# Message #2629

From: schuma <mananself@gmail.com>

Subject: Re: [MC4D] MagicTile Solving

Date: Sat, 26 Jan 2013 08:15:03 -0000

I started from the solved state, and successfully created the parity case. Please find the steps in this file:

http://games.groups.yahoo.com/group/4D_Cubing/files/Nan%20Ma/MagicTileFiles/Skew447_49CE01410.xml

Although the whole process is 1000+ steps, the crucial moves are the first FOURTEEN turns. You can open the file, ctrl-z to the beginning and ctrl+y to see how it was done. All the rest moves are solving the side effects…

To create this parity, we need to make some turns such that

(1) the edges on each horizontal line (in the default view) are turned an even number of times;

(2) the edges on each vertical line are turned an even number of times;

(3) all the edges in the "\" direction are turned an odd number of times;

(4) all the edges in the "/" direction are turned an odd number of times.

(1) and (2) guarantee that the diamond-shaped pieces can be solved by commutators. (3) and (4) create the parity.

The simplest way to create the parity, I think, is to choose one diagonal line in the "\" direction, and turn all the seven pieces on it; then choose one diagonal line "/" and turn all the seven pieces on it. So the total number of moves to create a parity is 14. The total picture would be like a big "X". It’s easy to verify that this sequence satisfy (1)~(4), (this argument relies on the fact that 7 is odd).

I didn’t use this pattern because the side effect doesn’t have much symmetry. So I choose to turn seven edges on one line "\", and the adjacent seven edges in the "/" direction.

Ed, nice discovery. This is indeed a parity that I’ve never seen before. Thanks!

Nan

— In 4D_Cubing@yahoogroups.com, Roice Nelson wrote:

>

> On the parity issue, I don’t know the solution, but I have a few thoughts:

>

> - A single twist is odd for edges (3 2-cycles). Doesn’t this mean you

> could fix your issue with by making a single twist, then solving with an

> even number of twists from there?

> - I wonder if studying this past thread, Parity on MC

> m^n ,

> would help. Levi talks about the "double odd" situation of the 3^3, which

> feels like it might be relevant.

>

> I look forward to hearing the actual solution.

>

> Roice

>

> P.S. I agree with Melinda about what counts as a solve. Proving you can

> solve a puzzle is definitely worthwhile too, even if you don’t carry out

> all the motions. This was enough for me on the 120-cell, for instance :)

> But it seems like the wiki list should be reserved for actual solves. And

> in any case, it sounds like this puzzle is still unsolved from either

> perspective.

>

>

>

> On Tue, Jan 22, 2013 at 6:30 PM, Eduard Baumann wrote:

>

> > **

> >

> >

> > Sending "around the horn" doesn’t help because the torus is to simple.

> > I tried these "sendings".

> > The two radii are the same (7).

> >

> >

> > —– Original Message —–

> > *From:* Melinda Green

> > *To:* 4D_Cubing@yahoogroups.com

> > *Sent:* Wednesday, January 23, 2013 12:41 AM

> > *Subject:* Re: [MC4D] MagicTile Solving

> >

> >

> >

> > Oh my. I don’t feel that a puzzle has been solved unless it has been

> > completely finished from an appropriately large scramble. Other opinions,

> > anyone?

> >

> > Like Roice, I wonder whether one or more pieces need to be sent "around

> > the horn". In this case there are two ways to do that involving the small

> > and large radius of the torus.

> >

> > -Melinda

> >

> >

>