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From: SCHMIDTG@iccgcc.cle.ab.com
Date: Mon, 1 Sep 1997 16:46:33 -0400 (EDT)
To: cube-lovers@ai.mit.edu
Message-Id: <970901164633.20217b13@iccgcc.cle.ab.com>
Subject: Re[2]: Open and Closed Subgroups of G
Oh, and I forgot to mention...
My ultimate goal of understanding parity would be such that someone could
hand me an arbitrary permutation puzzle and I'd be able to examine it and
determine from the set of legal moves both the parity constraints and also
be able to construct a parity test valid from any given puzzle state.
I find it interesting that the method seems to differ across puzzles.
For example, 15 puzzle parity can be determined by the number of pairwise
exchanges required to solve the puzzle, whereas with the cube, it seems
a more direct approach is possible by examining cubie orientations with
respect to marked cubicles.
Still, I'm somewhat mystified.
Regards,
-- Greg Schmidt