From cube-lovers-errors@curry.epilogue.com Wed Jun 5 19:51:48 1996 Return-Path: cube-lovers-errors@curry.epilogue.com Received: from curry.epilogue.com (localhost [127.0.0.1]) by curry.epilogue.com (8.6.12/8.6.12) with SMTP id TAA07836 for ; Wed, 5 Jun 1996 19:51:47 -0400 Precedence: bulk Errors-To: cube-lovers-errors@curry.epilogue.com 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