# Message #582

From: "thibaut.kirchner" <thibaut.kirchner@yahoo.fr>

Subject: Re: Permutation formula updates

Date: Mon, 22 Sep 2008 14:53:16 -0000

— In 4D_Cubing@yahoogroups.com, David Smith <djs314djs314@…> wrote:

> I’ve updated my formula for the upper bound for the number of

> reachable positions of an n^4 Rubik’s cube (it contained

> some errors), and also finished a similar formula for the

> supercube. Until now, I’ve only been using combinatorial arguments

> and concepts of higher dimensions in my work.

I’m amazed by the complexity of the formula. I suggest you to split it

into two formulas, one for the odd-sized hypercubes, and on for the

even-sized hypercubes. I’m sure the two formulas would be easier to

read than this one, and I’m not sure it’s interesting to group the two

formulas into a single one.

Also, if you put the factors associated with a single type of piece by

row, it could help the reader (and group somewhere the constraints

which link several type of piece).

Thibaut.