From: jmb184@frontiernet.net (John Bailey)
Newsgroups: sci.math,rec.puzzles
Subject: Re: The size of Rubik's hypercube group?
Date: Fri, 18 Dec 1998 11:38:15 GMT

On Thu, 17 Dec 1998 12:27:00 -0600, Jim Ferry
<jferry@delete_this_field.uiuc.edu> wrote:

>How many positions P(n,k) are possible for a k x k . . . x k,
>n-dimensional Rubik's cube?  (I.e., what is the order of its
>symmetry group?)
Have a look at Charlie Dickman's tutorial at
http://wauug.erols.com/~bagleyd/4d/TesseractDOC.html
Don't be put off by the elementary beginning.  The cube group
discussion comes somewhere in the middle.  

I believe, but the margins of this page are too small to contain the
proof, that as the dimensions of a Rubik-cube like object get higher,
the solution gets easier because the number of paths to a solution is
increasing faster than the number of positions.
See my solution to the 2x2x2x2 at
http://www.frontiernet.net/~jmb184/interests/puzzles/4Cube/solution/

John