From cube-lovers-errors@curry.epilogue.com Wed Jun 5 19:51:48 1996
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Date: Wed, 5 Jun 96 18:54:44 EDT
From: hoey@aic.nrl.navy.mil
Message-Id: <9606052254.AA22046@sun34.aic.nrl.navy.mil>
To: Jim Mahoney
Cc: Cube-Lovers
Subject: Re: A essay on the NxNxN Cube : counting positions and solving it
> All the
> real mechanical 3x3x3, 4x4x4, 5x5x5 Cubes that I've seen only have
> cubies on the outside, but if you can put back all N^3 cubies in the
> one I'm describing then you can certainly do the real ones.
> (In Dan Hoey's notation, I believe that this means I treat the Cube as
> the G+C group, where G is generated by the outer slice rotations, and
> C is the rotations of the entire thing....
Actually, the distinction between G and G+C is that in the latter we
draw a distinction between cubes that differ by a whole-cube move as
different.
When we take account of the internal cubies I call it the "Theoretical
Invisible cube", described in my Invisible Revenge article 9 August
1982. A solution method is given in
Eidswick, J. A., "Cubelike Puzzles -- What Are They
and How Do You Solve Them?", 'American Mathematical
Monthly', Vol. 93, #3, March 1986, pp. 157-176.
that is pretty much like yours, I think.
As for counting the positions, I haven't got around to checking the
numbers in "Groups of the larger cubes", 24 Jun 1987. You might want
to see how they compare to yours.
Dan Hoey
Hoey@AIC.NRL.Navy.Mil