Message #482

From: Roice Nelson <>
Subject: Re: [MC4D] Introduction to the 4D_Cubing Group
Date: Tue, 29 Apr 2008 10:15:56 -0500

Hi David,

Very nice to make your acquaintance, and welcome! I’m sure others will have
more to say, but I thought I’d point you to two resources on the mathematics
I’ve seen in the mean time. The first (because it is shorter) is a paper
Melinda pointed me to because it had the calculation for the number of
permutations of the 3^5. It is titled "The Rubik Tesseract" and you can
find it here:

Secondly, there is a book by David Joyner called "Adventures in Group
Theory". It is a course on group theory focused around the 3D Rubik’s
cube. Though it doesn’t discuss the higher-d puzzles, it could be a useful
source for extending the relevant mathematical skills.

I’ll look forward to hearing about your investigations. As someone else who
finds this very interesting but lacks related formal mathematical training,
I’ve always felt lacking in the group theory aspects of these puzzles…

All the best,


On Mon, Apr 28, 2008 at 9:29 PM, David Smith <> wrote:

> 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
> 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