From cube-lovers-errors@mc.lcs.mit.edu Fri Nov 26 17:37:28 1999
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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.)