# 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