# Message #489

From: Roice Nelson <roice3@gmail.com>

Subject: Re: [MC4D] Introduction to the 4D_Cubing Group

Date: Sun, 04 May 2008 10:30:06 -0500

Excellent, this sounds like a great approach. If you are interested in

writing it up, I’m sure some would enjoy reading about your general

algorithm to cycle 3 pieces of any type, but not worries too if you don’t

feel like doing it (if you’d rather just focus on the problem :))

I’ll let Eric and/or others comment on the possible 5^4 permutation

calculation issues for now because I’ll still need to hunker down and do

some study myself before I’m in a position to contribute there.

All the best,

Roice

P.S. As a teaser, I’m going to present a new permutation calculation problem

soon (hopefully this evening) that I hope you guys will be able to help me

figure out!

On Sat, May 3, 2008 at 10:02 PM, David Smith <djs314djs314@yahoo.com> wrote:

> Hi Roice,

>

> Once again, thank you for all of your help! I really appreciate

> the time you take to reply with your excellent advice.

>

> Right after I read your post, I had an idea for achieving what

> I want to do without writing a program at all! My idea basically

> consists of discovering general algorithms (using MagicCube4D) that

> can show that any possible permutation within the constraints I

> will discover is possible, for any sized cube. I have taken some

> algorithms from Keane and Kamack’s paper as given, which will help

> me. If I decide to do 5-dimensional cubes after this, I will not

> have this luxury! The MagicCube4D program is essential for

> discovering the required algorithms, so I do not think I will

> discover a general formula for any-sized any-dimensional cubes

> without an advanced group theory approach (although I may discover

> the upper bound without proving equality).

>

> Right now, I am working out the final details of a general algorithm

> that can perform a 3-cycle of any three hypercubies in the same

> family on any sized cube. This only produces any even permutation,

> but I will also show that for an arbitrarily-sized cube, certain

> permutation parity restrictions exist, and will also show that all

> of the other parities can be generated. Then, my 3-cycle algorithm

> will show that for each possible parity condition, I can generate

> any possible permutations for that parity, and this means that all

> possible permutations can be reached. If you want the details of

> this algorithm, I can email them to you (or post it on this group,

> whichever you feel is most appropriate) and send you macro files

> showing some specific examples of the general algorithm. I still

> have to do something similar for orientations, although Keane

> and Kamack’s paper helps me out with the corner and central edge

> algorithms they discovered.

>

> I have also discovered what I believe to be two mistakes in the

> calculation of the 5x5x5x5 cube’s permutations on the MagicCube4D

> website written by Eric Balandraud. They appear to be fairly

> obvious mistakes (once you understand the logic of the paper), and

> I would not say this if I were not at least 95% certain of it, but

> anyone may feel free to correct me if I am wrong. I think that

> the term ((3!)^31) should be (((3!)^31)*3) and that the term

> (16!) should be ((16!)/2), making the answer given correct if we

> multiply it by (3/2). The author of the paper has clearly shown

> himself to be very proficent in this area, so I believe these

> errors are typos or an oversight, but once again, anyone please

> let me know if I am wrong.

>

> Once again, Roice, thank you for your advice and support. I look

> forward to hearing from you!

>

> Best Regards,

>

> David

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