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