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 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