From kon@bach.stanford.edu  Tue May 14 21:14:14 1991
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Date: Tue, 14 May 91 18:14:11 PDT
From: kon@bach.stanford.edu (Ronnie Kon)
Message-Id: <9105150114.AA00195@bach.Stanford.EDU>
To: mindcrf!ronnie@peabody.mindcraft.com, ncramer@bbn.com
Subject: Re:  5by cubes
Cc: cube-lovers@life.ai.mit.edu

>>	I suspect this is why there are (and will probably never be) cubes of
>>orders greater than 5.  I believe (though have not proved) that the 5 cube 
>>contains all the complexity that is possible.  Adding more cubies would only
>>increase the amount of time needed to solve.
>
>On the other hand, a 5X (or any cube of odd order) will still have the
>constraints imposed by a fixed center.  As a single example, the 4X here in
>my office is completely "solved" except that two opposite corners are
>swapped.  That's not something that can happen on a cube of odd order (at
>least I don't think so, but I would love to be proved wrong ;).

Wow!  I could have sworn I have gotten to this position before, but you are
very definitely correct.  The state with two diagonal corners swapped is in
the orbit with edge cubies exchanged.

				Ronnie