Path: utzoo!attcan!utgpu!jarvis.csri.toronto.edu!cs.utexas.edu!uunet!mfci!murphy
From: murphy@mfci.UUCP (Tom Murphy)
Newsgroups: comp.graphics
Subject: Re: Rubiks Cube
Message-ID: <1154@m3.mfci.UUCP>
Date: 6 Dec 89 19:13:49 GMT
References: <256@<4382> <207400039@s.cs.uiuc.edu> <17537@netnews.upenn.edu> <24647@cup.portal.com> <1149@m3.mfci.UUCP> <1989Dec5.090928.9422@cs.eur.nl>
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Reply-To: murphy@mfci.UUCP (Tom Murphy)
Organization: Multiflow Computer Inc., Branford Ct. 06405
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In article <1989Dec5.090928.9422@cs.eur.nl> rener@cs.eur.nl (Rene Roelofs) writes:
>murphy@mfci.UUCP (Tom Murphy) writes:
>>(40,320)(2,187)(239,500,800)(2028) = 43,252,003,274,480,856,000 possible
>>permutations if we are unconcerned about the orientation of the center, 
>>which is true for non-logo'd cubes.
>
>Not exactly true! If you take the cube and turn around say one corner
>(by breaking it out and replacing it again) then it is not possible to
>solve the puzzle.
>Therefore the permutation are less. ( I'm not gonne give a correct list )
>And so the solving on a computer with the assumed speed should go faster, 
>maybe it is when you leave all the 'wrong' permutations out, it is possible
>to solve in in less then ONE MILLION YEARS :-))).

And maybe not :-) .
The numbers I stated were for different valid positions. Physically altering 
locations of cubes can make solution time quite long :-). 
Most of the factors in the above expression are smaller than what they would
be if you allowwed use of a screwdriver in the solution of the cube. It may
be faster (and more straightforward) to solve the Towers of Hanoi than
to brute force the cube.
Tom Murphy                        internet: murphy@multiflow.com
Multiflow Computer, Inc.          uucp:     uunet!mfci!murphy
12 Del Rio Ct                     fax:      (415) 943-1574 (call voice first)
Lafayette, CA 94549               voice:    (415)943-6293