Message #1072

From: Brandon Enright <bmenrigh@ucsd.edu>
Subject: Re: [MC4D] Re: Faces problem with 4^4
Date: Sun, 25 Jul 2010 05:38:54 +0000

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On Fri, 23 Jul 2010 13:49:20 -0000 or thereabouts "deustfrr"
<deustfrr@yahoo.ca> wrote:

> I have tried a few algorithms and they didn’t work. How does swapping
> the pieces help with flipping another 2? What does Brandon mean by
> flipping over the whole group? I’ve been stuck for days now. And yes,
> I solved the centers intuitively — In 4D_Cubing@yahoogroups.com,
> "deustfrr" <deustfrr@…> wrote:
> >
> > I really don’t know what to do about this problem. And do I only
> > swap 2 or can I swap 2 pairs?

deustfrr,

I’m not sure I can explain in text better than I already have. What
I’m trying to describe is intuitive for me. It is difficult to
convey intuition using only mechanical steps. Also, I’d hate to rob
you of a "Eureka!" moment figuring out yourself.

With that said, I have created log files to replicate each of your
situations here:

http://games.groups.yahoo.com/group/4D_Cubing/files/bmenrigh-misc/

I have tried to make the logs as straight-forward as possible. They
aren’t short but they are simple and moves are quite symmetrical
because they consist entirely of commutators built on commutators with
just a sprinkling of setup and undo sequences.

If you look at the 1c 3-cycle file, you will see that it is roughly:

setup1, (double-3 cycle commutator), setup1’,
setup2,
setup1, (double-3 cycle commutator)’, setup1’,
setup2’

Even though it looks like it swaps two pieces, it is actually a 3-cycle
where two of the three pieces are indistinguishable. Really all I’m
doing is turning the double-3 cycle into a single 3-cycle by
commutating it with the second setup move.

With regard to using a 3-cycle to flip a pair of pieces, here is a
commented example from the ordinary 3x3x3 cube:

/* Simple 3-cycle */
[R2,U’,F,B’,R2,B,F’,U’,R2],
/* Take a cycled piece, flip it, and put it back */
[F’,L,D,F2],
/* Undo the first 3-cycle */
[R2,U,F,B’,R2,B,F’,U,R2],
/* Undo the flipping */
[F2,D’,L’,F]

The above concept is exactly how I built the 2c 2-flip log file.

Good luck and happy hypercubing!

Brandon

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