# Detecting early if 4x4 is in parity.



## Magmatic (Aug 23, 2020)

I'm new to this forum, but not new to cubing.

When solving a 4x4, I hated ending with a dedge parity, so I came up with a way to detect that early in the solve. If anyone cares to detect parity early, you can see how here.






How to Solve a Parity Error in a 4x4x4 Rubik's Cube Without Memorizing a Long Algorithm | timkoop | timkoop







timkoop.com


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## Christopher Mowla (Dec 13, 2020)

Nice observation, but a (Rr) turn is just (by definition) what odd parity algorithms are built from. There are some very short (and much less "destructive") moves you can do to resolve the parity. To me, one of the greatest joys that the 4x4x4 brings is all that comes with understanding how parity algorithms work.

As an example of what I mean by the first sentence, I highly recommend my video Solving 4x4x4 Parity Intuitively (For Real).


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## Nir1213 (Dec 14, 2020)

Christopher Mowla said:


> Nice observation, but a (Rr) turn is just (by definition) what odd parity algorithms are built from. There are some very short (and much less "destructive") moves you can do to resolve the parity. To me, one of the greatest joys that the 4x4x4 brings is all that comes with understanding how parity algorithms work.
> 
> As an example of what I mean by the first sentence, I highly recommend my video Solving 4x4x4 Parity Intuitively (For Real).


im not sure if he is around anymore, but when i get a 4x4 i might watch your video!


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## JakeCanSolve (Dec 14, 2020)

Nir1213 said:


> im not sure if he is around anymore, but when i get a 4x4 i might watch your video!


he hasen't been on this forum since september


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## abunickabhi (Dec 18, 2020)

Cale has tried detecting parity early in speedsolve, and I also tried it a bit in 2017. It is not worth it, as it takes up a lot of bandwidth to recognise and bad edges in multiple of 4s and then do the number of slices accordingly.


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## dudefaceguy (Dec 18, 2020)

If you really hate 4x4 odd parity you can just use a direct solving method and leave one slice unsolved until the end. You can then detect the parity state instantly, and switch between even and odd parity with a quarter turn of the unsolved slice. Here's my method based on this concept: https://www.speedsolving.com/threads/intuitive-4x4-method-with-parity-avoidance.73049/

I call it QTPI (cutie pie) Method, or Quarter Turn Parity Intuitive Method. It's not really a speed method, but you can use it if you really hate parity algs (or really love understanding parity as a concept).


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## Christopher Mowla (Dec 19, 2020)

I am surprised that no one has not said anything, but if someone *really* wants to *avoid* parity algorithms AND parity fixes (which are more than 1 move *to fully resolve the parity*), they need to determine whether the permutation of the *24* wing edges is odd or even before the third composite center is completed. This is definitely okay if they are *not* *worried about speed*, but cycle counting is a sure way to avoid OLL parity -- when starting with a fully scrambled 4x4x4.

I guess no one said anything because that's not what Magmatic's post is about -- just *detecting* parity. Fair enough. But still surprised.



dudefaceguy said:


> If you really hate 4x4 odd parity you can just use a direct solving method and leave one slice unsolved until the end.


Five things:

If someone doesn't like to learn *one* (parity) algorithm, why would they choose to learn an entirely new (well, your method is like Sandwich, which is more than a decade old -- or Cage, which is about two or maybe even three decades old) method which requires *many* algorithms? *(See footnote 1.)*

Especially if they knew the full truth behind it (and its *false* promises). The worst part of Sandwich, cage, etc., is sometimes it happens that a 2-cycle of wings will appear in the last slice unintentionally. *So you have to fix the parity anyway.* (It's not a fool-proof *avoidance* approach. It just increases your chances of _not_ getting it. But you will have to constantly "fight it off" during the solve like a fly buzzing in your ear.)


I think Magmatic's chosen way to *detect* if OLL parity exists is most "cost effective" for beginners. (Of course, this concept is rudimentary to some of us, but it was new to him and he wanted to share. So that's a nice gesture.)

The only premise for "Magmatic's approach" is that someone is solving the 4x4x4 with Reduction (or one of its variants) and that they need to learn what a "good edge" and a "bad edge" is. (Which is obviously a rather useful skill for Petrus, Heise, etc.) It doesn't require them to learn a method which is *overkill* just for the sake of *avoidi*ng parity algorithms -- a method which does not guarantee that at all as stated in bullet point #1.)


Your method doesn't help to "understand parity as a concept" any more than doing an inner slice quarter turn and then see what happens. As a matter of fact, all you are doing is solving a cube until it becomes in the same state as if someone did a slice quarter turn to a cube. So you would rather spend at least 50 moves more, make the solving process harder three fold, just to arrive at the same state that you could get from the end of reduction (that is, if you just simply choose to fix the parity by doing an inner layer slice quarter turn)?


Some people have solved the 4x4x4 rather quickly with Cage, Sandwich, etc. (Essentially with your chosen method.) So it most certainly can be a speed method. It may not be a WR method, but solving the 4x4x4 in around a minute with it isn't unheard of.


How did my video (that I linked to previously in this thread) not help understand fixing parity (without wrecking the cube)* intuitively*? Just curious.

(Again, I might be a little biased, but in that video I explicitly stated that "You can use any moves you wish, as long as you write down the moves you use" to make a certain pattern of centers in a 4x4x4 inner layer slice.)

As a simile, the "method" in my video is to fixing parity as laser surgery can help remove an obstruction with precision and "as little mess" as possible. Your chosen approach is to fixing parity as shuffling someone's insides until you feel the obstruction . . . where when you "feel it", you may keep moving it around before you actually get it out.

My video may be 17 minutes long, but I repeated myself quite a bit.
*Footnotes:*

Yes, I love commutators and *I can say I know my fair share* about them. But *they ARE algorithms*. They don't come natural, but with memorization based on successful results from experimentation.


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## dudefaceguy (Dec 21, 2020)

Christopher Mowla said:


> I am surprised that no one has not said anything, but if someone *really* wants to *avoid* parity algorithms AND parity fixes (which are more than 1 move *to fully resolve the parity*), they need to determine whether the permutation of the *24* wing edges is odd or even before the third composite center is completed. This is definitely okay if they are *not* *worried about speed*, but cycle counting is a sure way to avoid OLL parity -- when starting with a fully scrambled 4x4x4.
> 
> I guess no one said anything because that's not what Magmatic's post is about -- just *detecting* parity. Fair enough. But still surprised.
> 
> ...


I'm sorry if it sounded like I was attacking you in some way - I haven't watched your video and my post was not directed towards you at all. I'm not trying to prove anything or refute anything. I just thought this was a friendly discussion about ways to detect 4x4 parity, which is a very interesting subject that can be approached in many ways.

Please forgive me if I don't respond to your questions - I'm not interested in having a debate or argument. Thanks for all of your great work on parity - I've read many of your threads.


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## Christopher Mowla (Dec 21, 2020)

No offense taken and no offense intended. Just rhetorical questions to hopefully give people insight into something that I _obviously_ had thought about for a while. I have made my _fair share_ of inefficient (and complicated) methods that I thought were interesting but were much too impractical for anyone but enthusiasts to maybe _glance_ at.

(So sorry if I came off strong or direct, but I too believed as you (did?) about Sandwich, Cage, etc., because that's what I read when I started puzzle theory also.)

Huge respect for your efforts on intuition though. And thanks for the compliments and *professional* reply to my post which can easily be taken as offensive!


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## ABCubeTutor (Dec 31, 2020)

a parity is caused when an invisible center is off a quarter turn. if you make the quarter turn and then solve, parity disappears, no memorization. see https://www.speedsolving.com/wiki/index.php/ABCube_Method for details.


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## dudefaceguy (Jan 1, 2021)

ABCubeTutor said:


> a parity is caused when an invisible center is off a quarter turn. if you make the quarter turn and then solve, parity disappears, no memorization. see https://www.speedsolving.com/wiki/index.php/ABCube_Method for details.


Cool intuitive method - this is basically how I solve, plus some other modifications. The key aspect of leaving a single slice unsolved so that you can easily toggle parity is the same.

It seems to me that such elegant solutions are really unsuitable for speed cubing though - you just need a parity alg and that's that. Of course you can have your cake and eat it too by studying and understanding the algs as Christopher has done.


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## ABCubeTutor (Jan 1, 2021)

dudefaceguy said:


> Cool intuitive method - this is basically how I solve, plus some other modifications. The key aspect of leaving a single slice unsolved so that you can easily toggle parity is the same.
> 
> It seems to me that such elegant solutions are really unsuitable for speed cubing though - you just need a parity alg and that's that. Of course you can have your cake and eat it too by studying and understanding the algs as Christopher has done.




ah, thanks, you called my method elegant. you are right, it does not lend itself for speed, it is a trade-off. i never went down the speed side of things. i guess that makes me the exception to the rule here.


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## ray5 (Jan 1, 2021)

Is it possible to check parity by counting the number of inner turns in the scramble?


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## DNF_Cuber (Jan 1, 2021)

ray5 said:


> Is it possible to check parity by counting the number of inner turns in the scramble?


it would be kinda impossible in a competition. If you know the scramble, you could just inverse it anyway.


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## Christopher Mowla (Jan 1, 2021)

ray5 said:


> Is it possible to check parity by counting the number of inner turns in the scramble?


To answer your question, yes. You count every wide (double layer) turn like Rw, (Rr), etc. And you count every inner layer slice turn. If there are an odd number of quarter (90 degree) turns, the scramble created parity. If even, then no parity.

Take the "Red Bull" algorithm as an example scramble. (Any move sequence, whether it scrambles the entire cube or just switches a few pieces can be considered a "scramble".)

Rw2 B2 U2 l U2 r' U2 r U2 F2 r F2 l' B2 Rw2

There is a total of *9 *inner layer quarter turns. So the above algorithm causes/fixes parity.


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