167-1193-1
......................
FROM THE PREFACE:   
_______________________________
ORGANIZATION OF THE BOOK
------------------------------------
The book falls naturally into two parts.  The first, up to and including Chapter
7, can be used as the text for a geometry course at the undergraduate level -
...   The first few sections of chapter 1 are fundamental, however, chapter 2
deals mostly with tilings in which the tiles are regular polygons.  ...   The
general theory of tilings is presented in chapters 3 and 4, these chapters are
rather more technical than the rest of the book, and ...    In chapter 5 we
begin our discussion of the theory of patterns; this continues in chapter 7. 
...

the second part (chapters 8-12) presents detailed surveys of various aspects of
the subjects of patterns and tilings.  These include colored patterns and groups
of color symmetry, tilings by polygons, tilings in which the tiles are unusual
in a topological sense, as well as, a detailed and self-contained account of the
intriguing topic of aperiodic tilings.  ...
_____________________________
TABLE OF CONTENTS
1  BASIC NOTIONS
2  TILINGS BY REGULAR POLYGONS AND STAR POLYGONS
3  WELL-BEHAVED TILINGS
4  THE TOPOLOGY OF TILINGS
5  PATTERNS
6  CLASSIFICATIONS OF TILINGS WITH TRANSIVITY PROPERTIES
7  CLASSIFICATION WITH RESPECT TO SYMMETRIES
8  COLORED PATTERNS AND TILINGS
9  TILINGS BY POLYGONS
10 APERIODIC TILINGS
11 WANG TILES
12 TILINGS WITH UNUSUAL HINDS OF TILES
REFERENCES

...........................................

This is a great book on the subject with plenty of pictures for those of us who
can't visualize well.  

beckardec-lcss.arpa
33333333###################
------

Received: from ARDEC-LCSS.ARPA.ARPA (TCP 30003004013) by AI.AI.MIT.EDU 26 Aug 87 08:11:43 EDT
Date: 26 Aug 87 07:55:00 EST
From: "CLSTR1::BECK" <beck@clstr1.decnet>
Subject: PASTIME JIGSAW PUZZLES
To: "cube-lovers" <cube-lovers@mit-ai>
cc: beck
Reply-To: "CLSTR1::BECK" <beck@clstr1.decnet>


I am interested in information on the "Pastime Puzzles"  (jigsaw puzzles) made
by Parker Brothers in 1932/33/ and other puzzles of similar construction .  The
ones I have were sold by the Kohler Puzzle Exchange, 105 Roseville Ave, Newark
NJ  and if anybody has information on this firm I would also like the reference.

These puzzles are of the type currently being manufactured by "Stave", ie,
many pieces have shapes (eg, numbers, violins, fruits),  false corners and
edges, cuts where the colors change, etc


The Future is Puzzling but Cubing is Forever,

Pete beck                  <BECK@ARDEC-LCSS.arpa>
..................................

------

Received: from ARDEC-LCSS.ARPA.ARPA (TCP 30003004013) by AI.AI.MIT.EDU 27 Aug 87 08:10:48 EDT
Date: 27 Aug 87 08:06:00 EST
From: "CLSTR1::BECK" <beck@clstr1.decnet>
Subject: FRACTALS
To: "cube-lovers" <cube-lovers@mit-ai>
cc: beck
Reply-To: "CLSTR1::BECK" <beck@clstr1.decnet>

BOOK OF INTEREST

THE BEAUTY OF FRACTALS  by  H.-O. PEITGEN & P.H. RICHTER
  from SPRINGER-VERLAG  1986,   ISBN  3-540-15851-0  OR ISBN 0-387-15851

......................
FROM THE FLAP:   This book is an unusual attempt to publicize the field of
Complex Dynamics, ...  .  

In 88 full color pictures, and many more black and white illustrations, the
authors present variations of a theme whose repercussions reach far beyond the
realms of mathematics.  
...........................................

This is agreat first book on the subject with plenty of pictures for those of us
who can't visualize well.

beckardec-lcss.arpa
------

Received: from ARDEC-LCSS.ARPA.ARPA (TCP 30003004013) by AI.AI.MIT.EDU  3 Sep 87 08:58:50 EDT
Date: 3 Sep 87 08:38:00 EST
From: "CLSTR1::BECK" <beck@clstr1.decnet>
Subject: dutch newsletter #15
To: "cube-lovers" <cube-lovers@mit-ai>
Reply-To: "CLSTR1::BECK" <beck@clstr1.decnet>


SUBJECT :  Review of "Cubism For Fun" newsletterissue #15; the newsletter of the
"Dutch Cubists Club";  in english starting with issue 14 

1..  The table of contents >> annotated << from issue #15, august 87 follows (it
is 8 double sided folded 8 1/2 x 11 sheets, making a 32 page newsletter):

INTRODUCTION
LIVING WITH A CUBIST  BY  LUKAS  SCHOONHOVEN 
RUBIK'S MAGIC'S CUBE  BY  RONALD FETTERMAN  < HOW TO FOLD RUBIK'S               
               MAGIC INTO A CUBE<
LENGTH DATA FOR UPPER TABLE PROCESSES  BY  ANTON  HANEGRAAF
MARC WATERMAN'S ALGORITHM , PART; CONTINUED FROM ISSUE 14 
                 - ANNEKE TREEP & MARC  WATERMAN
THE MAGIC NUMBER CUBE  BY  WALLY  WEBSTER > MARKING WITH NUMBERS A              
3X3X3 RUBIK'S CUBE SO THAT ALL OF THE 3X3 VERTICALS AND                      
HORIZONTALS ADD UP TO 42<<
THE MAGIC MOSAICS BY RONALD FETTERMAN  > SIMILAR TO THE CATALOGUE               
     OF RUBIK'S MAGIC POSITIONS POSTED ON CUBE LOVERS WITH A                    
  DIFFERENT NOTATION AND WITH THE ADDITION OF A                                 
      NOMENCLATURE AND A MOVE SEQUENCE TO GET TO EACH ONE                       
    FROM START<<
MAGIC AND AND IS NHO MAGIC BY TOM VERHOEFF  > A GROUP THEORY                    
            ANALYSIS OF RUBIK'S MAGIC<
MAGIC VARIATIONS BY PETER BECK >PREVIOUSLY POSTED TO CUBE LOVERS<
PRETTY CUBIC PATTERNS  BY  ANNEKE TREEP
NEWS AND LETTERS TO THE EDITOR  >  a list of collectors wanting to trade        
                        cubes/puzzles;  a statement that Guus Schultz has built 
                               MAGICs where the number of squares is not a
multiple                                   of "4" <<
LIST OF MEMBERS

2.   Membership for 1987 is  US$5.   A photocopied set of the newsletters,
issues 1-13, written in DUTCH (in the feature selected articles will be
available in english) is also available for  US$7.    To order either of these
send an 'INTERNATIONAL"  POSTAL MONEY ORDER to:  Anton Hanegraaf, 
Heemskerkstraat,  6662 AL ELST,  The Netherlands.

3.  If anybody would like further details please ask!

CUBING IS FOREVER      PETER BECK

<BECK@ARDEC-LCSS>  OR  <PBECK@ARDEC>

------

Received: from GTEWIS.ARPA (TCP 3201600102) by AI.AI.MIT.EDU 22 Sep 87 12:25:05 EDT
Date: Tue, 22 Sep 87 11:49:12 EDT
From: rdavenport@GTEWIS.ARPA
Subject: Where's ITC?
To: CUBE-LOVERS@AI.AI.MIT.EDU







      Greetings fellow cube lovers,

         I have only learned to solve the cube this summer, and now am working
 on R*bik's Revenge (and Magic) and I was wondering if anyone out there knows
 of any publications dealing with solving them and any dealing with the theory
 behind them - as I have really enjoyed Frey & Singmaster's _Cubik Math_.

         I have tried writing to Ideal Toy Corporation as mention in the Revenge
 product but they seem to have moved - anybody know where they are?


          thanks in advance,

                  Rob



^^^^^^^^^^^^^^^^^vvvvvvvvvvvvvvvvv^^^^^^^^^^^^^^^^vvvvvvvvvvvvvvvvv^^^^^^^^^^^^^

Rob Davenport                  Arpanet :  RDAVENPORT@GTEWIS.ARPA
GTE
Billerica, Massachusetts
(617) 671-5180

vvvvvvvvvvvvvvvvv^^^^^^^^^^^^^^^^^vvvvvvvvvvvvvvvv^^^^^^^^^^^^^^^^^vvvvvvvvvvvvv

Received: from ARDEC-LCSS.ARPA.ARPA (TCP 30003004013) by AI.AI.MIT.EDU 28 Sep 87 13:05:50 EDT
Date: 28 Sep 87 12:41:00 EST
From: "CLSTR1::BECK" <beck@clstr1.decnet>
Subject: ROTA & GD TIMES, BAD TIMES
To: "cube-lovers" <cube-lovers@mit-ai>
Reply-To: "CLSTR1::BECK" <beck@clstr1.decnet>

1.  For the collectors, I recently obtained a new to me shape variant of the
2x2x2.  It is a cylinder, mine is half black and half white.  It was made by the
Swiss company NAEF and is called "ROTA".  It is very similar in size to the
standard cube.  It should cost about $15.

2.  Has anybody played a game called "GOOD TIMES, BAD TIMES".  It uses the
PYRAMINX in some fashion and I believe it was developed/marketed by MEFFERT.

Thanks in advance.

CUBING IS FOREVER ----    PETER BECK
                                          <BECK@ARDEC-LCSS.ARPA>
                                OR      <PBECK@ARDEC.ARPA>
......................................................................
------

Received: from Xerox.COM (TCP 1200400040) by AI.AI.MIT.EDU  2 Oct 87 10:44:46 EDT
Received: from Gamay.ms by ArpaGateway.ms ; 02 OCT 87 07:35:05 PDT
Date: 2 Oct 87 07:35:00 PDT (Friday)
From: Hoffman.es@Xerox.COM
Subject: Rubik's Magic article
To: Cube-Lovers@AI.AI.MIT.EDU
Message-ID: <871002-073505-5351@Xerox>

The October '87 issue of 'Scientific American' is completely devoted to
Advanced Computing, so it is probably of interest to many of us.  In
addition, the 'Amateur Scientist' column in that issue (by Jearle
Walker, pages 170-173) is all about Rubik's Magic (the original, 8-panel
version).  It includes tables and diagrams of permutations, and a
complete solution with pictures.

  -- Rodney Hoffman

Received: from ARDEC-LCSS.ARPA.ARPA (TCP 30003004013) by AI.AI.MIT.EDU 14 Oct 87 14:14:13 EDT
Date: 14 Oct 87 13:53:00 EST
From: "CLSTR1::BECK" <beck@clstr1.decnet>
Subject: MAZES
To: "cube-lovers" <cube-lovers@mit-ai>
Reply-To: "CLSTR1::BECK" <beck@clstr1.decnet>



FOR FUN, JAPAN TURNS TO MAZES

The Sunday NY TImes of 10/11/87 Travel section, pg3 had a small piece on
amusement park mazes.

Some random quotes:

"A lot of people are willing to pay the $3 fee that most of the approximately 20
outdoor mazes charge for the opportunity to become confused."

"The object, ...,  is to get through the maze as fasy as possible.  On average,
it takes 45 minutes to escape or give up."

"each maze has a theme - such as the Paris-Dakar Rally Maze in Tokyo and the
Sherlock Maze in Osaka."

MORE INFORMATION:  JAPAN NATIONAL TOURIST ORGANIZATION,  630 FIFTH AVE,  SUITE
2101, NY, NY 10111;   212/757-5640.

...........................................................
PS If anybody has other references I would like them.

Thanks

pete beck

<BECK@ARDEC-LCSS>

..........................
------

Received: from po5.andrew.cmu.edu (TCP 20000417001) by AI.AI.MIT.EDU 22 Oct 87 14:20:59 EDT
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Message-Id: <kVTYcPy00Uo1gws0=j@andrew.cmu.edu>
Date: Thu, 22 Oct 87 14:10:35 edt
From: ap1a+@andrew.cmu.edu (Andrew Balen Philips)
To: Cube-Lovers@ai.ai.mit.edu
Subject: More Expensive Cubes


To anyone out there:

I am currently involved in a research project on the Rubik's Cube and expert
solving of it.  The conventional cubes sold in most stores fall apart in the
hands of the expert, because corners catch.  For awhile there were cubes
manufactured that have tiles for colored plates.  We have one of these, but
would like to have some more.  If anyone knows where we may look for these
cubes or has access to these cubes, please notify me.

								Thank you,
										Andy
Philips, ap1a+@andrew.cmu.edu

Send mail direct or post.
By the way, this bboard is very cool!



Received: from po2.andrew.cmu.edu (TCP 20000574551) by AI.AI.MIT.EDU 22 Oct 87 19:12:50 EDT
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Message-Id: <wVTcssy00UkZB080Uy@andrew.cmu.edu>
Date: Thu, 22 Oct 87 19:01:12 -0400 (EDT)
From: dt+@andrew.cmu.edu (David Tilbrook)
To: ap1a+@andrew.cmu.edu (Andrew Balen Philips), Cube-Lovers@ai.ai.mit.edu
Subject: Re: More Expensive Cubes
In-Reply-To: <kVTYcPy00Uo1gws0=j@andrew.cmu.edu>

The cubes to which you refer were manufactured in Korea.

I purchased three or four in Toronto at a Korean trade show about six years
ago,
and still have them in perfect working order.

Sorry I can't give you anymore information than that,
other than to say that they are trully amazing in that they
have lasted extremely well and require absolutely no maintenance.

The red's a little hard to distinguish from the orange
in the wrong light but that is the only problem.

While we are on the subject, does anyone know where to acquire
a 5x5x5?  There was a source in London two years ago but they ran out
and haven't been seen since.

Also I'd like to acquire the globe
on which the equator, greenwich and 90' meridians rotate.

david tilbrook



Received: from ARDEC-LCSS.ARPA.ARPA (TCP 30003004013) by AI.AI.MIT.EDU  5 Nov 87 08:53:44 EST
Date: 5 Nov 87 08:40:00 EST
From: "CLSTR1::BECK" <beck@clstr1.decnet>
Subject: CMU CUBE RESEARCHERS
To: "cube-lovers" <cube-lovers@mit-ai>
Reply-To: "CLSTR1::BECK" <beck@clstr1.decnet>

TO:  R DEUSER, A PHILLIPS, D TILLBROOK

MY MAILER SAYS THAT YOUR ADDRESSES ARE VALID BUT I SUSPECT THAT MY MSGS ARE
NOT GETTING THROUGH.  I AM TRYING TO RESOLVE THIS PROBLEM.  IF YOU HAVE ANY
SUGGESTIONS (MAYBE THE PROBLEM IS AT YOUR END) THEN HELP ME.  I HAVE RECEIVED
YOUR PREVIOUS MSGS.

SORRY CUBE LOVERS FOR THIS PERSONAL MSG.

PS  THE DELUXE CUBES YOU WANT ARE ON THE WAY.

PETE BECK  <PBECK@ARDEC.ARPA>
......................................
------

Received: from ARDEC-LCSS.ARPA.ARPA (TCP 30003004013) by AI.AI.MIT.EDU  5 Nov 87 08:54:10 EST
Date: 5 Nov 87 08:46:00 EST
From: "CLSTR1::BECK" <beck@clstr1.decnet>
Subject: MAGIC VARIANT
To: "cube-lovers" <cube-lovers@mit-ai>
Reply-To: "CLSTR1::BECK" <beck@clstr1.decnet>
I SAW IN THE STORE THE OTHER DAY A GRAPHICS VARIATION OF "MAGIC" FROM MATCHBOX.
IT IS CALL ED RUBIK'S MAGIC CUBE.  THE OBJECT IS TO MAKE THREE DIMENSIONAL 
SHAPES THAT ARE IN HARMONY WITH THE ALTERNATE GRAPHICS.  ANYBODY OUT THERE
INVESTIGATE THIS VARIANT OR THE MAGIC GAME?  I WOULD APPRECIATE ANY IMPRESSIONS.

A REMINDER!!!   FOR ALL OF YOU BOSTON PEOPLE, THE PUZZLE EXHIBIT STILL HAS SOME
TIME TO RUN AT THE MIT MUSEUM BRFORE FADING IN TO NEVER NEVER LAND - SO GET OUT
AND SEE IT.  I THINK YOU HAVE UNTIL JAN.

PETE BECK  <PBECK@ARDEC.ARPA>
..............................
------

Received: from WILMA.BBN.COM (TCP 20026200730) by AI.AI.MIT.EDU  5 Nov 87 10:31:44 EST
Date:     Thu, 5 Nov 87 10:26:29 EST
From:     Bernie Cosell <cosell@WILMA.BBN.COM>
To:       cube-lovers@AI.AI.MIT.EDU
cc:       jr@WILMA.BBN.COM, beeler@WILMA.BBN.COM, alatto@WILMA.BBN.COM
Subject:  Deluxe Magic

I picked up a "deluxe Rubik's Magic" at Games People Play the other day.
It is a twelve-square magic.  Has anyone solved this guy yet?  My wife
has been hacking on it some and and has managed to run it from the
starting state (2x6) to the target state (as in the normal Magic, but
moreso), but not enough comprehension of it all yet to get all the
circle pieces in the right places, yet.

It seems to be more fun that the normal magic because if you ignore
the circles you can make a bunch of interesting shapes (the big-hollow-
square was neat to blunder into).

  /Bernie\

ps, a while back someone (pete?) posted a pointer to some magazine (foreign,
maybe?) that had an article about folding a Magic into a cube.  I don't
remember if I've asked this before or not, but... can anyone send me hints
about how the fold-magic-into-a-cube goes?  tnx /b\

Received: from 40700016315 by AI.AI.MIT.EDU via Chaosnet; 5 NOV 87  13:08:11 EST
Received: by mit-nc.MIT.EDU with sendmail-5.31/4.7 
	id <AA03499@mit-nc.MIT.EDU>; Thu, 5 Nov 87 13:08:45 EST
Date: Thu, 5 Nov 87 13:08:45 EST
From: meister@mit-nc.MIT.EDU (phil servita)
To: cube-lovers@ai.ai.mit.edu
Subject: in search of...


I have been in search of anyplace in the USA where i can obtain a Skewb. 
So far, in about a year, no luck. Games of Berkeley keeps claiming that they
have an order in, but it never seems to get there.  Does anybody out there have
one that they would be willing to sell me? 

                                            -meister

(reply either to the list, or to meister@eddie.mit.edu)


Received: from WAIKATO.S4CC.Symbolics.COM (TCP 20024231532) by AI.AI.MIT.EDU  5 Nov 87 14:00:38 EST
Received: from ROCKY-MOUNTAINS.S4CC.Symbolics.COM by WAIKATO.S4CC.Symbolics.COM via CHAOS with CHAOS-MAIL id 141683; Thu 5-Nov-87 13:55:41 EST
Date: Thu, 5 Nov 87 13:55 EST
From: Allan C. Wechsler <ACW@WAIKATO.S4CC.Symbolics.COM>
Subject: Deluxe Magic
To: cosell@WILMA.BBN.COM, cube-lovers@AI.AI.MIT.EDU
cc: jr@WILMA.BBN.COM, beeler@WILMA.BBN.COM, alatto@WILMA.BBN.COM
In-Reply-To: The message of 5 Nov 87 10:26 EST from Bernie Cosell <cosell@WILMA.BBN.COM>
Message-ID: <871105135516.1.ACW@ROCKY-MOUNTAINS.S4CC.Symbolics.COM>

    Date:     Thu, 5 Nov 87 10:26:29 EST
    From:     Bernie Cosell <cosell@WILMA.BBN.COM>

    I picked up a "deluxe Rubik's Magic" at Games People Play the other day.
    It is a twelve-square magic.  Has anyone solved this guy yet?  My wife
    has been hacking on it some and and has managed to run it from the
    starting state (2x6) to the target state (as in the normal Magic, but
    moreso), but not enough comprehension of it all yet to get all the
    circle pieces in the right places, yet.

Well, /my/ wife solved it. 

    It seems to be more fun that the normal magic because if you ignore
    the circles you can make a bunch of interesting shapes (the big-hollow-
    square was neat to blunder into).

You bet!  As a matter of fact the order-6 puzzle is so much more fun 
than the order-4 that I am wondering whether higher orders might be 
even more fun.  In my opinion the order-4 cube was /less/ fun than the 
order-3, and it's a pleasure to see a puzzle where bigger really is
better.

Jenny and I have a conjecture that if a given flat shape is possible,
a flat shape that is derived from the possible one by moving a single
square one step diagonally -- is impossible.  There is probably a parity
argument lurking somewhere that can prove this.

Is a similar puzzle with triangular tiles possible?


Received: from WAIKATO.S4CC.Symbolics.COM (TCP 20024231532) by AI.AI.MIT.EDU  5 Nov 87 17:01:13 EST
Received: from ROCKY-MOUNTAINS.S4CC.Symbolics.COM by WAIKATO.S4CC.Symbolics.COM via CHAOS with CHAOS-MAIL id 141683; Thu 5-Nov-87 13:55:41 EST
Date: Thu, 5 Nov 87 13:55 EST
From: Allan C. Wechsler <ACW@WAIKATO.S4CC.Symbolics.COM>
Subject: Deluxe Magic
To: cosell@WILMA.BBN.COM, cube-lovers@AI.AI.MIT.EDU
cc: jr@WILMA.BBN.COM, beeler@WILMA.BBN.COM, alatto@WILMA.BBN.COM
In-Reply-To: The message of 5 Nov 87 10:26 EST from Bernie Cosell <cosell@WILMA.BBN.COM>
Message-ID: <871105135516.1.ACW@ROCKY-MOUNTAINS.S4CC.Symbolics.COM>

    Date:     Thu, 5 Nov 87 10:26:29 EST
    From:     Bernie Cosell <cosell@WILMA.BBN.COM>

    I picked up a "deluxe Rubik's Magic" at Games People Play the other day.
    It is a twelve-square magic.  Has anyone solved this guy yet?  My wife
    has been hacking on it some and and has managed to run it from the
    starting state (2x6) to the target state (as in the normal Magic, but
    moreso), but not enough comprehension of it all yet to get all the
    circle pieces in the right places, yet.

Well, /my/ wife solved it. 

    It seems to be more fun that the normal magic because if you ignore
    the circles you can make a bunch of interesting shapes (the big-hollow-
    square was neat to blunder into).

You bet!  As a matter of fact the order-6 puzzle is so much more fun 
than the order-4 that I am wondering whether higher orders might be 
even more fun.  In my opinion the order-4 cube was /less/ fun than the 
order-3, and it's a pleasure to see a puzzle where bigger really is
better.

Jenny and I have a conjecture that if a given flat shape is possible,
a flat shape that is derived from the possible one by moving a single
square one step diagonally -- is impossible.  There is probably a parity
argument lurking somewhere that can prove this.

Is a similar puzzle with triangular tiles possible?


Received: from ARDEC-LCSS.ARPA.ARPA (TCP 30003004013) by AI.AI.MIT.EDU 10 Nov 87 12:55:04 EST
Date: 10 Nov 87 12:26:00 EST
From: "CLSTR1::BECK" <beck@clstr1.decnet>
Subject: WORLD GAME REVIEW
To: "cube-lovers" <cube-lovers@mit-ai>
Reply-To: "CLSTR1::BECK" <beck@clstr1.decnet>

ARE THERE ANY SUBSCRIBERS TO THE WORLD GAME REVIEW (MIKE KELLER) OUT THERE.
IN PARTICULAR I'VE HEARD RUMORS THAT ISSUE #7 (ABOUT 6 MONTHS IN COMING) IS
OUT.  IS THIS TRUE?  ANYBODY SEEN IT?

PETE BECK  <PBECK@ARDEC.ARPA>

------

Received: from WILMA.BBN.COM (TCP 20026200730) by AI.AI.MIT.EDU 10 Nov 87 12:55:36 EST
Date:     Tue, 10 Nov 87 12:51:48 EST
From:     Bernie Cosell <cosell@WILMA.BBN.COM>
To:       cube-lovers@AI.AI.MIT.EDU
cc:        alatto@WILMA.BBN.COM, math@WILMA.BBN.COM, jr@WILMA.BBN.COM
Subject:  New "Recreations in Math" editions

Oxford U Press continues to produce entries in their "Recreations in
Mathematics" series.  I got #s 1 & 2 last year I just got vol 4.  I've
never seen vol 3.

To review, #1 was "Mathematical byways ..." by Hugh ApSimon.  I thought
it was BORING, but it did discuss one thing I've never seen: *how* you
set up a problem so it is both interesting and solvable.  He runs
through starting with some idea for a puzzle (something like the
"you put an X foot ladder up against a wall and it just touches a
box that is Y feet on a side, what's inside the box?") and gives the
"composer's problem" related to that topic: how to get the problem set
up.  Interesting, sort of, but overall pretty boring stuff (especially
since they are for the most part old, stuffy, dull problems).

#2: Ins and Outs of Peg Solitaire.  Really quite definitive reference
to the jump-the-pegs-and-leave-one-in-the-middle puzzle.  I can't remember
where, but I've actually seen most of that material before.  Maybe
Mathematics magazine, or JRM.  But in any event, this is a great book
if you're at all interested in this kind of problem.

#3: Rubik's Cubic Compendium, by Rubik, et al.  I've *never* seen this
anywhere.  I'd love to get/have/see a copy.  If any of you have a lead
to this guy, please let me know.

#4 Sliding Piece Puzzles (Hordern).  I just picked this up at the
Harvard Coop today.  Not much theory on either the design or solution
of this kind of puzzle.  Just page after page of example puzzles.  This
is more of a catalog than a math book.  One cute touch: there is a pocket
inside the back cover with push-out paper "shapes"   I guess that there
are enough miscellaneous shapes on the card (about 2"x4") so that you
can piece together a large number of the puzzles described in the
book.  My first impressions are that this book will be a definite
"Ho Hum".

  /Bernie\

Received: from BFLY-VAX.BBN.COM (TCP 20026200235) by AI.AI.MIT.EDU 10 Nov 87 14:59:58 EST
To: Bernie Cosell <cosell@cosell.bbn.com>
cc: cube-lovers@ai.ai.mit.edu, alatto@cosell.bbn.com, math@cosell.bbn.com, 
    jr@cosell.bbn.com, dm@bfly-vax.bbn.com
Subject: Re: New "Recreations in Math" editions
In-reply-to: Your message of Tue, 10 Nov 87 12:51:48 EST.
Date: 10 Nov 87 14:56:04 EST (Tue)
From: dm@bfly-vax.bbn.com


In Bernie's defense, I'll point out that he didn't name his machine
after himself -- it got named after him by the computer center staff,
who were installing workstations faster than we could think of
cute names for them, and adopted a simple, if boring algorithm for
coming up with machine names.



Received: from ARDEC-LCSS.ARPA.ARPA (TCP 30003004013) by AI.AI.MIT.EDU 17 Nov 87 18:36:50 EST
Date: 17 Nov 87 10:51:00 EST
From: "CLSTR1::BECK" <beck@clstr1.decnet>
Subject: CUBE DAY 87
To: "cube-lovers" <cube-lovers@mit-ai>
Reply-To: "CLSTR1::BECK" <beck@clstr1.decnet>

<><><><><><><><><><><><><><><><><><><><><><><><><><><><>
INVITATION   FROM  GUUS RAZOUX SCHULTZ
TO   ----->>  CUBE DAY  1987
..........................................
SAT 12 DEC 1987,  10AM - 17PM
AT:  GUUS RAZOUX SCHULTZ  -- RESIDENCE, PHONE 053-359617
       CORT VAN DER LINDENLAAN 30,
       ENSCHEDE, NETHERLANDS
<><><><><><><><><><><><><><><><><><><><><><><><><><><><>
PROGRAM:
  COMPETITIONS FOR CUBE AND MAGIC
  VIDEO SHOW ON PREVIOUS CUBE DAYS BY KLAAS STEENHUIS
  LECTURE ON GOD'S ALGORITHM BY GUUS RAZOUX SCHULTZ
  LECTURE ON THE SKEWB ??
  INTRO TO SUPER MAGIC (MASTER/GENUIS???) BY TOM VERHOEFF
  DEMO OF 6,10,16 PANEL MAGICS BY GUUS RAZOUX SCHULTZ
  
anyone who has interesting puzzles, books, articles, news, correspondence,
tables, posters, etc is asked:  please, don't hestitate to take it all with you!

Anyone who has computer programs for the cube, magic or other combinatorial
puzzles, please let us know what equipment is needed for demo.  

Anyone who has video tapes on puzzle events is also gladly invited! (We are
still looking for someone who has a recording of the MAGIC - championship.
...............................................................................
above received in mail.  If somebody out there stops in it would be great if
they take notes and post.

CUBING IS FOREVER!!!

PETE BECK
------

Received: from ARDEC-LCSS.ARPA.ARPA (TCP 30003004013) by AI.AI.MIT.EDU 10 Dec 87 10:54:43 EST
Date: 10 Dec 87 10:43:00 EST
From: "CLSTR1::BECK" <beck@clstr1.decnet>
Subject: WHO'S WHO OF PUZZLES
To: "cube-lovers" <cube-lovers@mit-ai>
Reply-To: "CLSTR1::BECK" <beck@clstr1.decnet>


COLLECTORS AND PUZZLE DESIGNERS WHO WISH TO BE INCLUDED IN AN UNOFFICIAL
DATABASE CAN SEND THEIR NAME AND ADDRESS AND PHONE NUMBER WITH A BRIEF DESCRIPTION OF THEIR PUZZLE INTEREST TO:

ROBERT HOLBROOK
5225 CARROLTON RD
ROCKVILLE, MD 20853.

THIS WILL GET YOUR NAME ARROUND AND YOU WILL PROBABLY RECEIVE JUNK MAIL FROM
PEOPLE SELLING PUZZLES.  TO THE BEST OF MY KNOWLEDGE THIS IS A HARDCOPY LIST.


THE FUTURE IS PUZZLING

PETE BECK

<PBECK@ARDEC>

------

Received: from ARDEC-LCSS.ARPA.ARPA (TCP 30003004013) by AI.AI.MIT.EDU 10 Dec 87 10:54:43 EST
Date: 10 Dec 87 10:43:00 EST
From: "CLSTR1::BECK" <beck@clstr1.decnet>
Subject: WHO'S WHO OF PUZZLES
To: "cube-lovers" <cube-lovers@mit-ai>
Reply-To: "CLSTR1::BECK" <beck@clstr1.decnet>


COLLECTORS AND PUZZLE DESIGNERS WHO WISH TO BE INCLUDED IN AN UNOFFICIAL
DATABASE CAN SEND THEIR NAME AND ADDRESS AND PHONE NUMBER WITH A BRIEF DESCRIPTION OF THEIR PUZZLE INTEREST TO:

ROBERT HOLBROOK
5225 CARROLTON RD
ROCKVILLE, MD 20853.

THIS WILL GET YOUR NAME ARROUND AND YOU WILL PROBABLY RECEIVE JUNK MAIL FROM
PEOPLE SELLING PUZZLES.  TO THE BEST OF MY KNOWLEDGE THIS IS A HARDCOPY LIST.


THE FUTURE IS PUZZLING

PETE BECK

<PBECK@ARDEC>

------

Received: from ARDEC-LCSS.ARPA.ARPA (TCP 30003004013) by AI.AI.MIT.EDU 10 Dec 87 16:11:44 EST
Date: 10 Dec 87 15:53:00 EST
From: "CLSTR1::BECK" <beck@clstr1.decnet>
Subject: cff #16
To: "cube-lovers" <cube-lovers@mit-ai>
Reply-To: "CLSTR1::BECK" <beck@clstr1.decnet>


SUBJECT :  Review of "Cubism For Fun" newsletter issue #16; the newsletter of
the "Dutch Cubists Club";  in english starting with issue 14 

1..  The table of contents for issue #16, NOV 87 follows (it is 8 double sided
folded 8 1/2 x 11 sheets, making a 32 page newsletter):

INVITATION TO "CUBISTS DAY"  BY Guus Schultz 
MY PATTERNS COLLECTION BY CECIL SMITH
THE UPPER TABLE AVERAGED BY BEN JOS WALBEEHM
PRETTY CUBIC PATTERNS BY ANNEKE TREEP 
PRETTY MAGIC STRUCTURES BY RONALD FLETTERMAN  
NOTES ON RUBIK'S MAGIC BY Guus Schultz 
RUBIKS MASTER MAGIC BY ED HORDERN
MINIMAL SOLUTIONS FOR THE 12-MAGIC BY TOM VERHOEFF 
MARC WETERMAN'S ALGORITHM , PART 3; CONTINUED FROM ISSUE 14/15 
                 - ANNEKE TREEP & MARC  WATERMAN
THE INVISIBLES B RONALD FLETTERMAN  
NEWS AND LETTERS TO THE EDITOR  
LIST OF MEMBERS

2.   Membership for 1987 is  US$5.   A photocopied set of the newsletters,
issues 1-13, written in DUTCH (in the future selected articles wy|l be available
in english) is also available for  US$7.    To order either of these send an
'INTERNATIONAL"  POSTAL MONEY ORDER to:  Anton Hanegraaf,  Heemskerkstraat, 
6662 AL ELST,  The Netherlands.

3.  If anybody would like further details please ask!

CUBING IS FOREVER      PETER BECK

<BECK@ARDEC-LCSS>  OR  <PBECK@ARDEC>

------

Received: from ARDEC-LCSS.ARPA.ARPA (TCP 30003004013) by AI.AI.MIT.EDU 11 Dec 87 10:39:46 EST
Date: 11 Dec 87 10:19:00 EST
From: "CLSTR1::BECK" <beck@clstr1.decnet>
Subject: jigsaws
To: "cube-lovers" <cube-lovers@mit-ai>
Reply-To: "CLSTR1::BECK" <beck@clstr1.decnet>


For puzzler's who like to plan ahead...d there will be a "JIGSAW" puzzle
exhibition in the summer of 1988.  It will be at:

Bates College Museum of Art,
Lewiston, Maine 04240 (I think)
May 19-Aug 12 1988.

The guest curator is:

Anne D. Williams
49 Brooks Ave
Lewiston, ME 04240.

The exhibit will have over 100 jigsaws in it, dating back to 1766.


The Future is Puzzling, 
but Cubing is Forever.

Pete beck                  <PBECK@ARDEC>
..................................



------

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[]

Please put me on the CUBE-LOVERS mailing list.

(Sorry if this goes to the whole list, but the -request address
does not seem to work!)

Thanks,
           Sergiu Hart
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Date: Sun, 27 Mar 88 16:33:28 EST
From: Alan Bawden <ALAN@AI.AI.MIT.EDU>
Subject:  Subscription
To: hart%TAURUS.BITNET@MITVMA.MIT.EDU
cc: CUBE-LOVERS-REQUEST@AI.AI.MIT.EDU, CUBE-LOVERS@AI.AI.MIT.EDU
In-reply-to: Msg of Sun 27 Mar 88 19:43:11 +0200 from hart%TAURUS.BITNET at MITVMA.MIT.EDU
Message-ID: <348312.880327.ALAN@AI.AI.MIT.EDU>

    Date: Sun, 27 Mar 88 19:43:11 +0200
    From: hart%TAURUS.BITNET at MITVMA.MIT.EDU
    Please put me on the CUBE-LOVERS mailing list.
    (Sorry if this goes to the whole list, but the -request address
    does not seem to work!)

Let's not start any rumors.  Cube-Lovers-Request works just fine.  I added
you to the list three days ago, and I mailed you an acknowledgment at that
time.  Perhaps some mailer between here and there ate my message for lunch,
but I certainly can't help that.  

Cube-Lovers is an extremely low-volume mailing list these days, so the fact
that your mailbox didn't immediately fill with Cube-Lovers mail means
nothing.  (The previous Cube-Lovers mail was sent last December 11th.)

Received: from ARDEC-AC4.ARPA (TCP 30003004020) by AI.AI.MIT.EDU 28 Mar 88 16:00:38 EST
Date:     Mon, 28 Mar 88 15:54:07 EST
From:     Peter Beck (LCWSL) <pbeck@ARDEC.ARPA>
To:       cube-lovers@AI.AI.MIT.EDU
Subject:  magic polyhedra
Message-ID:  <8803281554.aa20390@ARDEC-AC4.ARDEC.ARPA>

a puzzle fool's view of plate tectonics
by peter beck   april 1, 1988

what follows is an unfounded speculation of how "magig polyhedra" can be used to
understand the manifistations of plate tectonics.  my imagination was piqued
while manipulating the "megaminx" (a dodecahedron with flat pentagon shaped
faces, marketed in the usa by tomy) because the puzzle locks up when an attempt
is made to turn too many faces simultaneously.  this causes the surface to
distort and when too much force is excerted the puzzle comes apart in an
explosive fashion.  

i, impusively concluded that the geometric principles governing this explosion
are analogous to what happens when the surface plates of the earth are rotated
by the forces behind plate tectonics.  this analogy is useful because it
provides a macro model with physical parity constraints to study plate
tectonics, eg, by helping forecasters tie together observable events around the
world a better understanding of individual events could be obtained.  another
area of study could be the parity constraints on the motion of the plates, ie, 
the directions of plate rotation are constrained by their neighbors, because
each plate does not move independently (see fig. 465.10 in fuller's book
"synergetics").   [it should be noted that other dodecahedron magic polyhedra
may be more appropriate for the study of plate tectonics; ie, the "impossiball"
or 'alexander's star".]

now that my fantasizing is in high gear i will expand my speculation to consider
the engine that drives plate tectonics.  i have decided that if one knew some
physics it could probably be shown that a rotating sphere with a liquid center
would develop 12 local circulations which the surface plates would float on. 
thus, plate tectonics can on a macro scale be reduced to a simple problem of
fluid dynamics and some geometric parity constraints which can be displayed with
magic polyhedra.

the future is puzzling, but cubing is forever !!


distribution:
   cff
   wgr
   cube-lovers@mit

Received: from WAIKATO.S4CC.Symbolics.COM (TCP 20024231532) by AI.AI.MIT.EDU 28 Mar 88 16:50:43 EST
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Date: Mon, 28 Mar 88 16:48 EST
From: Allan C. Wechsler <ACW@WAIKATO.S4CC.Symbolics.COM>
Subject: Magic Polyhedra and parity constraints
To: Cube-Lovers@MIT-AI.ARPA
Message-ID: <19880328214819.9.ACW@ROCKY-MOUNTAINS.S4CC.Symbolics.COM>

In response to Peter Beck's thought-provoking idea about connecting
Rubikoid puzzles to plate tectonics, I have two slight spoilers.

First, plate tectonics involves spreading zones, which are places where
new crust is created, and subduction zones, where crust is destroyed.
In any permutation group, the things being permuted are not allowed to
appear or disappear.  So it seems unlikely that group theory can be
directly applied to tectonics.

Second, just because a puzzle is Rubikoid does not mean it has parity
constraints.  Consider the "Magic Octohedron", which has eight
triangular faces.  You can grab any pyramidal cluster of four faces and
rotate it.  This is really the 2x2x2 Cube in disguise.  In this form, it
has no parity constraints, that is, all the 8-factorial different
configurations are achievable.  So even if group theory could be applied
to tectonics, we couldn't assume parity constraints in the general case.



Received: from ardec-lcss.arpa (TCP 30003004013) by AI.AI.MIT.EDU  2 May 88 13:29:41 EDT
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       Mon,  2 May 88 13:29:02 EST
Date: Mon,  2 May 88 13:28:09 EST
From: BECK@ardec-lcss.arpa
Subject: new puzzles
To: cube-lovers@ai.ai.mit.edu
X-VMS-Mail-To: EXOS%"cube-lovers@mit-ai"
Message-ID: <880502132809.202004A3041@ardec-lcss.arpa>


I VISITED BY "KAY-BEE" toy store at the mall today.  


REPEAT:  For those of you who like 3-d assembly puzzles a set of 2 GEO-LOGIC
(TAURUS&CETUS) puzzles for $7 .   These puzzles are plastic, and were designed
by Stuart Coffin and manufactured by Skor-Mor (OUT OF BUSINESS).   The full
collection of these puzzzles is called the GEO-LOGIC series.  They are each made
of 6 identical pieces (different for each puzzle) that can be assemblied into an
interlocking self supporting solid.   These puzzles are hard to find.   So if
you may be interested don't delay - call up your KAY BEE now.

NEW FOR 1988
  GRIPPLE as seen on TV for $10.  This is a sequential movement puzzle more
similar to missing link then the cube.

  YOSHI'S (shortening of designers name) PUZZLE for $12 from Parker Bros.  This
is a re-release of a formerly unbranded item, circa 1982 called miraculous cube.
 It is composed of a loop of tetrahedrons taped together to form hinges.   Yoshi
designed/invented two puzzles like this. The other is called the Shisei Mystery
and it works like a Rubik's magic with depth.

  Mattel has a cube puzzle made up of magnetic cubies called "Magic Force" 
I think.  not at kay-bee.
 

The Future is Puzzling, 
but Cubing is Forever.

Pete beck                  <PBECK@ARDEC>
..................................

Received: from ardec-lcss.arpa (TCP 30003004013) by AI.AI.MIT.EDU  5 May 88 09:22:15 EDT
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       Thu,  5 May 88 09:20:50 EST
Date: Thu,  5 May 88 09:20:15 EST
From: BECK@ardec-lcss.arpa
Subject: JIGSAW PUZZLE EXHIBIT
To: CUBE-LOVERS@ai.ai.mit.edu
X-VMS-Mail-To: EXOS%"CUBE-LOVERS@MIT-AI"
Message-ID: <880505092015.2100026E041@ardec-lcss.arpa>


UPDATE:    The "Jigsaw" puzzle exhibition will be May 19 - Aug 12, 1988.   There
will be an open house Sunday 22 May.  

It will be at the:
    Museum of Art, Olin  Arts Center, Bates College
    Lewiston, Maine 04240 

Exhibit/museum hours:
    Tuesday - Sat, 10-4PM
    Sunday  1-5PM
    Closed Mondays and holidays.

The guest curator is:
     Anne D. Williams
     49 Brooks Ave
     Lewiston, ME 04240.

The exhibit will have over 100 jigsaws in it, dating back to 1766.


The Future is Puzzling, 
but Cubing is Forever.

Pete beck                  <PBECK@ARDEC>
..................................

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       Thu, 19 May 88 12:27:29 EST
Date: Thu, 19 May 88 12:26:10 EST
From: BECK@ardec-lcss.arpa
Subject: cube museum
To: cube-lovers@ai.ai.mit.edu
X-VMS-Mail-To: EXOS%"cube-lovers@mit-ai"
Message-ID: <880519122610.2020087F051@ardec-lcss.arpa>


-->   CUBE  MUSEUM  <--

On April 29, 1988 a museum devoted to Rubik's cube opened in  Grand Junction,
CO.   The museum is run by  Cecil Smith and is located in his home at 329 Ouray
Ave;  245-6734.

Cecil is primarily a documentor of pretty patterns and has 4,900 cubes in his
collection.  SO when in Grand Junction don't miss this one of a kind museum.  If
you know of or have something that should be in this museum please contact
Cecil.

REFERENCE:  The front page of the May 1, 1988  issue of the Grand Junction, Co
Daily Sentinel (Vol 96, No 153).

the future is puzzling,
but  CUBING is forever !!

pbeck@ardec.arpa

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[]

Please put me on the CUBE-LOVERS mailing list.

Thank you,
           Sergiu Hart
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       Fri,  3 Jun 88 09:59:01 EST
Date: Fri,  3 Jun 88 09:56:08 EST
From: BECK@ardec-lcss.arpa
Subject: cube memorabilia
To: cube-lovers@ai.ai.mit.edu
X-VMS-Mail-To: EXOS%"cube-lovers@mit-ai"
Message-ID: <880603095608.2080015B041@ardec-lcss.arpa>

Hi CUBE-LOVERS,

I am a "collector" of Rubik's cubes and other magic polyhedra.  As a
collector I am not only interested in the puzzles themselves but also
in the literature about them, the packaging of them and the
merchandise/events that traded on the popularity of the cube.    Below
is a crude taxonomy with  items I have identified.  I would appreciate
criticism of the taxonomy and additions to the specific items . 
 Also, if anybody has or knows where to obtain any items of this genre
please let me know.   Since I am not personally a collector of most
books, articles or solution algorithms about the cube (Bandelow, Helm,
Singmaster, et al are doing that) please do not provide citations
unless they are especially noteworthy.

TAXONOMY for RUBIK'S CUBE ITEMS (5/26/88 REV)

0.  CUBE PATENTS
0.1  US PATENT#3,081,089,  william Gustafson, 1958
0.2  Frank Fox, 1970
0.3  US PATENT#  , LARRY Nichols, 1972  
0.4  HUGARIAN PATENT, ERNO RUBIK, 1975
0.5  JAPANESE PATENT,  Terutoshi Ishige, 1976

1.  RUBIKOID PUZZLES - see photo on page 138/139 of "PUZZLES OLD &
NEW"  (PON) by Jerry Slocum & Jack Botermans

2.  CUBE EPHEMERA  -   
2.1 ADVERTISING - 
2.1.1  counter display boxes; I have for 20mm keychain size cubes and
for the 3x3x3, Rubik's Revenge, Alexander's Star, and Missing Link ITC
solution books.
2.1.2 CATALOGS & FLYERS
2.1.2.1 BANDELOW'S CATALOG
2.1.2.2 MEFFERT'S FLYERS
2.2 PACKAGING -
2.2.1  cardboard diplay box used by ITC for original cube shrink
wrapped
2.2.2  clear plastic display cylindrical dome for black plastic base
used by ITC for DELUXE cube
2.3  ANNOUNCEMENTS OF CUBE RELATED EVENTS, EG, CONTESTS,  CONFERENCES,
2.3.1  A contest announcement -> BUDAPEST INTERNATIONAL - HAVE A GO  
  WITH RUBIK, CHALLENGE THE WORLD CHAMPION, it also has a photo Rubik
holding a cube and one of Singmaster wearing a cube T-shirt; OBTAINED
FROM DAVID SINGMASTER
2.3.2  1987 (11/18-11/28) puzzle exhibition (expsoition casse-tete) by
Marcel Gillen & Carlo Gitt in Luxembourg

3.  BOOKS - not my area of interest

4.  ARTICLES - not my area of interest

5.  CLUBS/NEWSLETTERS/MUSEUM/EXHIBITS
5.1   On April 29, 1988 a museum devoted to Rubik's cube opened in
 Grand Junction, CO.   The museum is run by  Cecil Smith and is
located in his home at 329 Ouray Ave;  245-6734.   REFERENCE:  The
front page of the May 1, 1988  issue of the Grand Junction, Co Daily
Sentinel (Vol 96, No 153).Press release of opening
5.2  Wally Webster's exhibit in Kirkland, WA.  Press release of

6.  SOLUTION ALGORITHMS INCLUDING COMPUTER PROGRAMS
6.1  A 33RPM LP record with a solution to the cube:  "How to Solve the
Cube Puzzle", The Marko Van Eckelen's Method - Guiness 36 second
record holder; Gateway Records (GSLP-4506)^), GENCOM INC, POB 5087,
FDR STATION, NY, NY 10150
6.2  COMPUTER PROGRAMS
6.2.1  cartridge for RADIO SHACK TRS-80 microcomputer called "COLOR
CUBES";  sold with the cartridge, book, and keyboard cover.

7.   PRETTY PATTERNS

8.  CUBE ACCESSORIES  -  
8.1 REPLACEMENT STICKERS
8.1.1 cube covers; PON
8.1.2 CUbe Mates (Cinderella Co., POB 265, Skykesville, MD 21784) is a
set of 54 lettered stickers to put on your cube in order to play word
games;  CC# 5&6, pg 5
8.1.3  (Eidolon LTD, Vancouver V6B 3X9); a)  computer font numbers,
 b) solid silver foil
8.1.4  (Steven Mfg Co, Hermann MO 65041); large selection
8.2 REPAIR/BUILD-A-CUBE KIT; PON

9.  FAN ITEMS  -  

9.1  DECALS - 
9.1.1  An oval shaped 5"x3" decal with a picture of the cube in the
center, saturn on the left, earth on the right and written at the top
is "I do the cube" and at the bottom "RUBIK'S CUBE CLUB"; OBTAINED
FROM DAVID SINGMASTER in 1986
9.1.2  A sticker of the cube approximately 1 1/2" by SANDYLION, 340
Alden road, Markham, Ontarion, Canada L3R 4C1,  416/475-0554.
9.2  A thin rubberized magnet approximately 1 1/2".
9.3  CAR STRIPS - A car strip (goes on inside of window) that says
'CUBISTS DO IT IN 52 MOVES"; OBTAINED FROM DAVID SINGMASTER in 1986
9.4  BUMPER STICKERS
9.5  BUTTONS- I "heart" Rubik's cube & buttons with sayings and
pictures of cubes from Singmaster in 1986;  PON
9.6  Hungarian POSTAGE STAMP & FIRST DAY COVER (6/4/82), PON &CC# 5&6,
pg 28
9.7  CLOTHING  - 
9.7.1  A childs Tee shirt with a picture of a cube above which is
 written 'RUBIK'S CUBE"; OBTAINED FROM DAVID SINGMASTER in 1986
9.7.2  A mans necktie; black with a cube on it;  PON
9.7.3  A childs halloween costume, size large (12-14), fits an 8-10
year old, from Collegeville Flag & MFG Co., Collegville, PA 19426 (I
have some for trade)
9.7.4  Sew on patch from ITC cube club; PON
9.8  Ink stamp - I have a rubber ink pad stamp of a cube
9.9  POSTER OF THE JIGSAW PUZZLE
9.10  CUBE IN BOTTLE; PON
9.11  CUBE SMASHER; PON
9.12  UTILITARIAN ITEMS TRADING ON CUBE -  
9.121 COASTERS - A set of coasters to put glasses on:  Six 3"x3"
lucite pieces with 9 silk screened squares each colored one of the
colors of a cube, comes in a lucite holder and is called "Cubics
Coasters in Six Winning Colors", a quality product from Caryl Craig
Studios, c 1982, Box 2221 Sepulveda, CA 91343 (I got mine from Greg
Stevens in 1987)
9.12.2  PENCILS with I "heart" Rubik's cube printed on them; PON
9.12.3  SHOELACES in both 27" & 40" lengths made in Taiwan for
Goodties of LA, CA.  Imprinted with a solution algorithm (Greg Stevens
has for trade)
9.12.4  LUNCH BOXES
9.12.5  BOOK BAGS - I have a red canvas briefcase type bag
9.12.6  COFFEE CUPS
9.12.6.1  "IT'S A Mugs GAme",  plain white mug with decals pasted