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Date: Tue, 3 Dec 1996 11:18:42 -0500
From: der Mouse <mouse@holo.rodents.montreal.qc.ca>
Message-Id: <199612031618.LAA12721@Collatz.McRCIM.McGill.EDU>
To: edwards@city-net.com
Subject: Re:  Rubic's Revenge
Cc: cube-lovers@ai.mit.edu

> Does a 5x5 matrix Rubic's [sic] cube exist?  I think I know the
> general solution, as an extrapolation from the solution to a 4x4.

Yes, a 5-Cube exists; I own one.  And yes, if you can solve the 3-Cube
and the 4-Cube, no higher order presents any qualitatively new
challenges to a human.  In theory, the 6-Cube would, because it's the
first one that has one-visible-face cubies that are not on a plane of
symmetry.  The 5-Cube has a 3x3 grid of one-face cubies on each face,
but they are all either (a) face center, (b) non-(a) center slice, or
(c) non-(a) face diagonal.  On the 4-Cube, the four one-face cubies are
all face diagonal, and on the 3-Cube, there's only one (face center)
one-face cubie.  However, at least based on my own experience, I
believe that these new cubies on the 6-Cube will not add any additional
challenge - the one-face cubies are one of the easiest parts of the
cube anyway, and the same basic operations that work for the (c) cubies
on the 4-Cube (and the (b) and (c) cubies on the 5-Cube) will work
equally well for these new cubies.

Incidentally, does anyone know if a physical 6-Cube has ever been made?
If so, and it's not too outrageously priced, I'd be interested in
buying one.

					der Mouse

			       mouse@rodents.montreal.qc.ca
		     7D C8 61 52 5D E7 2D 39  4E F1 31 3E E8 B3 27 4B