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From: rice@ernie.Berkeley.EDU (Daniel S. Rice)
Newsgroups: sci.math,comp.theory
Subject: Re: Rubik's Cube Problem
Message-ID: <33312@ucbvax.BERKELEY.EDU>
Date: 19 Dec 89 21:13:10 GMT
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Reply-To: rice@ernie.Berkeley.EDU.UUCP (Daniel S. Rice)
Organization: University of California, Berkeley
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>  == Mike Schilling
>> == 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?
>> 
>No, there's three kinds of *parity* preserved by any legal move:
[ Argues correctly that cube positions fall into 12 orbits]

	Mike's response correctly notes that *switching positions
of cubies* can result in 11 families of unsolvable cubes.  The original
post asked about moving *stickers*.  Clearly, there must be one side
cubie that is blue and red, one that is blue and green, etc., etc.,
for the puzzle to even make sense.  A corner cubie that is, say, all
orange can never be part of a solved cube.  So, strictly speaking, there
are many more than 11 unsolvable cube families if replacement of stickers
is allowed.  I suppose this is a nitpick but it seemed as if others
were answering the wrong (but mathematically much more interesting)
question.

						Dan