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 Post subject: Problem with parity in a Witeden 3x3x9Posted: Sat Mar 17, 2012 10:22 am

Joined: Mon Feb 27, 2012 10:57 am
Location: In my study drooling over my puzzle hoard - Precioussssss!
Hi guys,

I'm new to this (30 years since my original twisties!) so go easy on me.
It's all your fault that I have bought nearly 30 of these damn things in 2 months!

I have managed to solve my Witeden 3x3x9 using 3x3x3 techniques first to get top, bottom and middle layers done. After this I solve it layer by layer from the middle out using 2x2x3 techniques. About 1 in 4 occasions it will just solve but I find that the rest of the time I end up with parity down the right hand face and top/bottom. The slow way to solve this is to rotate R to correct the parity and then exchange 1 small centre on the right face from upper to lower half and then redo the pair of slices.

Sometimes this parity can occur several times, making the solve very laborious! Is there a way to remove my edge piece parity without breaking up and restarting the slice pair I am working on.

I hope it makes sense to you twisty freaks out there! I have just read what I have written and barely understand it myself!

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 Post subject: Re: Problem with parity in a Witeden 3x3x9Posted: Sat Mar 17, 2012 10:26 am

Joined: Sat Jan 16, 2010 11:48 am
Location: In Front Of My Teraminx (saying WTF?)
It's actually not parity, it's a 3-cycle with two pieces of the same color. Try switching blue->red->red see if it works =)

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 Post subject: Re: Problem with parity in a Witeden 3x3x9Posted: Sat Mar 17, 2012 10:36 am

Joined: Mon Feb 27, 2012 10:57 am
Location: In my study drooling over my puzzle hoard - Precioussssss!
RubixFreakGreg wrote:
It's actually not parity, it's a 3-cycle with two pieces of the same color. Try switching blue->red->red see if it works =)

Maybe parity is the wrong word! When I do an adjacent centre swap in the top of the layer pairs it causes all the R face pieces between the layers to be swapped back to front so I end up with a large chunk of the R face the wrong way around with the slices above and below correct.

Does this help explain my issue - it's kind of difficult without pictures!

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 Post subject: Re: Problem with parity in a Witeden 3x3x9Posted: Sun Mar 18, 2012 3:17 am

Joined: Tue Feb 08, 2011 3:17 am
Location: Australia
Hi Puzzlemad,

I think I know what you mean. See pics (it is always recomended if you want help to include a picture, because it saves a lot of confusion)..

If this is your problem you don't need to fix it continually throughout the solve (unless you would like to for your own visual clarity). All you need to do is to plan your sequences to affect the same RHS coloured pieces (column), by making appropriate U & D layer turns as setups in the `slice` you are working on (so that it switches and then `switches back` the same RHS pieces). You will only `need` to perform the `type of parity` sequence once at the end by choosing the appropriate variant.

The base one is first:
(Uuu2 F2 R2) uu2 (R2 F2 Uuu2)
The variants:
(Uuu2 F2 R2) --u2 (R2 F2 Uuu2)
(Uu-2 F2 R2) -u-2 (R2 F2 Uu-2)

I hope this helps and that the notation is understandable,
Cheers,
Burgo.

 Attachments: 339.jpg [ 913.54 KiB | Viewed 2149 times ]

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 Post subject: Re: Problem with parity in a Witeden 3x3x9Posted: Sun Mar 18, 2012 7:50 am

Joined: Mon Feb 27, 2012 10:57 am
Location: In my study drooling over my puzzle hoard - Precioussssss!
Burgo wrote:
If this is your problem you don't need to fix it continually throughout the solve (unless you would like to for your own visual clarity).

The base one is first:
(Uuu2 F2 R2) uu2 (R2 F2 Uuu2)
The variants:
(Uuu2 F2 R2) --u2 (R2 F2 Uuu2)
(Uu-2 F2 R2) -u-2 (R2 F2 Uu-2)

Thanks very much for this! It is exactly what I needed. I definitely need it for my own clarity - if I try to proceed to other layers with these the wrong way around then I get completely confused! I am a very simple soul and need to make things as easy as possible.

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 Post subject: Re: Problem with parity in a Witeden 3x3x9Posted: Sun Mar 18, 2012 2:20 pm

Joined: Thu Sep 17, 2009 6:07 am
Location: Germany, Bavaria
Puzzlemad wrote:
...Thanks very much for this! It is exactly what I needed. I definitely need it for my own clarity - if I try to proceed to other layers with these the wrong way around then I get completely confused! I am a very simple soul and need to make things as easy as possible.
I'm glad that Burgo could help you.

I think the term `parity` is misleading in this case.
People usually call something like this a "parity":

Seemingly, the red and green centre pieces need to be swapped.
Because the number of permutations would be "1", the parity would be "odd" and people refer to such situations as "parity".

I said `seemingly` because what you actually need in the shown case is a 3-ycle, e.g. of two green pieces and one red.
Greg was referring to such a situation.
I have learned that the term `parity` is used incorrectly by twisty puzzlers very often.
So, please, do not feel embarrassed, this is just a piece of information.

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 Post subject: Re: Problem with parity in a Witeden 3x3x9Posted: Sun Mar 18, 2012 4:16 pm

Joined: Mon Feb 27, 2012 10:57 am
Location: In my study drooling over my puzzle hoard - Precioussssss!
Konrad wrote:
I said `seemingly` because what you actually need in the shown case is a 3-ycle, e.g. of two green pieces and one red.
Greg was referring to such a situation.
I have learned that the term `parity` is used incorrectly by twisty puzzlers very often.
So, please, do not feel embarrassed, this is just a piece of information.

I don't really feel embarassed - I am all new to this really!

I got the term parity from some YouTube vids I had been watching and just thought it might apply to this.

Why is it called a 3-cycle or 3-ycle when there can be many more than 3 pieces involved? For example in the first of Burgo's pics there are 4 blue/orange and 4 green orange pieces the wrong way around.

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 Post subject: Re: Problem with parity in a Witeden 3x3x9Posted: Sun Mar 18, 2012 5:21 pm

Joined: Thu Sep 17, 2009 6:07 am
Location: Germany, Bavaria
Puzzlemad wrote:
....
Why is it called a 3-cycle or 3-ycle when there can be many more than 3 pieces involved? For example in the first of Burgo's pics there are 4 blue/orange and 4 green orange pieces the wrong way around.

I was talking about the situation in my picture:

If we call the green face F, the white Face U, the slice above the D face d and the slice below U u, I need a cycle of three centre pieces dF -> dR -> uF -> dF.
Whenever three pieces are permuted like here, we speak about a "3-cycle".
A pure 3-cycle is always an even permutation, an even number of swaps of two pieces.
Burgo's pictures show several double swaps of two pieces (2-2 swaps in our jargon).
Double swaps are even permutations by definition.

Many people will call the situation in my picture a `parity` (puristically speaking this is incorrect).

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