From cube-lovers-errors@mc.lcs.mit.edu Mon Sep 1 23:26:56 1997 Return-Path: Received: from sun30.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.1/mc) with SMTP id XAA05957; Mon, 1 Sep 1997 23:26:56 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Mail-from: From SCHMIDTG@iccgcc.cle.ab.com Mon Sep 1 16:50:08 1997 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