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From: rener@cs.eur.nl (Rene Roelofs)
Newsgroups: comp.graphics
Subject: Re: Rubiks Cube
Message-ID: <1989Dec5.090928.9422@cs.eur.nl>
Date: 5 Dec 89 09:09:28 GMT
References: <256@<4382> <207400039@s.cs.uiuc.edu> <17537@netnews.upenn.edu> <24647@cup.portal.com> <1149@m3.mfci.UUCP>
Organization: Erasmus Universiteit Rotterdam, dept. CS (Informatica)
Lines: 40


murphy@mfci.UUCP (Tom Murphy) writes:
>Intuitive Justification for numerical claims => 
>	1) There are eight corners which gives 8!=40,320 permutations of 
>	   where they can be.
>	2) Each corner has three positions it can be in one of which are 
>	   correct. Positioning seven turns out to automatically position 
>	   the eigth. Thus have 3^7=2187 different orientations of the
>	   corners.
>	3) This leaves placing the 12 edge blocks in the correct 
>	   position. It turns out there are 12!/2=239,500,800 different
>	   permutations of them. 
>	4) There are two positions  each of the edge blocks can be in.
>	   Positioning 11 automatically positions the twelfth. Thus we 
>	   have 2^11=2048 different orientations of the edges.
>	5) Each of the six centers of the faces can be in one of four 
>	   positions. It turns out there are 4^6/2 = 2048 different ways
>	   to orient them.

>(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 :-))).

 
 
 

-- 
    |-----\                        Rene Roelofs 
    |     |                        Dept. of Computer Science
   /|-----/                        Erasmus University Rotterdam, The Netherlands
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