Message #617

From: David Smith <djs314djs314@yahoo.com>
Subject: 5D Cube Permutation Formula
Date: Thu, 22 Jan 2009 02:11:51 -0000

Hi everyone,

In yet another attempt to redefine the spirit of taking things too far,
I
have found the formula for the number of reachable configurations
of an n^5 Rubik’s Cube. I have carefully checked the formula many
times and am very confident it is free of error. It is quite complex,
but I don’t think I want to split it into multiple formulas. Roice has
encouraged me to write explanations of how I derived my Cube
formulas, which I intend to do eventually. This would give more
insight to the group of how the formulas were arrived at (if the
group is interested), and also help me verify their validity.

Here <http://gravitation3d.com/david/n%5E5_Cube.pdf> is the formula,
my thanks once again goes to Roice for the use of
his website. Also, despite what I said in my last post, I am not giving
up on the general n^d formula, and have gained even more insight
on how I might approach that problem from finding this formula.
I do intend to work on the super and super-super variants for 5D
Cubes first, though.

I would also like to congratulate Melinda for her achievement in
solving MagicCube4D! Of course, if it were not for that program,
I probably would never have gotten interested in the mathematics
of higher-dimensional Rubik’s Cubes, so I am naturally indebted
to her.

Despite the formula’s appearance, it was not that hard to figure out;
the real challenge will be the general formula. I hope that the
formulas I have found somehow contribute to the programs created
by Melinda, Don, and Roice.

David