# Avoiding parity problems in big cubes



## brunson (Jun 29, 2008)

Is there anything I can look for earlier than after my 4x4 or 5x5 is fully reduced to recognize that I have a parity problem so I can address it before OLL which is usually where I figure it out. At that point repairing the damage that fixing the parity causes easily adds a full minute to my solve, of not more. I'm still around 5 minutes on 4x4, I haven't devoted that much time to it.


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## joey (Jun 29, 2008)

Umm, if you learn a good parity fix, nothing is destoryed.


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## masterofthebass (Jun 29, 2008)

There's no real feasible way to do so. There is one idea that involves counting cycles during inspection and then making sure you do the correct amount of slice turns, but that's almost impossible to do, especially when you are at 5 minutes.


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## brunson (Jun 29, 2008)

joey said:


> Umm, if you learn a good parity fix, nothing is destoryed.


Hmmm... Okay, maybe I'll hunt for some better algs. I've been using commutators on my 5x5, I didn't feel like memorizing all the parity algs on big cubes, but if that's your advice, them I'll start grinding them.

Thanks Joey and Dan, both, for your replies.


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## pjk (Jun 29, 2008)

The parity algs for 4x4 and 5x5 are both pretty easy to remember. Check out bigcubes.com. You should also learn the alg that fixes OLL/PLL parities at the same time (or creates a PLL parity).


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## Lucas Garron (Jun 29, 2008)

Actually, I recommend my OLL parity alg.  

But when Per reads this: Does anyone know a good OLL parity fix at the beginning of the 3x3x3 stage? I need it for 4x4x4 FMC averages.


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## Kenneth (Jun 29, 2008)

For OLL parity the problem is a even/odd situation. If the scramble had an even number of SQTM turns then the solution must also have an even number of turns, else a OLL parity occures, same thing if its an odd number. (this is also true for 3x3x3 BLD).

As masterofthebass says, the solution is to count cycles (impossible in 15 seconds) and then alter between algs of proper lengths when pairing edges.

Forget it and do as Joey says, learn the parity alg 

Lucas: it's the same thing in the beginning as it is in the end, same lenth of the algs I'm afraid.


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## masterofthebass (Jun 29, 2008)

Kenneth, there can perhaps be a shorter alg that doesn't preserve f2l, it just flips the edge and doesn't worry about preserving the position of any other ones. In FMC you can check to see if you get OLL parity and then fix it before you do any 3x3 moves.


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## Mike Hughey (Jun 30, 2008)

Sorry, I have to brag. The OLL and PLL parity algorithms can't be that bad for you to learn - my 7-year-old daughter learned them well enough to do them in competition.


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## brunson (Jun 30, 2008)

Oh yeah? Well, does she know all 57 3x3 OLLs? ;-)

That's actually really cool, Mike. My little girl is 3 right now and I'm looking forward to the day she or her little brother expresses an interest in solving daddy's cube. 

Are all three Hughey girls with WCA records your daughters?


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## ROOT (Jun 30, 2008)

the PLL parity alg is not hard to learn. at davinci i taught this one guy sitting next to me the alg in a few minutes which he used later in comp


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## AvGalen (Jun 30, 2008)

Kenneth said:


> For OLL parity the problem is a even/odd situation. If the scramble had an even number of SQTM turns then the solution must also have an even number of turns, else a OLL parity occures, same thing if its an odd number. (this is also true for 3x3x3 BLD).
> 
> As masterofthebass says, the solution is to count cycles (impossible in 15 seconds) and then alter between algs of proper lengths when pairing edges.
> 
> ...


There is a mistake there Kenneth, so just to keep it short and simple:
The problem with OLL parity is indeed the even/odd situation. For 4x4x4 that means that if the scramble has an odd number of wide/inner-slice turns (counted in quarter turn metric) you will have to solve the *centers* with an odd number of wide/inner-slice turns also. So fixing parity during the centers-stage of reduction requires only 1 move. During edge-pairing people always use an even number of wide/inner-slice turns so fixing parity at that moment is not possible (I am assuming normal reduction method, otherwise everything is possible)

And for 4x4x4 FMC (averages???) you shouldn't fix parity at the 3x3x3 stage, period. Maybe an alg could be found that saves 2 or 3 moves (I doubt it) but you would still be wasting 10 moves on something that should have been done in 1

For the topic-starter: Just learn two parity-fixes (PLL= 2 minutes, OLL = 15 minutes) and you will save about 1 minute every other solve. There is no faster way to improve your times on 4x4x4.


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## Mike Hughey (Jun 30, 2008)

brunson said:


> Oh yeah? Well, does she know all 57 3x3 OLLs? ;-)


Heh - not yet. 



brunson said:


> That's actually really cool, Mike. My little girl is 3 right now and I'm looking forward to the day she or her little brother expresses an interest in solving daddy's cube.


Does she not want to try? My 3-year old daughter can solve a cube that has been "scrambled" with a two-move scramble, pretty much every time. I'm very proud of that.  A three-move scramble is a little beyond her, though.



brunson said:


> Are all three Hughey girls with WCA records your daughters?


Umm, actually, the one with the slow times is my wife. She was gracious enough to try it in competition because I wanted to get on the husband-wife team solve unofficial record page.


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## Swordsman Kirby (Jun 30, 2008)

brunson said:


> Oh yeah? Well, does she know all 57 3x3 OLLs? ;-)



I've gotten two sub-12 averages, and I only know 50.


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## Kenneth (Jun 30, 2008)

masterofthebass said:


> Kenneth, there can perhaps be a shorter alg that doesn't preserve f2l, it just flips the edge and doesn't worry about preserving the position of any other ones. In FMC you can check to see if you get OLL parity and then fix it before you do any 3x3 moves.



Maybe so but you will at the most save an AUF-turn, not more (I cannot prove this but I tried a lot of ways to solve paritys and my intuition says I'm correct).



AvGalen said:


> There is a mistake there Kenneth, so just to keep it short and simple:
> The problem with OLL parity is indeed the even/odd situation. For 4x4x4 that means that if the scramble has an odd number of wide/inner-slice turns (counted in quarter turn metric) you will have to solve the *centers*...



Yes, but it's the same. after centres are done they are always restored again if they are broken at some point (edge pairing), the 3x3x3 stage does not break centres.

I actually tried to solve parity using intuition by first doing r (one turn parity fix) and then replace the F2L pieces that was lost from that without restoring the r-turn (U2 r U2 r' and so on). and then solve the LL by commutators (not using reduction, it was direct). It works fine.


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## brunson (Jun 30, 2008)

Mike Hughey said:


> brunson said:
> 
> 
> > That's actually really cool, Mike. My little girl is 3 right now and I'm looking forward to the day she or her little brother expresses an interest in solving daddy's cube.
> ...


I should start her off slowly like that and see if she wants to play. I wasn't sure if it was too early.


Mike Hughey said:


> brunson said:
> 
> 
> > Are all three Hughey girls with WCA records your daughters?
> ...


Very nice. My wife is completely disinterested. I think it's sweet when I tell her about my Sunday Contest times and she congratulates me, beyond that, I may as well be telling her about the clever programming algorithm I came up with at work. It's the glazed look plus, "That's nice, Dear."


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## Mike Hughey (Jun 30, 2008)

brunson said:


> Mike Hughey said:
> 
> 
> > brunson said:
> ...


The thing that got her going was seeing her bigger sisters doing speedsolves on a stackmat. She really loved that, and wanted to use the stackmat to "solve" the cube. At first, that would just mean picking up the cube, twisting it a bit, then dropping it and stopping the timer. It's only been the last month or two that she has actually understood the difference between a solved and an unsolved cube. Once she understood the difference, it was pretty easy to get her to solve a 2-turn scramble - my oldest daughter Marie figured out how - you just tell her to "solve the yellow face first", or whatever face can be solved with one turn. Then she can figure out the rest. After a few solves like this, she got where she didn't need to be told what color to solve first.


brunson said:


> Mike Hughey said:
> 
> 
> > brunson said:
> ...


I'm very proud of the fact that my wife understands my addiction so well that she actually bought me extra 3x3x3 cubes as a present without my asking for them, since she knows that even though I already have more than 10 3x3x3s, I want more (for multiBLD). Now that is an amazingly empathetic cubing wife! (She's bringing back 3 more from China - I'm really looking forward to seeing what they're like. She says 2 of them actually turn pretty well.)

I am sorry for hijacking this thread like this - brunson, maybe you should PM me if you want to continue this discussion. (This is even worse than my usual hijacking - I'm sorry for that.) Now back to the discussion on avoiding parity on big cubes...


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## rjohnson_8ball (Jun 30, 2008)

@brunson, Chris Hardwick's alg only swaps an "l" cubie with a "r" cubie in a super edge:
r2 B2 U2 l U2 r' U2 r U2 F2 r F2 l' B2 r2
Nothing else gets altered. This is useful for a big "even x even" cube like 4x4 or 6x6 where you cannot [easily] tell which cubies in the edge are right or wrong until you are done with F2L, and you don't want that progress messed up. For big "odd x odd" cubes, you can see and fix the parity problem right away, before F2L, and use (Rr) and (Ll) in place of r and l to twist faster.

Did I answer your question, or did I misunderstand?

I am not fast with big cubes. I only use this one OLL parity algorithm, and only one PLL parity algorithm (the one that swaps UF and UB super edges). Oh yeah, and an alg for fixing center cubies in really big cubes.


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