Message #505

From: David Smith <djs314djs314@yahoo.com>
Subject: [MC4D] Re: Magic120Cell Realized
Date: Fri, 09 May 2008 01:29:46 -0000

Roice, that was a great article! Some of those numbers make
the number I found look like nothing! Thank you again for
putting my result on your website.

spel_werdz_rite, thank you for verifying this result! I had
no idea anyone else had calculated this number.

I recently had another idea for Magic120Cell before I go
back to the n^4 cube. It seems like it will be very difficult,
but I am going to try to find the number of visually different
positions of each of the other variations of puzzles (the
2-colored, both 9-colored, and the 12-colored versions) of
Magic120Cell. This will involve accounting for the similarly
colored pieces (4-colored pieces with the same colors may not be
visually identical due to their orientation, and counting the pieces
will require the use of the Magic120Cell program), and the similarly
colored centers (accounting for apparently different positions
acctually being visually identical due to rotations of the entire
puzzle in 4-space; the corner orientation logic would also apply
to the centers for counting how many ways the they can be visually
identical when rotated. This would be made eaiser by imagining the
0-colored piece that Roice mentioned.) These are just a few quick
observations, there may be more complications I am not yet aware of.

All the best,
David

— In 4D_Cubing@yahoogroups.com, "Roice Nelson" <roice3@…> wrote:
>
> You guys will likely find this article interesting and a fun read:
>
> http://www.scottaaronson.com/writings/bignumbers.html
>
> Charlie shared it with me some time ago and it discusses truly
unbelievably
> unimaginably big numbers (not that the number David presented
doesn’t fall
> into this category ;))
>
> David, thank you *so much* for your writeup on this!! I fixed my
incorrect
> listing of the number of pieces on the site (I apparently
accidentally
> multiplied by 2 instead of dividing by 2 when calculating the
number of 2C
> pieces, which is also why my quick permutation estimate was so far
off).
> For the total I wrote there, I also included the 0C (120-cell
shaped)
> interior and hidden piece of the puzzle.
>
> Roice
>
>
> On Wed, May 7, 2008 at 1:43 AM, 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