Message #677

From: David Smith <>
Subject: 4D Paper Complete
Date: Sun, 21 Jun 2009 02:56:46 -0000

Hello all,

I am pleased to say that I have finally finished my paper which derives the number of possible positions of an n^4 Rubik’s Cube! I actually can’t say it is truly finished yet until it is studied by more people, so I am hopeful that maybe a few of you will take a look at it. Feel free to post any questions, comments, suggestions, or corrections, or email me at

Here is the paper:

My deepest thanks goes out to Roice for all of his contributions! (and the use of his website, as always.)

Here is the formula by itself:^4_Cube.pdf

Some of you may have noticed that the formula changed. Actually, it only changed in appearance; I just expanded the binomial coefficient in the exponent of the last term. I did this because it allows a simpler discussion in the paper when I discuss the exponent’s derivation.

I would like to thank Melinda, Don Hatch, and Jay Berkenbilt for creating Magic Cube 4D and thus opening my mind to such a fascinating concept that I have enjoyed studying very much.

I am planning to work on an n^5 Cube paper, but first I want to try finding that n^d Cube formula again, which may prove too difficult for me. But I will give it a try anyway.

Thanks so much for everyone’s support, and even if nobody reads my paper, I am still happy I wrote it. I hope that it somehow contributes to the legacy of Magic Cube 4D, even if only in a small way.

All the best,