# Understanding Parities



## CubeDude17 (Jan 21, 2013)

This is a place to talk about what you think causes parity on different cubes. There is 4x4, 5x5, 6x6, Void cube and many others.:confused:


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## MaeLSTRoM (Jan 21, 2013)

​What causes Actual parities, is a 2-cycle of some type of pieces, an example is OLL parity, which is a 2cycle of wing edges.
There are also vitrual parities, which are cases that are called parity, but are not, such as PLL parity, which is a 2+2 cycle, but if the case was on a 3x3, it would be a parity.

As for solving them, Once you know the algs, its easy


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## Username (Jan 21, 2013)

There are many types of parity. On a 4x4 All parity is basically that the cube has been reduced from an even layered cube to an odd layered cube in a way it couldn't have been scramble (as an odd layered cube). I don't own a void cube, but i believe that to avoid parity you must know the color scheme (correct me if i'm wrong)


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## blackzabbathfan (Jan 21, 2013)

I don't think any of them are particularly difficult to fix, but 7x7 edge parity is the most awkward to fix to me.


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## Username (Jan 21, 2013)

MaeLSTRoM said:


> ​What causes Actual parities, is a 2-cycle of some type of pieces, an example is OLL parity, which is a 2cycle of wing edges.
> There are also vitrual parities, which are cases that are called parity, but are not, such as PLL parity, which is a 2+2 cycle, but if the case was on a 3x3, it would be a parity.
> 
> As for solving them, Once you know the algs, its easy



You can't cycle 2 pieces (unless it's a 2x2) on a nxnxn cube. On a 4x4 it isn't about cycling 2 pieces, it's about placing the center pieces in the wrong order. For example: The OLL-Parity algorithm (All L and R moves are inner slices only) R2 B2
U2 L U2 R' U2 R U2 F2 R F2 L' B2 R2) Flips one edge (two pieces) and Rotates the top center by 180 degrees. Obviously you don't notice this when the center is all the same color, but Do a Bw move and then do the algortihm, you'll notice it.


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## cmhardw (Jan 21, 2013)

Username said:


> You can't cycle 2 pieces (unless it's a 2x2) on a nxnxn cube. On a 4x4 it isn't about cycling 2 pieces, it's about placing the center pieces in the wrong order.



Your first sentence is not completely correct. You are missing a non-trivial special case where you _can_ perform a pure 2-cycle on an nxnxn cube. I won't tell you which n, though. I'll let you figure it out 

Your second sentence is not true :/

As to the OP:

"Fixing" parity is done by simply turning a quarter turn on a slice that contains the piece that is in an odd permutation such as to create an odd permutation. As an example turning *U* would not fix wing parity (it does two 4-cycles of wings), but turning *u* would fix wing parity (it does a 4-cycle of wings). So in that sense fixing any parity comes down to performing only 1 quarter turn, so they are all very easy to fix. Of course I know that you mean to fix them in a speedsolving sense, without destroying the progress you've already made on the puzzle while solving it after reduction. In _that_ sense I'd say that I think void cube parity is the most involved for me. I don't have any cool memorized algs for that one and I just do an M or M' slice turn and solve the DF and DB cross edges again Roux methods and intuition (I don't solve the void cube often).


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## MaeLSTRoM (Jan 21, 2013)

Username said:


> You can't cycle 2 pieces (unless it's a 2x2) on a nxnxn cube. On a 4x4 it isn't about cycling 2 pieces, it's about placing the center pieces in the wrong order. For example: The OLL-Parity algorithm (All L and R moves are inner slices only) R2 B2
> U2 L U2 R' U2 R U2 F2 R F2 L' B2 R2) Flips one edge (two pieces) and Rotates the top center by 180 degrees. Obviously you don't notice this when the center is all the same color, but Do a Bw move and then do the algortihm, you'll notice it.



I know, but since the rotation is a 180 on the centre, this is a 2+2 cycle of centres, which can be solved purely using comms and doesn't change the parity of other pieces. The parity of edges and centres isn't connected in the sense that one determines the other.


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## cubernya (Jan 21, 2013)

cmhardw said:


> Your first sentence is not completely correct. You are missing a non-trivial special case where you _can_ perform a pure 2-cycle on an nxnxn cube. I won't tell you which n, though. I'll let you figure it out



This one I do know! It's 4x4


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## Bh13 (Jan 21, 2013)

I only have a 4x4 and void, but the permutation parity on the void is hard for me because the alg I know fixes the permutation, but messes up the orientation.


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## vcuber13 (Jan 21, 2013)

Bh13 said:


> I only have a 4x4 and void, but the permutation parity on the void is hard for me because the alg I know fixes the permutation, but messes up the orientation.



void cube parity can be solved with M


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## Stefan (Jan 21, 2013)

CubeDude17 said:


> This is a place to talk about what you think causes parity on different cubes.



Awesome, thanks so much, without you we wouldn't be able to talk about it! You're so generous.


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## CubeDude17 (Jan 21, 2013)

Stefan said:


> Awesome, thanks so much, without you we wouldn't be able to talk about it! You're so generous.



You're welcome!:tu:tu

And do you know what's weird? I'm barely 12 and I am collect and solve many twisty puzzles.

Oh, and thank you for teaching me how to solve the Rubik's Clock!
And teaching so many people BLD.

You are so great, Stefan Pochmann...


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## applemobile (Jan 22, 2013)

I am 12 and what is this?


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## CarlBrannen (Jan 22, 2013)

None of my cubes have ended up with parity except after they've been scrambled and I tried to solve them. I'm pretty sure that's what causes parity to appear, trying to solve after a scramble.

I'd vote for the 6x6x6, but I don't know know what the void parity problem is. Maybe it's worse.


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## uniacto (Jan 22, 2013)

Stefan said:


> Awesome, thanks so much, without you we wouldn't be able to talk about it! You're so generous.





CubeDude17 said:


> You're welcome!:tu:tu



I believe Stefan was being sarcastic there.


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## Owen (Jan 22, 2013)

What about square-1? The algorithm is hard to remember, and it's tricky to do fast without making a mistake and having to start over again.


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## Jokerman5656 (Jan 22, 2013)

Owen said:


> What about square-1? The algorithm is hard to remember, and it's tricky to do fast without making a mistake and having to start over again.



You know there isn't just 1 parity alg for square-1 right? If are referring to the adj parity alg then i can understand but there are many other algs that fix parity on the puzzle while affecting other edges and they are quite a bit easier. Just sayin'


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## Noahaha (Jan 22, 2013)

uniacto said:


> I believe Stefan was being sarcastic there.



I share in this belief.


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## Petro Leum (Jan 22, 2013)

Noahaha said:


> I share in this belief.



and still its pretty useless adressing this to a 12-year-old who [probably] doesnt understand sarcasm


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## SenileGenXer (Feb 4, 2013)

My biggest parity problem with a 4x4 is looking ahead. When I get to OLL parity I have two a algs. I like the longer 1-up, 2-up, 3down thing but it will add PLL parity if it isn't there or cancel out PLL if it is. The standard speedsolving alg doesn't do this. If I could see to the next few steps I could avoid one type of parity by choosing the right alg to apply.


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## Noahaha (Feb 4, 2013)

SenileGenXer said:


> My biggest parity problem with a 4x4 is looking ahead. When I get to OLL parity I have two a algs. I like the longer 1-up, 2-up, 3down thing but it will add PLL parity if it isn't there or cancel out PLL if it is. The standard speedsolving alg doesn't do this. If I could see to the next few steps I could avoid one type of parity by choosing the right alg to apply.



I recommend just choosing your favorite one and doing it by default, and only doing the other one when you happen to recognize the case. PLL parity doesn't take *that* long, so it's not worth a couple seconds of recognition to avoid. But if you get an easy case like having permuted edges or corners and you can recognize it quickly, then choose which alg to do.


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## CubeDude17 (Feb 6, 2013)

Oh, and for people out there who can't fix 4x4x4 OLL Parity, Here's the algorithm!

Rr2 B2 U2 Ll U2 Rr' U2 Rr U2 F2 Rr F2 Ll' B2 R2

Recognised with this pattern on top:

O_ _O
_O O_
_O O_


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## JasonK (Feb 6, 2013)

CubeDude17 said:


> Oh, and for people out there who can't fix 4x4x4 OLL Parity, Here's the algorithm!
> 
> Rr2 B2 U2 Ll U2 Rr' U2 Rr U2 F2 Rr F2 Ll' B2 R2
> 
> ...



Or you could use a good algorithm.

r U2 x r U2 r U2 r' U2 l U2 r' U2 r U2 r' U2 r'


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## cuBerBruce (Feb 6, 2013)

CubeDude17 said:


> Oh, and for people out there who can't fix 4x4x4 OLL Parity, Here's the algorithm!
> 
> Rr2 B2 U2 Ll U2 Rr' U2 Rr U2 F2 Rr F2 Ll' B2 R2



I note that you seem to be assuming Rr2 means the same as R2 r2 or (Rr)2. Similar with Rr' and Ll'. If you type that alg text into alg.garron.us, the result is not what you expect.


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