From ronnie@cisco.com  Fri Jul 30 00:46:55 1993
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To: Cube-Lovers@life.ai.mit.edu
Subject: Re: Hint wanted for 4x4x4 
Date: Thu, 29 Jul 1993 21:46:48 -0700
From: "Ronnie B. Kon" <ronnie@cisco.com>

Thanks to all who responded.  I haven't yet got what I consider a
solution for my problem (shift a slice and resolve is my current
method which is slow and ugly) but at least I understand my problem
slightly better.

A few questions:

1.  What is the definition of parity by which commutators are even,
but slice turns are odd?  I haven't been able to come up with a
cube-wide parity.  (I know no group theory).

2.  How many orbits does the order 4 cube have?  I can only think of
three (twirling a corner cubie).  Then again, I haven't painted the
facelets yet, so there could be orbits I haven't begun to see
involving them.

3.  Would an order 6 cube have any challenge beyond the order 4?  I
think the answer is no--if you are able to solve the 3-cube and the
4-cube you can solve any cube.