# Message #501

From: David Smith <djs314djs314@yahoo.com>

Subject: [MC4D] Re: Magic120Cell Realized

Date: Wed, 07 May 2008 11:59:55 -0000

That was a great analogy!

I did a quick calculation - the number is approximately

2.3 x 10^8240, therefore not even one hundred layers of

universes would be enough!!!

I realized right after I submitted my post that I made

a minor error. When I said:

> To show this number is exact, we will have to find 3 algorithms:

> one that performs a 3-cycle of any three 2-coloreds without

> affecting any other 2-coloreds, a 3-cycle of any three 3-coloreds

> without affecting any other 3-coloreds, and a 3-cycle of any

> three 4-coloreds without affecting any other 4-coloreds. These

> three algorithms, when combined with each other and conjugates

> (setup moves), can produce any possible permutation of the

> pieces.

I should have said:

> To show this number is exact, we will have to find 3 algorithms:

> one that performs a 3-cycle of any three 2-coloreds without

> affecting any other pieces, a 3-cycle of any three 3-coloreds

> without affecting any other pieces, and a 3-cycle of any

> three 4-coloreds without affecting any other pieces. These

> three algorithms, when combined with each other and conjugates

> (setup moves), can produce any possible permutation of the

> pieces.

where each algorithm performs its task without affecting

any other pieces, instead of any other pieces with the same

number of colors. But this error is minor, and does not

affect the final answer!

Also, I won’t worry about the length of my posts anymore!

Roice mentioned an interest in my general algorithm that

performs a 3-cycle of any three pieces on any sized 4D

cube, so I will post it soon, although I do think it is

relatively simple. However, I think similar techniques

could be used for the pieces of the 120-cell, which

would help validate the number I calculated. Also,

I looked up the section in "The Rubik Tesseract" in

Appendix A on the algorithms they discovered to validate

their calculation of the 3^4 cube. They managed to

obtain all of the required algorithms for the 4-coloreds

we would need to find (20 different algorithms!)

using a single pair of twists! I believe similar methods

could be used on the 120-cell.

-David

— In 4D_Cubing@yahoogroups.com, Melinda Green <melinda@…> wrote:

>

> What a number indeed!

>

> So let me get this straight. If you imagine all the particles in

the

> universe, and then imagine that each one really consists of

another

> entire universe, and for each particle in those universes, another

> universe, and so on ten times, you would still not have enough

particles

> so that each one could represent one unique state of this puzzle?

OK, I

> suppose that counts as a big number. :-)

>

> BTW, don’t worry about the length of your posts David. It’s easy

enough

> for anyone who’s not interested to just delete them. Any subject

even

> remotely on-topic should be fair game. Even if the posts become

too

> frequent for some people, they can choose to get daily digests or

even

> no email at all and just read the messages on the web site when

they

> feel like it.

>

> -Melinda