# Message #481

From: David Smith <djs314djs314@yahoo.com>

Subject: Introduction to the 4D_Cubing Group

Date: Tue, 29 Apr 2008 02:29:59 -0000

Hello, everyone! My name is David Smith, and I hope to

be a contributive member to this unique and highly

interesting group. My interests besides the cube are

mathematics, physics, chess, computer programming,

and retrograde analysis (a very remarkable type of

chess problem).

Reading the posts made by various members has gotten

me very interested in the solving of higher-dimensional

cubes. It seems like a very challenging task, and

congratulations to everyone who has solved a four or

five-dimensional Rubik’s Cube! I will definitely try it

soon. What I am interested in now, however, is the

mathematics of the Rubik’s Cube. I wonder if any of

you also have an interest in this area?

I am currently working on an interesting problem -

finding a formula for the number of reachable

configurations of the NxNxNxN Rubik’s Cube. I

believe I will have an answer to this question

soon, so I would be very glad to share it with

the group, or perhaps only the members who are

interested in mathematics, if any. The paper

written by Eric Balandraud on the MagicCube4D

website has been very helpful, but I am

currently stuck on a minor detail with his

calculation of the number of permutations of

the 5x5x5x5 cube, but I believe I will

discover my error soon.

After this, I want to find the same formula

for 4-dimensional supercubes and super-supercubes.

(see http://www.speedcubing.com/chris/cubecombos.html

for a definition of these terms) After that, I

will (perhaps foolishly!) attempt to find formulae

for cubes, supercubes, and super-supercubes of

any size and any dimension.

I apologize if this post has been too long, but

I wanted to give a detailed introduction of myself

and my current tasks, and I hope that at least some

of you would be interested in discussing these

problems and their solution. I am trying to do

this without any formal mathematics training, so

my solution, when I find it, may be long but

relatively simple to understand.

I wish to thank everyone who has contributed the

the theory of Rubik’s Cube knowledge, helped

in the creation of Rubik’s Cube software, or

otherwise done amazing things with Rubik’s Cubes.

Happy Hypercubing!

Best Regards,

David