# Understanding Parity.



## andyt1992 (Mar 13, 2010)

I often hear people say if you can understand why parity happens you can work out how to solve it, I am not just talking about 4x4's here but about any cube or non cube puzzle that can get parity.
The puzzles I am most interested in understanding why parity happens are:

SQ-1
Fisher Cube
4x4 and upwards
Void Cube - Shifted Centers?

The reason is I dont want to have to remember a load of algorithms and solve cubes in robot mode, I wish to have a greater understanding of the logic of each puzzle and be able to solve each intuitively.


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## whauk (Mar 13, 2010)

fisher cube has parity?


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## dada222 (Mar 13, 2010)

I'd like to know that too.


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## cmhardw (Mar 13, 2010)

First hint: Parity is the same concept on all puzzles. It refers to the parity of the permutation of the pieces. If the overall piece permutation parity is odd, then you have "parity error." If the overall piece permutation is even you do not have "parity error." Also, "parity error" is a very poor choice of wording, as the real concept behind what we term parity is really referring to odd parity permutations.

Search for parity on this forum for some other topics with much more detailed explanations. Consider this only a nudge in the right direction.

Chris


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## masterofthebass (Mar 13, 2010)

Fisher Cube doesn't have parity, it only has rotated centers like a picture cube would have. 

The case of a void cube parity is quite simple. If you were to take a 3x3, and solve your f2l with the Eslice centers cycled clockwise (red cross piece on the green center, green piece on the orange center, etc.) you would get the same scenario as you do on a void cube. This happens on the void cube quite easily, obviously, because you don't have the centers there to reference off of.

I personally still don't get how sq-1 parity works, and I'll let you search around for the bigcube edge parity.


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## Kirjava (Mar 13, 2010)

cmhardw said:


> First hint: Parity is the same concept on all puzzles. It refers to the parity of the permutation of the pieces. If the overall piece permutation parity is odd, then you have "parity error." If the overall piece permutation is even you do not have "parity error." Also, "parity error" is a very poor choice of wording, as the real concept behind what we term parity is really referring to odd parity permutations.
> 
> Search for parity on this forum for some other topics with much more detailed explanations. Consider this only a nudge in the right direction.
> 
> Chris




Either cubers don't use this exact definition or "PLL Parity" is really badly named.


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## vcuber13 (Mar 13, 2010)

PLL parity basically means a 2 cycle, so you switch only 2 corners or 2 edges (sq-1, even cubes 4x4+, etc.). On big cubes I think the OLL parity is caused by an odd number of twists in the inner layers like Rw, and the parity alg does another odd with makes the total even. I don't know but I think sq-1 parity happens while you get it into a cube.


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## Kirjava (Mar 13, 2010)

vcuber13 said:


> PLL parity basically means a 2 cycle, so you switch only 2 corners or 2 edges




PLL parity is not a single 2 cycle, rather two sets of 2 cycles. In Chris' definition, this is not parity.


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## vcuber13 (Mar 13, 2010)

Kirjava said:


> vcuber13 said:
> 
> 
> > PLL parity basically means a 2 cycle, so you switch only 2 corners or 2 edges
> ...



Well, I meant i can be thought of like a 2 cycle. (or 4 cycle (O-Perm) and so fourth)

And, two 2 cycles isn't parity, a Z and H Perm arn't


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## Kirjava (Mar 13, 2010)

vcuber13 said:


> Kirjava said:
> 
> 
> > vcuber13 said:
> ...




I'm specifically addressing Chris' definition here; you're forgetting that an edge pair is two pieces.

However, PLL parity is defintely *not* a 4 cycle.



vcuber13 said:


> And, two 2 cycles isn't parity, a Z and H Perm arn't




Nice edit. You do know that I stated exactly this in the post you replied to, right?


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## Stefan (Mar 13, 2010)

masterofthebass said:


> Fisher Cube doesn't have parity, it only has rotated centers like a picture cube would have.


So... center orientation parity?



masterofthebass said:


> The case of a void cube parity is quite simple. If you were to take a 3x3, and solve your f2l with the Eslice centers cycled clockwise


More direct perspective, not talking about something that isn't there:
Turning an inner slice is a 4-cycle of edges, that's an odd permutation right there.



masterofthebass said:


> I personally still don't get how sq-1 parity works


Not even the setup-to-turn-six-corners solution?



cmhardw said:


> Search for parity on this forum for some other topics with much more detailed explanations.


These are also good:
http://www.jaapsch.net/puzzles/theory.htm
http://en.wikipedia.org/wiki/Parity_of_a_permutation



Kirjava said:


> PLL parity is not a single 2 cycle


It *is* from the perspective of solving as a 3x3x3, where it's a 2-cycle of dedges.


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## Kirjava (Mar 13, 2010)

StefanPochmann said:


> Kirjava said:
> 
> 
> > PLL parity is not a single 2 cycle
> ...




I know it is if you reduce the puzzle into another group, but Chris' definition doesn't allow that abstraction, referring specifically to pieces.


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## vcuber13 (Mar 13, 2010)

Kirjava said:


> Nice edit. You do know that I stated exactly this in the post you replied to, right?



No you said it


Kirjava said:


> PLL parity is *not a single 2 cycle, rather two sets of 2 cycles*. In Chris' definition, this is not parity.


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## Kirjava (Mar 13, 2010)

vcuber13 said:


> Kirjava said:
> 
> 
> > Nice edit. You do know that I stated exactly this in the post you replied to, right?
> ...




I don't know what this is supposed to mean, but here's what I meant that you didn't understand;



Kirjava said:


> PLL parity is not a single 2 cycle, rather two sets of 2 cycles. In Chris' definition, this is not parity.




I'm saying PLL Parity is really two sets of 2 cycles. Which is not parity. (I thought this was obvious)



vcuber13 said:


> And, two 2 cycles isn't parity, a Z and H Perm arn't




And then you seem to tell me this as if I haven't already stated it.

Now, tell me how you think PLL Parity is a 4 cycle please.


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## Stefan (Mar 13, 2010)

Kirjava said:


> Chris' definition doesn't allow that abstraction, referring specifically to pieces.



I have no problem considering a dedge to be a piece.


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## vcuber13 (Mar 13, 2010)

Kirjava said:


> vcuber13 said:
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> > Kirjava said:
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if your saying pll parity is really two 2 cycles, then what do you call it when 2 adjacent / opposite edges are switched on a 4x4?


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## Kirjava (Mar 13, 2010)

StefanPochmann said:


> Kirjava said:
> 
> 
> > Chris' definition doesn't allow that abstraction, referring specifically to pieces.
> ...




I do, my problem is that it's two pieces.



vcuber13 said:


> if your saying pll parity is really two 2 cycles, then what do you call it when 2 adjacent / opposite edges are switched on a 4x4?




two 2 cycles (assuming you meant dedges and not edges, if you did mean edges (which I seriously doubt) I would simply call it a 2 cycle)


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## Stefan (Mar 13, 2010)

Kirjava said:


> StefanPochmann said:
> 
> 
> > Kirjava said:
> ...



You're wrong, it's at least *four* pieces, don't forget the stickers!


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## Kirjava (Mar 13, 2010)

StefanPochmann said:


> Kirjava said:
> 
> 
> > StefanPochmann said:
> ...




Come on, you know what I mean. You do however make a valid point. It seems silly to me to think of it as a single piece when they weren't always a single one in the solve, and can return to being two.

It just irks me that it's universally referred to as "PLL Parity" when it's a matter of perspective. For example, vcuber doesn't even understand what I'm talking about.


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## Stefan (Mar 13, 2010)

Kirjava said:


> it's universally referred to as "PLL Parity"



Is it? Do *you* refer to it as that? Or is it just universally referred to that in the pseudo-3x3x3 context? There I think it's alright.



Kirjava said:


> You do however make a valid point.



Yeah, I was hoping to . What one considers a piece depends on the purpose and usage.



Kirjava said:


> It seems silly to me to think of it as a single piece when they weren't always a single one in the solve, and can return to being two.



Good point, though if you insist that it shouldn't be called piece, you're just as stubborn as people who insist it should be. Like you said, matter of perspective. And neither is wrong except for calling the other wrong.


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## vcuber13 (Mar 13, 2010)

Kirjava said:


> StefanPochmann said:
> 
> 
> > Kirjava said:
> ...



Wait...
Did you mean 2 2 cycles of single edges? Because I meant 1 2 cycle of dedges, like the UF dedge and the UB dedge switch.

If not i still dont really understand you, but I dont mean im right and your wrong im just not understanding what you mean completely.

2 2 cycles is not parity 
and
1 2 cycle is right?

I have a question:
Do you use K4?
Because if you do your probably right since I know nothing about it (I use reduction)


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## Kirjava (Mar 13, 2010)

StefanPochmann said:


> Kirjava said:
> 
> 
> > it's universally referred to as "PLL Parity"
> ...




I usually refer to it as PLL Parity in real life for clarity. To be honest, I never really discuss it enough to have the opportunity to call it anything else. I think you'll be hard pressed to find many that don't call it "PLL Parity". It's a reducer's world out there.



StefanPochmann said:


> Kirjava said:
> 
> 
> > You do however make a valid point.
> ...




Yeah, but does it not feel odd to you to change what is defined as a piece depending on the stage of the method you are on?



StefanPochmann said:


> Kirjava said:
> 
> 
> > It seems silly to me to think of it as a single piece when they weren't always a single one in the solve, and can return to being two.
> ...




Indeed. I think not calling it a piece is more valid (without context), but I don't think calling it a piece is incorrect (with context).


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## Stefan (Mar 13, 2010)

Kirjava said:


> I think you'll be hard pressed to find many that don't call it "PLL Parity". It's a reducer's world out there.



Well... http://www.worldcubeassociation.org...gionId=&years=&show=100+Persons&single=Single 



Kirjava said:


> does it not feel odd to you to change what is defined as a piece depending on the stage of the method you are on?



Not at all.

Again the analogy: When assembling a DIY 3x3x3, one might count maybe not the stickers but at least the centers/core and perhaps the screws/caps/etc as pieces. Once the cube is assembled and we solve it as such, we usually mean just the edges and corners when we say pieces. What's done is done, no need to look back and think in obsolete terms. Unless we have stickered wrongly and need to go back to stickers to fix it, or have reduced wrongly and need to go back to 4x4x4 edges to fix it.



Kirjava said:


> I think not calling it a piece is more valid (without context)



Agree.


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## antoinejobin (Mar 13, 2010)

If I have the parity pattern on the up and bottom face of my SQ-1, is it possible to solve it WITHOUT the parity alg? Does it have to be a parity if it's on both sides?


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## Muesli (Mar 13, 2010)

antoinejobin said:


> If I have the parity pattern on the up and bottom face of my SQ-1, is it possible to solve it WITHOUT the parity alg? Does it have to be a parity if it's on both sides?


That's not a parity... Do a 4 cycle ((1,0) / (0,3) / (-1,-1) / (1,-2) / (-1,0)) and you'll end up with two 3 cycle-able cases on the top and the bottom.


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## Kirjava (Mar 13, 2010)

StefanPochmann said:


> Kirjava said:
> 
> 
> > I think you'll be hard pressed to find many that don't call it "PLL Parity". It's a reducer's world out there.
> ...




Haha, you have me there.



StefanPochmann said:


> Kirjava said:
> 
> 
> > does it not feel odd to you to change what is defined as a piece depending on the stage of the method you are on?
> ...




So upon discovering parity in the reduced group, you are again seeing dedges as two pieces until you have finished executing the algorithm. So while the case is correctly labeled, does this mean the algorithm is incorrectly labeled as it is executed in the non-reduced state? I never considered that until parities are fixed, the cube isn't truly reduced.

However, I understand that "PLL Parity" when referring to the algorithm really means "PLL Parity Fix" so I'm willing to let that slide 


EDIT;



vcuber13 said:


> Kirjava said:
> 
> 
> > vcuber13 said:
> ...




A 2 cycle of dedges *is* a 2x2 cycle of edges.



vcuber13 said:


> 2 2 cycles is not parity
> and
> 1 2 cycle is right?




Depends how you look at the 2x2 cycle. Your question provides no context.



vcuber13 said:


> I have a question:
> Do you use K4?




lol.


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## cmhardw (Mar 13, 2010)

masterofthebass said:


> I personally still don't get how sq-1 parity works, and I'll let you search around for the bigcube edge parity.



This may not technically be correct, but I like to think of it this way:

Each of the 8 corners is really two 30 degree edge pieces bandaged together. This means that there are actually 24 "edge" pieces to the Square-1 and the concept of corner is really only that each one is two bandaged edges taken together.

Whenever you do a 30 degree turn you are actually performing a 12 cycle of "edges" (some of which may or may not be bandaged together). Regardless though this is still a 12 cycle of pieces, and this toggles the parity of the "edge" permutation (remember that corners do not exist per se).

Here is the part where I haven't analyzed this fully, when the puzzle is no longer in cube shape you always interchange 6 "edges" from the top with 6 "edges" from the bottom on each twist (verify?). If you break this down into "edge" cycle notation (remember, corners are still only bandaged edges) this is like doing 6 double swaps, which is an even permutation.

So the parity toggling manipulation on square-1 is a 30 degree turn of either layer. Can someone either discount or verify this analysis?

Chris


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## vcuber13 (Mar 13, 2010)

Musli4brekkies said:


> antoinejobin said:
> 
> 
> > If I have the parity pattern on the up and bottom face of my SQ-1, is it possible to solve it WITHOUT the parity alg? Does it have to be a parity if it's on both sides?
> ...



Or you can do (-2,0)/(3,0)/(-1,-1)/(-2,1)/(2,0) [adj-adj]
Or (1,0)/(-1,-1)/(6,0)/(1,1)/(5,0) [opp-opp]


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## Kirjava (Mar 13, 2010)

Musli4brekkies said:


> That's not a parity... Do a 4 cycle ((1,0) / (0,3) / (-1,-1) / (1,-2) / (-1,0))




What is it with you people and calling random things 4 cycles?


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## Stefan (Mar 13, 2010)

Kirjava said:


> A 2 cycle of dedges *is* a 2x2 cycle of edges.



A twisted 2-cycle of dedges is a 4-cycle of edges.



cmhardw said:


> Whenever you do a 30 degree turn you are actually performing a 12 cycle of "edges"



Seems rather contrary to what we usually consider parity. You'd call (1,0) at cube shape a parity changer and you wouldn't call a 6-corners-cycle a parity changer. Do you find that perspective useful?


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## vcuber13 (Mar 13, 2010)

Kirjava said:


> vcuber13 said:
> 
> 
> > Kirjava said:
> ...



I consider 2 2 cycles like a Z or H Perm
and 1 2 cycle (dedges) like the second image
and the first image a 2 cycle of singel edges


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## Stefan (Mar 13, 2010)

You're still not providing the contexts, but probably that's:
Parity, parity, no parity.


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## Haste_cube (Mar 13, 2010)

vcuber13 said:


> I have a question:
> Do you use K4?



Do you know what K4 stands for?


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## cmhardw (Mar 13, 2010)

StefanPochmann said:


> cmhardw said:
> 
> 
> > Whenever you do a 30 degree turn you are actually performing a 12 cycle of "edges"
> ...



Yes true, I would consider a 6 cycle of corners to be an even permutation on a square-1 (with bandaged edges in place of corners). However, this would be "parity" in the same sense that 4x4x4 PLL parity is with bandaged dedges.

From a pure puzzle standpoint a 6 corner cycle is even in my view, but it counts as a 3x3x3 reduction "parity error" when solving. Just like PLL parity is a "parity error" when reducing a 4x4x4.

Chris

P.S. "Oooooh Parity!!!! Oooooh Parity!!!! Oh how you haunt my speeeedsooooooolves!!"


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## vcuber13 (Mar 13, 2010)

cmhardw said:


> StefanPochmann said:
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> > cmhardw said:
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I agree


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## Kirjava (Mar 13, 2010)

StefanPochmann said:


> Kirjava said:
> 
> 
> > A 2 cycle of dedges *is* a 2x2 cycle of edges.
> ...




I assume he didn't mean double parity, but yeah, that's how I labeled it.



vcuber13 said:


> I consider 2 2 cycles like a Z or H Perm
> and 1 2 cycle (dedges) like the second image
> and the first image a 2 cycle of singel edges




Anyway, the second image is somewhat ambiguous. Since you referred to the pieces as dedges though, I'll assume it'd be after attempting to reduce the cube to a 3x3x3 and this would be a parity case.

However, if the cube is directly solved, it would not be a parity.

It all depends on context. At the moment, it's more like schrodinger's parity.


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## vcuber13 (Mar 13, 2010)

Okay, i understand now (finally)
and to be clear I use reduction.


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## andyt1992 (Mar 13, 2010)

masterofthebass said:


> Fisher Cube doesn't have parity, it only has rotated centers like a picture cube would have.



That is parity?? Also that isnt a problem i can solve it and understand what i need to do to always avoid it.
BUT what about on the LL where one of the pieces is pointing up and all the others are solved??


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## Johannes91 (Mar 13, 2010)

andyt1992 said:


> BUT what about on the LL where one of the pieces is pointing up and all the others are solved??


EO parity, what about it? Shouldn't be hard to figure out why it can happen and how to solve it.


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## Chuck (Mar 14, 2010)

vcuber13 said:


> I think the OLL parity is caused by an odd number of twists in the inner layers like Rw..



Can somebody tell me, is this true?


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## miniGOINGS (Mar 14, 2010)

Chuck said:


> vcuber13 said:
> 
> 
> > I think the OLL parity is caused by an odd number of twists in the inner layers like Rw..
> ...



Yes.


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## Stefan (Mar 14, 2010)

Chuck said:


> vcuber13 said:
> 
> 
> > I think the OLL parity is caused by an odd number of twists in the inner layers like Rw..
> ...



Inner layer quarter turns, yes. And you're joking, right? I'd expect any good big cube blindsolver to know this...


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## Chuck (Mar 14, 2010)

Yes, I'm totally joking.



Spoiler



No I'm not  I rarely solve big cubes with open eyes, thus I never thought why I get orientation parity. Stupid me.



Thank you


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## qqwref (Mar 14, 2010)

Parity means two different things in math and cubing. In math, parity refers to whether a cycle is even or odd - whether you can construct it out of 3-cycles or not. This is sometimes a useful concept in cubing, for instance in BLD solving, but most of the time it isn't (since a parity constraint can only exist if there are some single turns which change parity, but then fixing it is trivial so it isn't helpful to talk about it).

In cubing, the idea of parity comes about when you think you have reduced a puzzle into a given group, so that the puzzle can hopefully now be solved using a more restrictive set of moves. Basically, there is parity when the puzzle can't be solved with only those moves (but *looks* like it can) and so you have to do a special algorithm to move back into the solvable group. Generally each set of positions with a given type of parity is the same size as the set of solvable positions. The pure-math analogue of this idea is the coset.

This sounds a bit contrived, maybe, but it's easy to see why this definition is useful if you think about common cubing scenarios where people would say there can be a parity problem. In 4x4, once you reduce to 3x3, the assumption is that the puzzle can be solved with outer-layer turns only; if it can't, you have a parity problem. In fact, in this case, there are three parity conditions (OLL parity, PLL parity, double parity). In void cube, we can define the set of allowed moves to be "algorithms that, on a 3x3, would keep F2L intact", so if we are on the last layer and see two edges swapped we have encountered a parity case. In Square-1, the idea is that once you get to cubeshape you'll never have to leave (and in fact every non-parity cubeshape position can be solved without ever leaving square/square), but if you get parity you have to go outside of your restricted set of moves. All of these cases fit into the coset-like definition of parity we use in cubing, but they don't all fit into the mathematical definition. (In the mathematical definition, a pure swap of two corners doesn't change parity, but a (1,0) does - not very useful!)


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## Innocence (Mar 15, 2010)

> I have a question:
> Do you use K4?



As you still seem to be oblivious to the hilarity, let me spell it out for you.



Spoiler






Spoiler



Kirjava invented it. :O


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## masterofthebass (Mar 15, 2010)

I know I'm a little late on this response:



StefanPochmann said:


> masterofthebass said:
> 
> 
> > Fisher Cube doesn't have parity, it only has rotated centers like a picture cube would have.
> ...


I don't think this should be still considered parity as in all actuality at least 2 centers need to be rotated. One of the centers just has to be trivially rotated along with the piece that needs solving.



StefanPochmann said:


> masterofthebass said:
> 
> 
> > I personally still don't get how sq-1 parity works
> ...


I have never looked into the inner workings of sq-1 parity, so my original statement stands. I seem to understand it a little now, based off of chris's explanation of the corners just being bandaged edges.


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## Sakarie (Mar 15, 2010)

Innocence said:


> > I have a question:
> > Do you use K4?
> 
> 
> ...



That doesn't mean somebody still necessary use it. Pochmann doesn't use Classic Pochmann, in spite of that it's his "classic" solvingmethod.


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## Stefan (Mar 15, 2010)

masterofthebass said:


> I don't think this should be still considered parity as in all actuality at least *2 centers need to be rotated. One of the centers just has to be trivially rotated along with the piece that needs solving.*


And how do you know that? That you can't just rotate one center alone (by 90 degrees)?


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## qqwref (Mar 15, 2010)

StefanPochmann said:


> masterofthebass said:
> 
> 
> > I don't think this should be still considered parity as in all actuality at least 2 centers need to be rotated. One of the centers just has to be trivially rotated along with the piece that needs solving.
> ...


I guess what he was saying was that you don't need to know whether that's possible. Even if the 3x3 did have a center orientation parity issue, where one could be 90 degrees off, you wouldn't have to be able to solve that for a Fisher Cube because the two-center-twist commutator is intuitive/straightforward and would fix that problem. So it's not really right to call it a parity, just a tricky situation that is part of the puzzle, when the solution is just a matter of realizing you can do a commutator on a piece you want solved and a piece that doesn't show orientation.


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## Neo63 (Mar 15, 2010)

Square-1 parity happens i think because of an odd permutation occuring outside of cube shape, so when you get it back to cube shape you get parity.


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## Lucas Garron (Mar 15, 2010)

Neo63 said:


> Square-1 parity happens i think because of an odd permutation occuring outside of cube shape, so when you get it back to cube shape you get parity.


That is very vague and almost false. 
But you can say that move sequences from one cube shape state to another can have odd net permutation parity.
It's just not that "an odd permutation occurs" except as an abstraction (or using some precise definition, which I don't think you really had in mind). Square-1 is just confusing.


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## Neo63 (Mar 15, 2010)

All I know is that something that is uncertain gets changed (bad way to phrase it)
like void cube, parity happens because the centres can be changed
4x4 because centres can be changed as well (at least this causes permutation parity i think)
and square-1 it's because of the cube shape.

and yeah square-1 is very confusing


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## Stefan (Mar 16, 2010)

Neo63 said:


> *void cube*, parity happens because the *centres can be changed*


Void cube doesn't have centres.



Neo63 said:


> 4x4 because centres can be changed as well (at least this causes permutation parity i think)


No.


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## cmhardw (Mar 16, 2010)

Here is how I view Square-1 Parity.

Perhaps I view parity the way I do because Square-1 is the only puzzle I truly did learn to solve on my own, with no help at all - even parity. I was angry at myself for always using the internet to either learn parity for the big cubes, or to learn the entire 3x3x3 solution.

Ok, so to me and in my own personal view the Square-1 is a reduction style puzzle. It is made up of twenty four 30 degree edges pieces, and the 2 pieces of the middle layer. What has happened is that the puzzle has been solved, reduction style, so that 8 bandaged corners have been created each out of two 30 degree edges. Every state of the Square-1 is the first stage of reduction of this 24 "edge" puzzle. Now, we choose to reduce it further (to cubeshape). By reducing to cube shape it is possible that the corner parity does not match the 30 degree edge parity.

Now keep in mind that, regardless of the parity of the corners, by viewing them as bandaged edges the "bandaged piece" parity is *always* even. Whether the corners are in an even or odd permutation, viewing them as bandaged edges they could always be solved, if they could be solved singly, with an even number of two swaps. Now the remaining 30 degree edges could be in either an even or odd permutation. This accounts for the fact that the Square-1 *has* the potential for odd permutations, and (1,0) from the solved state is a perfect example of an odd permutation when viewing the puzzle as 24 "edge" pieces all of 30 degrees.

So, the corners could have either even or odd parity, and the 30 degree edges could have either even or odd parity. This all implies after reducing to cube shape.

Ok, so to fix corner-parity-does-not-match-30-degree-edge-parity I undo cubeshape in such a way as to have 6 corners on one face, and I do a 60 degree turn. This 6 cycles the corners, toggling their parity to match the edges (as long as I redo cubeshape exactly in reverse as how I undid it, or at least in such as way as to not again toggle either corner or edge parity).

You could also fix parity by somehow changing the parity of the permutation of edges by undoing, and then redoing cubeshape. I don't know enough about Square-1 to know how to do this.

I hope this at least clears up the idea of Square-1 parity. There are, in fact, *two* parities. Michael described them very well in his post, so there is no need to redo it. Basically what we call "Square-1 parity" is actually "bandaged-edges/corner permutation parity does not match 30 degree edge parity" in my view.

Chris


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## c1829 (Mar 16, 2010)

masterofthebass said:


> Fisher Cube doesn't have parity, it only has rotated centers like a picture cube would have.


Fisher cube does have parity. You get a edge orientation parity when trying to solve the top cross if one of the edges with no obvious orientation is flipped.


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## Neo63 (Mar 16, 2010)

cmhardw said:


> Michael described them very well in his post, so there is no need to redo it.
> Chris



Can you please direct me to his post? I'm really curious about square-1 parity.


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## cmhardw (Mar 16, 2010)

Neo63 said:


> cmhardw said:
> 
> 
> > Michael described them very well in his post, so there is no need to redo it.
> ...



Post #44 in this thread.


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## Neo63 (Mar 16, 2010)

cmhardw said:


> Neo63 said:
> 
> 
> > cmhardw said:
> ...



ohh I searched this thread thinking that you were talking about Michael Hughey lol


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## Ranzha (Mar 16, 2010)

Fisher cube OLL "parity" occurs only when one middle edge is flipped.
Obviously, this is unnoticeable considering that they look oblivious to orientation, as a centre on a normal 3x3x3.
When I solve my Fisher, on the last slot I insert the edge first, check the orientation, and then insert the corner.
This way, parity is avoided.
Simple.

For centre parities, I made some algorithms that are in a thread here somewhere....
Too lazy to find it, but I like my idea of making Fisher Cube PLLs.


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## Moose Owl (Sep 8, 2015)

*Fisher cube 4x4*

I appreciate the R L F2 B2... algorithm, but it doesn't solve my problem, which is that I can't figure out how to change the top (yellow) edges around without messing everything else up.


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## Moose Owl (Sep 11, 2015)

I tried that algorithm to swap corners on the Fisher 4x4. It did exactly nothing.


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