From cube-lovers-errors@mc.lcs.mit.edu Fri Nov 26 17:37:28 1999 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id RAA13196 for ; Fri, 26 Nov 1999 17:37:28 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <381F6399.811C15C8@pressenter.com> Date: Tue, 02 Nov 1999 16:20:09 -0600 From: Joe Johnson To: David Singmaster Cc: cube-lovers@ai.mit.edu Subject: Re: 5X5X5 challenge References: <009E0848.8EC8F5C8.5@ice.sbu.ac.uk> David Singmaster wrote: > On 22 Sep, Dan sais one would discover something interesting > about the central pieces of the 5^3. I think this result is > entirely obvious once one thinks about the mechanics of these cubes. > DAVID SINGMASTER, Professor of Mathematics and Metagrobologist I'm not sure what you and Dan have discovered. [ Moderator's Note: I should have been less coy. I thought Joe Johnson might not have discovered that the supergroup contains positions in which a face center is rotated 180 degrees. I still think this is surprising. It's so easy to rotate the face centers by an amount adding up to an integral number of 360-degree rotations (see 9 January 1981 in the archives). Does anyone have a short process for rotating two face centers 90 degrees clockwise? --Dan ] What I have found is that the cross cubies and wing cubies are both involved in parity problems. i.e. if you repair the parity of the cross cubies then there will be no parity problems with the wing cubies, if you leave the parity problem with the cross cubies then there will be a parity problem with the wing cubies. One fix repairs both. The point cubies and edge cubies never have parity problems; simple 3 cubie exchanges are all that are necessary to place the point cubies (the only cubies that require orientation are the face, corner, and edge cubies - the others are automatically oriented correctly when they are placed correctly.)