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Date: Wed, 5 Jun 1996 22:22:26 -0400
From: Jim Mahoney <mahoney@marlboro.edu>
Message-Id: <199606060222.WAA13586@ marlboro.edu>
To: hoey@aic.nrl.navy.mil
Cc: cube-lovers@ai.mit.edu
In-Reply-To: <9606052254.AA22046@sun34.aic.nrl.navy.mil> (hoey@AIC.NRL.Navy.Mil)
Subject: Re: A essay on the NxNxN Cube : counting positions and solving it


>>>>> "hoey" == hoey  <hoey@AIC.NRL.Navy.Mil> writes:
    hoey> When we take account of the internal cubies I call it the
    hoey> "Theoretical Invisible cube", described in my Invisible
    hoey> Revenge article 9 August 1982.  A solution method is given
    hoey> in
    hoey> 	Eidswick, J. A., "Cubelike Puzzles -- What Are They
    hoey>       and How Do You Solve Them?", 'American Mathematical
    hoey>       Monthly', Vol. 93, #3, March 1986, pp. 157-176.

Thanks for the references.  I haven't seen Eidswick's paper yet,
but will check it out.

    hoey> As for counting the positions, I haven't got around to
    hoey> checking the numbers in "Groups of the larger cubes", 24 Jun
    hoey> 1987.  You might want to see how they compare to yours.

I just did, and for the specific case that I describe (which is "s:
Supergroup, i: theoretical invisible group") the formulas are exactly
the same.  I didn't consider nearly the range of alternatives discussed
in that article, but its nevertheless nice to see a confirmation of
the results.

Regards,

  Dr. Jim Mahoney                          mahoney@marlboro.edu
  Physics & Astronomy
  Marlboro College, Marlboro, VT  05344