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From: hoey@ai.etl.army.mil (Dan Hoey)
Newsgroups: sci.math,comp.theory
Subject: Re: Rubik's Cube Problem
Summary: Not bloody likely
Message-ID: <385@ai.etl.army.mil>
Date: 21 Dec 89 01:08:40 GMT
References: <5310@garfield.MUN.EDU> <4330@rtech.rtech.com>
Reply-To: hoey@ai.etl.army.mil (Dan Hoey)
Organization: Naval Research Lab, Washington, DC
Lines: 26

From article <5310@garfield.MUN.EDU>, by chris2@garfield.MUN.EDU (Chris Paulse):
> If I had a solved Rubik's cube, and the colors on each face were
> just stickers on the black plastic surface, if I exchanged some
> of the stickers, would the cube still be solvable in the normal way?

The probability, given an arrangement of the 54 stickers chosen uniformly from
the 54! possible permutations, is

      6     8     12
    9!  6! 3  8! 2   12!            40,122,452,017,152
    -------------------- = ---------------------------------------
           54! 12          130,253,249,618,151,492,335,575,683,325

                                         -16
                         = approx 3.08 10


The way this works is that there are 9!^6 6! ways of putting the stickers on so
that the cube is already solved, and 3^8 8! 2^12 12!/12 - 1 unsolved cubes
corresponding to each solved cube.

Previous posters answering ``1/12'' are responding to the question, ``if I put
the twelve edge pieces and eight corner pieces of a Rubik's cube together at
random, would it then be solvable in the normal way?

Dan