> < ^ Date: Tue, 22 Aug 1995 09:20:00 +0100 (WET)
> < ^ From: Martin Schoenert <martin.schoenert@math.rwth-aachen.de >
> < ^ Subject: Re: Rubik's Cube

Istvan T. Hernadvolgyi wrote in his e-mail message of 1995/08/15

I recently downloaded and installed gap. I do not know too much about the
package, but I would like to use it to develop algorithms to solve the
Rubik's Cube and similar puzzles. I would appreciate if someone could
provide a little help, especially if someone already programmed the Cube
or something similar in gap.

A representation of Rubik's cube as permutation group can be found in our
``README'' file. With this representation one can use GAP to find out
various group theoretical facts about Rubik's cube.

GAP can also find processes for elements (i.e., which faces one must turn
to reach a certain state). The best GAP package for this taks that I'm
aware of is Philip Osterlund's 'AbStab' (which can be found on our FTP
server 'ftp.math.rwth-aachen.de' in the directory 'pub/incoming/').
However GAP is not really well suited to find short (let alone shortest)
processes for elements of Rubik's cube.

The best algorithms to find short processes and/or to prove upper and
lower bounds on the diameter of the Cayley graphs of Rubik's cube group
have been implemented (usually as standalones in C) by members of the
Cube-Lovers mailing list. I suggest that you subscribe to this mailing
list (via e-mail to 'Cube-Lovers-Request@ai.mit.edu'), and check out the
archives of this mailing list (via FTP to 'ftp.ai.mit.edu' in directory
'pub/cube-lovers', or via WWW on 'http://WWW.Math.RWTH-Aachen.DE:8000/


-- .- .-. - .. -.  .-.. --- ...- . ...  .- -. -. .. -.- .-
Martin Sch"onert,   Martin.Schoenert@Math.RWTH-Aachen.DE,   +49 241 804551
Lehrstuhl D f"ur Mathematik, Templergraben 64, RWTH, 52056 Aachen, Germany

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