# 4x4 Parity Algorithms



## liljthedude (Mar 2, 2009)

I saw that there are only 2 algorithms. What are the two I need. I found 2r 2U 2r 2U* 2r 2u, and 2R* 2B 2U L* 2U (R' r ') 2U R* 2U 2F R 2F L*i 2B 2R*. But I don't know what "*(R' r')*" is.


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## byu (Mar 2, 2009)

(R' r') means to turn the right layer and the layer inside (two right layers) counterclockwise.


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## liljthedude (Mar 2, 2009)

Oh ok, they should've used a *.

THANKS!


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## byu (Mar 2, 2009)

The * isn't standard notation, (R' r') is much more commonly used.


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## liljthedude (Mar 2, 2009)

Oh, ok. I need to learn more versions of 4x4 notation.


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## pcharles93 (Mar 2, 2009)

Or just the official one. Lowercase letters denote inner slice turns. A letter with 'w' after it is denoting double layer turns. That's about all I remember learning when I got around to learning about 4x4ing.


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## liljthedude (Mar 2, 2009)

Yeah, I learned from Dan Brown. He used * so I am used to that. But I will definitely learn the official notation.


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## Gray (Mar 2, 2009)

liljthedude said:


> Yeah, I learned from Dan Brown. He used * so I am used to that. But I will definitely learn the official notation.



Yeah so did I. The notation just seemed easier to me.


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## James (Jun 2, 2009)

I have spent a while looking around and I can't find a collection of different 4x4 OLL parity algorithms in one place. What are your favorites?

I personally like Rw' U2 Lw F2 Lw' F2 Rw2 U2 Rw U2 Rw' U2 F2 Rw2 F2, but there are probably better ones.


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## AvGalen (Jun 2, 2009)

This is the biggest collection I have personnaly seen. Created by Michael Fung, former WR-holder


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## Robert-Y (Jun 2, 2009)

One day, we will all finish what Michael (plus a few others) have started


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## jcuber (Jun 2, 2009)

No case for the "corner" Parity? I want one.


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## Robert-Y (Jun 2, 2009)

jcuber said:


> No case for the "corner" Parity? I want one.



For now, it's best to do PLL parity + T perm or N perm (Depending on which one you're talking about). I don't know about any shorter algs.

EDIT: Oh wait, Clement has an alg for swapping two opposite corners, but I'm not sure if that's faster than PLL parity alg + N perm.


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## jcuber (Jun 2, 2009)

How long will it be before we get something like cube explorer (optimal or near-optimal) for a 4x4?


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## dougbenham (Jun 2, 2009)

http://www.stefan-pochmann.de/spocc/other_stuff/4x4_5x5_algs/


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## AvGalen (Jun 2, 2009)

jcuber said:


> How long will it be before we get something like cube explorer (optimal or near-optimal) for a 4x4?


Optimal: "never". Current optimal solvers are limited to about 13 moves and although 14, 15, 16 or maybe even 17 will be possible when computers get faster and faster it is unlikely that they ever will reach the "31" that I am personnaly guessing is the maximum length for "gods algorithm"
Near optimal: Well, as long as we don't know how many optimal is we really have no idea what "near optimal" would be, now don't we? But there is a 5-phase and a 6-phase solver for 4x4x4 that requires "about 60-something moves". You can find out more about this solver on http://cubezzz.homelinux.org/drupal/. I tried searching, but "4x4x4" gave me now hits


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## jcuber (Jun 2, 2009)

What about an alg generator for 4x4 LL only?


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## Kian (Jun 2, 2009)

AvGalen said:


> jcuber said:
> 
> 
> > How long will it be before we get something like cube explorer (optimal or near-optimal) for a 4x4?
> ...



never is a long time.


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## AvGalen (Jun 2, 2009)

jcuber: As long as the LL-alg won't be very long (remember, about 13 moves) you can try Clement Gallets solver
Kian: That's a pretty useless post. I already said "never" instead of never, but I challenge you to calculate the following: Let's say that 13 moves on a pc would only take 30 minutes and that computers will double in speed every 18 months. Now please calculate how long it would take to find a 30 move solution on a 4x4x4 NOW, and if you would still be alive when that can be done in 30 seconds. Seriously, please calculate this so you get a grasp about "big numbers"


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## Kian (Jun 2, 2009)

AvGalen said:


> jcuber: As long as the LL-alg won't be very long (remember, about 13 moves) you can try Clement Gallets solver
> Kian: That's a pretty useless post. I already said "never" instead of never, but I challenge you to calculate the following: Let's say that 13 moves on a pc would only take 30 minutes and that computers will double in speed every 18 months. Now please calculate how long it would take to find a 30 move solution on a 4x4x4 NOW, and if you would still be alive when that can be done in 30 seconds. Seriously, please calculate this so you get a grasp about "big numbers"



I can't begin to imagine how unbelievable those numbers would be. It would be astronomical. I wasn't really trying to challenge you, I certainly don't believe I'll be alive for a computer with power of that magnitude.


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## blah (Jun 3, 2009)

http://www.speedsolving.com/forum/showthread.php?t=11311

Ergonomy, anyone?


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## mrCage (Jun 3, 2009)

James said:


> I have spent a while looking around and I can't find a collection of different 4x4 OLL parity algorithms in one place. What are your favorites?
> 
> I personally like Rw' U2 Lw F2 Lw' F2 Rw2 U2 Rw U2 Rw' U2 F2 Rw2 F2, but there are probably better ones.


 
Hmm, why would you want this?? It suffices with only *one* such algorithm and a (commutator) 3-cycle. Then again, im not a hard-core speedcuber. What premethod would it be useful for? Certainly not the common ce3 method ...

Per


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## amostay2004 (Jun 3, 2009)

blah said:


> http://www.speedsolving.com/forum/showthread.php?t=11311
> 
> Ergonomy, anyone?



Was just about to point that out


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## V-cube7_101 (Jun 6, 2009)

For the corner parity error, hold the cube so that the 2 misplaced corners are facing you and are adjacent, then do the algorithm that is used when flipping the middle edge on a 5x5, and the move is R2 B2 U2 L U2 R' U2 R U2 F2 R2 F2 L' B2 R2.

Note: This move usually uses some middle layers, but this time, just move the outer layers. Their could be a shorter move but this is the one I use.


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## mrbiggs (Jun 6, 2009)

AvGalen said:


> jcuber: As long as the LL-alg won't be very long (remember, about 13 moves) you can try Clement Gallets solver
> Kian: That's a pretty useless post. I already said "never" instead of never, but I challenge you to calculate the following: Let's say that 13 moves on a pc would only take 30 minutes and that computers will double in speed every 18 months. Now please calculate how long it would take to find a 30 move solution on a 4x4x4 NOW, and if you would still be alive when that can be done in 30 seconds. Seriously, please calculate this so you get a grasp about "big numbers"



True, but not quite fair--cube solutions are not (in fact, can't be) calculated with a brute force algorithm. They use heuristics to tell them where to search. If the heuristic function satisfies certain properties, you can be guaranteed to get an optimal solution anyway.

So an improved heuristic function does have the potential to make a 4x4x4 optimal solver, possibly even on today's computers. Granted, as you point out, the accuracy of the heuristics we have today are far from what would be necessary for such an optimal solver; I'm just pointing out that the hardware restrictions are not necessarily the bottleneck.


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## qqwref (Jun 6, 2009)

Robert-Y said:


> jcuber said:
> 
> 
> > No case for the "corner" Parity? I want one.
> ...



This is what I use for opposite corners:
L U L' [PLL-parity] y' R U R' U' R' F R2 U' R' U' R U R' U' F'


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## Robert-Y (Jun 6, 2009)

qqwref said:


> Robert-Y said:
> 
> 
> > jcuber said:
> ...



Lol ok I'm wrong about the opposite corners thing then  (I'm gonna learn this alg )


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## blah (Jun 6, 2009)

I actually like opposite corners because I get to do my favorite N perm from any direction without AUF or cube rotations, then the PLL parity alg, with a 3/4 probability of having some sort of move cancellation. And the best case is when the "required AUF" is a U2 - this way it cancels with the annoying U2 at the start/end of the PLL parity alg (I use 2R2 U2 2R2 Uw2 2R2 Uw2).


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## EricReese (Mar 29, 2011)

*4x4 Parity*

I didn't really find anything to my interests on youtube. But could any of you who are particularly fast on doing 4x4 parity algs mind creating a video or explaining any fingertricks you do? I don't believe there is anything special to them, but right now I am just terribly slow at doing them and was looking for ways to improve, and i figured I would examine my parity algs


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## freshcuber (Mar 29, 2011)

r U2 r U2 r' U2 r U2 l' U2 r U2 r' U2 M r' U2 r'


Is that the one you already use?


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## TiLiMayor (Mar 29, 2011)

Ask waffo, he has some fast parity algs.


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## EricReese (Mar 29, 2011)

freshcuber said:


> r U2 r U2 r' U2 r U2 l' U2 r U2 r' U2 M r' U2 r'
> 
> 
> Is that the one you already use?


 Yea thats my pure flip. I already know how to fingertrick that from his video. But I was more talking about the standard r2 B2 one.


TiLiMayor said:


> Ask waffo, he has some fast parity algs.



I'll ask him for anything other then the pure flip. Although I love performing the pureflip. Its slower then my regular alg.


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## Kian (Mar 29, 2011)

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


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## EricReese (Mar 29, 2011)

Kian said:


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


 
I can't seem to get that to work


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## Kian (Mar 29, 2011)

EricReese said:


> I can't seem to get that to work


 
Take your time and don't do any X turns you don't see there. It will work.

Edit: Btw those the r and r' moves I listed are wide turns, not slice turns. Maybe that was your problem?


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## RyanReese09 (Mar 29, 2011)

EricReese said:


> I can't seem to get that to work


 
Try harder.


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## EricReese (Mar 29, 2011)

Kian said:


> Take your time and don't do any X turns you don't see there. It will work.
> 
> Edit: Btw those the r and r' moves I listed are wide turns, not slice turns. Maybe that was your problem?


 
Yea that was my problem. 

I quite like that OLL parity alg. With plenty of double flicks I think I can get that sub 3  thanks a bunch Kian


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## freshcuber (Mar 29, 2011)

Kian said:


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


 
That's a double parity alg. lancetheblueknight shows the same alg with a variation on execution. That's the only alg I use for OLL parity which sucks cause I give myself PLL parity a lot.


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## RyanReese09 (Mar 29, 2011)

freshcuber said:


> That's a double parity alg. lancetheblueknight shows the same alg with a variation on execution. That's the only alg I use for OLL parity which sucks cause I give myself PLL parity a lot.


 
PLL parity is still 50/50 shot so it's not like its *hurting* to do it.


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## Sa967St (Mar 29, 2011)

http://www.speedsolving.com/forum/showthread.php?11311-4x4x4-OP-DP-algorithms-(more-finger-friendly

Waffo doing a pure O parity in 2.94: http://www.youtube.com/watch?v=Cfjq6Tap8zE
Chester doing a DP parity in 3.1x http://www.youtube.com/watch?v=2q4jBnLsSfA


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## freshcuber (Mar 29, 2011)

True considering everytime I have OLL parity but not PLL parity it's cause I already solved it.


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## maggot (Mar 29, 2011)

For me dp is faster than pure.. last time I checked I was about low 4s on dp... and you know I'm not that fast turning.


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## waffle=ijm (Mar 29, 2011)

pure pure pure pure pure pure pure pure


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## EricReese (Mar 29, 2011)

WAFFOo

I texted you <3

You never responded


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## waffle=ijm (Mar 29, 2011)

the OLL is my main ya
and for PLL parity Rw2' F2 U2 r2 U2 F2 Rw2


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## Godmil (Mar 30, 2011)

freshcuber said:


> r U2 r U2 r' U2 r U2 l' U2 r U2 r' U2 M r' U2 r'





Kian said:


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



You get that the second one is just the inverse of the first one right? If you already do the first one with inner slices just make them wide turns and you may find it quicker.


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## Escher (Mar 30, 2011)

I should maybe start using the two Lucas algs too idk...


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## ZamHalen (Apr 3, 2011)

Kian said:


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


The alg becomes pure if you use just inner slices do variations on the last moves
.
And it's not DP it creates an f-permish sort of move


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## RyanReese09 (Apr 3, 2011)

He never claimed it to be a DP alg.


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## Vinny (Apr 3, 2011)

I just use the standard. I do the Rw's with my right hand, Lw's with my left hand, and all the U's are U2 so I just use my index and middle finger.

I suck though. It takes me over 5 seconds for OLL.


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## ZamHalen (Apr 3, 2011)

freshcuber said:


> That's a double parity alg. lancetheblueknight shows the same alg with a variation on execution. That's the only alg I use for OLL parity which sucks cause I give myself PLL parity a lot.


 
He did


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## EricReese (Apr 3, 2011)

ZamHalen said:


> He did


 
Then why did you quote Kian, and not include the quote from freshcuber? ........


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## James Cavanauh (Aug 11, 2011)

*4x4 parity algs?*

I have been searching around but havent found anything linking to the shortest parity algs for 4x4 around (particularly the oll one) does anyone know what the shortest one is?


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## wontolla (Aug 11, 2011)

I use:

orientation: r U2 x r U2 r U2 r' U2 l U2 r' U2 r U2 r' U2 r'

permutation: r2 U2 r2 u2 r2 U2

I'm not sure if they are the shortest, but they are not long either.


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## TiLiMayor (Aug 11, 2011)

Permutation:
Uw2 Rw2 U2 r2 U2 Rw2 Uw2


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## cuBerBruce (Aug 11, 2011)

See:

[post]526350[/post]
[post]531938[/post]
[post]540571[/post]


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## TMOY (Aug 11, 2011)

Shortest Oll parity alg: u
Shortest PLL parity alg: U
Since no 0-move alg can fix any parity, these two are of the shortest possible length. QED..


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## Kirjava (Aug 11, 2011)

TMOY said:


> Shortest Oll parity alg: u



OLL parity algs generally leave the centres solved.



TMOY said:


> Shortest PLL parity alg: U



This doesn't fix the parity.

also inb4 cmowla


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## chikato_tan (Aug 11, 2011)

Does anyone have an alg to solve this case ? The fast way ,of course.


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## Innocence (Aug 11, 2011)

chikato_tan said:


> Does anyone have an alg to solve this case ? The fast way ,of course.


 
R U R' U' r2 U2 r2 Uw2 r2 u2 U R U' R'


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## whauk (Aug 11, 2011)

R2 D' x is a shorter setup


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## chikato_tan (Aug 11, 2011)

Innocence said:


> R U R' U' r2 U2 r2 Uw2 r2 u2 U R U' R'


 are you sure it`s the right one , because i follow the alg and it becomes a mess , BTW , what`s the difference between u and Uw ?


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## Tentacius (Aug 11, 2011)

"u" is just the inner layer, and Uw is both the inner and outer layer. (WCA notation)

http://alg.garron.us/?alg=u_Uw&cube=4x4x4&notation=WCA


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## ben1996123 (Aug 11, 2011)

z Dw' m D Lw' Uw' r' Uw Lw Uw' Lw2 Bw' r' Bw Rw' R' u s Uw z'


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## reThinking the Cube (Aug 13, 2011)

cmowla said:


> cuBerBruce's post shows the shortest 4x4x4 algorithms which convert a 4x4x4 with parity into a pseudo 3x3x3,...



I know you and CB already know this, but I feel obligated to say it anyway - that the shortest AND (IMO) best way to do this, is by the first 13 turns of reParity™ = Rw U2 Lw' U2 x' Rw' U2 Lw U2 Rw' U2 Lw U2 Lw'


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## Cheese11 (Aug 16, 2011)

http://www.youtube.com/user/Erickulchycki?feature=mhee#p/u/7/rx5YKIlgOhs


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## Jorghi (Aug 16, 2011)

I've never done 4x4, but how many parity algorithms are there? Couldn't you do Parity + Edge Permutation then Corner permutation. That way if the corners are already permuted then you are lucky.


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## Hershey (Aug 16, 2011)

Jorghi said:


> I've never done 4x4, but how many parity algorithms are there? Couldn't you do Parity + Edge Permutation then Corner permutation. That way if the corners are already permuted then you are lucky.


 
You really need only 2-3 algs:
OLL parity
PLL 4 edge swap (aka PLL parity)
Double parity


PLL parity is technically not parity since there is an even number of swaps (2 swaps).


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## uberCuber (Aug 16, 2011)

For purposes of normal reduction solving, I've never really seen the point in a "double parity" alg. For it to be useful, you would have to recognize if there is PLL parity before even beginning OLL. Since you can tell if you will have OLL parity or not before you even finish F2L, how are you supposed to recognize PLL quickly enough to make it worthwhile, considering that you have to recognize it without the LL correctly oriented?


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## cubersmith (Aug 16, 2011)

Hershey said:


> You really need only 2-3 algs:
> OLL parity
> PLL 4 edge swap (aka PLL parity)
> Double parity
> ...


 
I didnt know it had to be an odd number of swaps to be parity?


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## uberCuber (Aug 16, 2011)

cubersmith said:


> I didnt know it had to be an odd number of swaps to be parity?


 
Define parity.


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## reThinking the Cube (Aug 16, 2011)

Hershey said:


> PLL parity is technically not parity since there is an even number of swaps (2 swaps).


 
Technically, it will be parity (unable to solve as a reduced 3x3x3 without using slice turns) if the corner permutation does not match the dedge permutation. What is described as PLL parity is a double swap of 4x4x4 edge pieces, but is also a 2-cycle of 3x3x3 dedge (odd dedge permutation) in the reduction state. If the corners are already solved - then the corner permutation is even and does not match that dedge permutation, and this is an impossibility with an actual 3x3x3, and therefore it must also be parity.


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## uberCuber (Aug 16, 2011)

Definitions of parity are so inconsistent. If using a direct-solve method, that exact same case would not be considered parity.


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## Hershey (Aug 16, 2011)

I think Chris Hardwick said somewhere that PLL parity is only called a parity when using reduction or something like that?

anyway I thought in cubing, parity is an odd number of swaps for edges/corners.



cmowla said:


> Not sure if this is faster, but you might like it:
> Rw' U R U Lw' U2 Rw' U2
> r2
> U2 Rw U2 Lw U' R' U' Rw


 
OMG alg.


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## Rpotts (Aug 16, 2011)

reThinking the Cube said:


> Technically, it will be parity (unable to solve as a reduced 3x3x3 without using slice turns)



this is not a technical definition of parity.


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## reThinking the Cube (Aug 16, 2011)

Rpotts said:


> this is not a technical definition of parity.



Technically, it is.


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## Hershey (Aug 16, 2011)

What is the definition of parity?

"Parity is a misnomer cubing term that is used colloquially to describe an odd permutation of pieces within a certain defined orbital"?



reThinking the Cube said:


> Technically, it is.



Oh really?


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## reThinking the Cube (Aug 16, 2011)

uberCuber said:


> Definitions of parity are so inconsistent. If using a direct-solve method, that exact same case would not be considered parity.



Show me a direct-solve parity case, so that I might define it consistently.


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## Rpotts (Aug 16, 2011)

it's an swap of two pieces.

OLL parity is parity in direct solve methods, or K4 ELL, but PLL parity is not, as its *two* two swaps


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## Hershey (Aug 16, 2011)

reThinking the Cube said:


> Show me a direct-solve parity case, so that I might define it consistently.


 
rU2r'U2r'U2lU2r'U2rU2F2r2F2l' is a direct solve parity.

rU2r'U2r'U2lU2r'U2rU2F2r2F2l'U2rU2r'U2r'U2lU2r'U2rU2F2r2F2l' is PLL parity done by doing direct solve parity case , U2, then the direct solve parity case again.


If you do OLL parity, U2, and then OLL parity again, you end up with two flipped edges (the <M,U> algorithm on 3x3).]
Basically doing an odd swap of edges then doing an odd swap again creates a case that is not parity.



Rpotts said:


> OLL parity is parity in direct solve methods, or K4 ELL, but PLL parity is not, as its *two* two swaps



Why not be consistent with definitions and consider PLL "parity" not to be parity at all? Lets not relate 4x4 to 3x3?


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## reThinking the Cube (Aug 16, 2011)

Not all odd permutations are parity, and not all parity are an odd number of odd permutations.


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## Hershey (Aug 16, 2011)

reThinking the Cube said:


> Not all odd permutations are parity, and not all parity are an odd number of odd permutations.


 
Then what is parity?


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## ianography (Aug 16, 2011)

A good PLL parity algorithm is Uw2 r2 U2 r2 U2 r2 Uw2. I use it sometimes


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## reThinking the Cube (Aug 16, 2011)

Rpotts said:


> it's an swap of two pieces.
> 
> OLL parity is parity in direct solve methods, or K4 ELL, but PLL parity is not, as its *two* two swaps



Technically, (lol) there can be no parity within the context of a direct-solve (unless the cube is in an illegal state requiring disassembly to solve correctly). Sure, you may get and recognize a direct solve case as being identical to some OLL/PLL reduction state parity case, but that does NOT make it a parity in the context of a direct-solve. When direct-solving, that reduction state OLL parity is simply just another 2-cycle of edges, with or without some usually unnoticed center piece cycles.


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## Christopher Mowla (Aug 16, 2011)

Hershey said:


> rU2r'U2r'U2lU2r'U2rU2F2r2F2l' is a direct solve parity.


Here's an entirely different algorithm for that case.
 Uw' Lw Uw l Uw' Rw' Uw Rw2 Bw l Bw' Lw L Uw' Rw z (16q, 15 btm)

Here are other conventional algorithms.
 l2 F2 U2 l' U2 l2 F2 l' U2 l2 U2 F2 l' F2 (25q, 14 btm)
 Lw U2 l' U2 l' U2 r U2 l' U2 l U2 r' l U2 l2 U2 Lw' (27q, 18 btm)





Hershey said:


> cmowla said:
> 
> 
> > Not sure if this is faster, but you might like it:
> ...


Does this mean you like it?


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## Jorghi (Aug 16, 2011)

reThinking the Cube said:


> Technically, (lol) there can be no parity within the context of a direct-solve (unless the cube is in an illegal state requiring disassembly to solve correctly). Sure, you may get and recognize a direct solve case as being identical to some OLL/PLL reduction state parity case, but that does NOT make it a parity in the context of a direct-solve. When direct-solving, that reduction state OLL parity is simply just another 2-cycle of edges, with or without some usually unnoticed center piece cycles.



Yeah this makes sense. People act like Parity is some legendary thing when its just part of the solve.


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## Hershey (Aug 16, 2011)

cmowla said:


> Here's an entirely different algorithm for that case.
> Uw' Lw Uw l Uw' Rw' Uw Rw2 Bw l Bw' Lw L Uw' Rw z (16q, 15 btm)
> 
> Here are other conventional algorithms.
> ...


 
Yes. Also, how do you find all of these 4x4 algorithms?


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## Christopher Mowla (Aug 16, 2011)

Hershey said:


> Yes. Also, how do you find all of these 4x4 algorithms?


The first one is a one move conjugation of the base for "The Holy Grail of Pure Edge Flip Algorithms." So that one was by hand. The second algorithm (25q/14 btm) I found with cube explorer using the center facelet twist option (the set-up was an N-Perm). The last algorithm I also found by hand, using the same techniques I have shown in my methods parity thread in puzzle theory.

EDIT:
Also, for the adjacent PLL parity algorithm, I found it by hand just using the technique of conjugating the move r2. As I have posted here in the K4 thread, here is a link to a large collection of 2 2-cycles using this technique.
View attachment 2_2-Cycles.txt
That technique has obviously been known a while, due to the prior existence of the algorithms [r2 F2 U2: r2] and [Uw2 r2 U2: r2]. I just looked at those algorithms in a different way to see the bigger picture. Under special circumstances, we can stretch this technique even to handle 4 2-cycles by conjugating (l2 r2) (or M2 on the 4x4x4). For example, [F2 r2 F2 U' M2 U: M2].

Also,
Here are possible optimal algorithms (in quarter turns, at least) for all of the other LL 2-cycle cases. (All found by hand, of course).

Opposite [Prior publicly known minimum until this post, 19q]
y r u Rw' Uw' r' Uw Lw Uw' r2 Fw' r' Fw r' Uw f' r' x y' (17q, 16 btm) (Optimal Algorithm in btm is 12).

Unoriented Adjacent 1 (minor modification of the HG Edge Flip Alg) [Prior publicly known minimum until this post, 21q] (Optimal alg in btm is 15)
z Dw' (M R') D Lw' Uw' r' Uw Lw Uw' Lw'2 Bw' r' Bw Rw' R' u y' (M' R) Uw x2 z' (19q, 18 btm)

Unoriented Adjacent 2 [Prior publicly known minimum until this post, 21q] (optimal alg in btm is 15).
Rw b' Dw r2 x' Uw' r' Uw x' r' Uw Lw' Uw' r' Uw Lw Uw2 x' d Rw' x' (19q, 17 btm)

Oriented Adjacent [Prior publicly known minimum until this post, 21q]
x' Uw l Uw' Rw2 x Uw' l' Uw Lw' L' x Uw Rw' Uw' l' Uw (Rw l') Uw' x (17q, 16 btm)


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## Nico1 (May 28, 2012)

I don't want to take credit for this extremely easy and fast algorithm because it is the creation of my friend, but here it is:

Lw U2 Lw U2 Lwi U2 Lw U2 Rwi U2 Lw U2 Lwi U2 Lw2 Rw U2 Lwi

This alg simply turns the UB dedge "in its socket."


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## Rpotts (May 28, 2012)

Most people would use y2 r U2 x r U2 r U2 r' U2 l U2 r' U2 r U2 r' U2 r' 

aka Lucas Parity. Your friend may have stumbled upon that, but it is already known.

Also, whoah 3 year necro.


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## cubernya (May 28, 2012)

Rpotts said:


> Most people would use y2 r U2 x r U2 r U2 r' U2 l U2 r' U2 r U2 r' U2 r'
> 
> aka Lucas Parity. Your friend may have stumbled upon that, but it is already known.
> 
> Also, whoah 3 year necro.


 
I prefer r' U2 r U2 r' F2 r2 U2 r U2 r' U2 _x U2 r2 U2 x'_
_Or F2 r2 F2_


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## Nico1 (May 28, 2012)

Rpotts said:


> Most people would use y2 r U2 x r U2 r U2 r' U2 l U2 r' U2 r U2 r' U2 r'
> 
> aka Lucas Parity. Your friend may have stumbled upon that, but it is already known.
> 
> Also, whoah 3 year necro.


 
Okay thanks!  Didn't know that had already been discovered (although i figured.) I prefer this way though because my sexy move on 3x3 M2i U M2i U Mi U2 M2i U2 Mi U2. I perform this with my left ring finger. Therefore, an Lwi is much easier for me than an Rw, also for some reason (I'm not left handed) Lw is easier with the left index finger than Rwi with the right index finger (probably because of the U2 not U2i that follows.) 

Also, this might seem like a dumb question, but what is "3 year necro."


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## vcuber13 (May 28, 2012)

i assume its referring to the bump


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## Rpotts (May 28, 2012)

3 year necro (necro bump) means you replied to a thread that hadn't been posted to in 3 years, you bumped a 3 year old thread to the front page.


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## BlackStahli (Jun 13, 2012)

James said:


> I personally like Rw' U2 Lw F2 Lw' F2 Rw2 U2 Rw U2 Rw' U2 F2 Rw2 F2, but there are probably better ones.


I use that one too^
However, these days I see all the fast 4x4 solvers like Mats and Feliks use the Lucas parity. Is that because of preference or just because it has a faster execution? I tried both but they're both equally fast for me, but the Lucas parity algorithm just doesn't feel as natural as the other one...


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## CubezUBR (Apr 11, 2013)

*4x4 pll. parity not seen before (help)*

So im new to 4x4 and found this parity/pll on the last layer. the whole cube is solved but the 2 edges are switched on 2 faces next to each other. here is a pciture
http://imgur.com/B2QJhFW
can you please tell me a algorithm to solve this or a link


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## JasonK (Apr 11, 2013)

R B (r U2 r U2 F2 r F2 l' U2 l U2 r2) B' R'
View at alg.garron.us


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## Cubenovice (Apr 11, 2013)

Makes me wonder which method you used?
Or did you just forgot / did not know how to pair up the last two edges?


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## CubezUBR (Apr 11, 2013)

i use reduction method for the first 3 layers but then use oll/pll to do the last layer. it works usually when i dont get this case and some others that i work out how to solve


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## scottishcuber (Apr 11, 2013)

CubezUBR said:


> i use reduction method for the first 3 layers but then use oll/pll to do the last layer. it works usually when i dont get this case and some others that i work out how to solve



I'm curious, what do you average with that?


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## kunparekh18 (Apr 11, 2013)

I don't think that's how it should be solved. First all centers, then all edges, then 3x3 stage.


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## Username (Apr 11, 2013)

kunparekh18 said:


> I don't think that's how it should be solved. First all centers, then all edges, then 3x3 stage.



Unless you're using K4 or any other method


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## kunparekh18 (Apr 11, 2013)

Username said:


> Unless you're using K4 or any other method



I should have specified. I meant reduction.


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## CubezUBR (Apr 11, 2013)

ok, i kind of made up that method because it was what i saw on bob burtons cubewhiz.com. what method do you recomend then?


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## Username (Apr 11, 2013)

CubezUBR said:


> ok, i kind of made up that method because it was what i saw on bob burtons cubewhiz.com. what method do you recomend then?



Yau


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## CubezUBR (Apr 11, 2013)

scottishcuber said:


> I'm curious, what do you average with that?



about 2 mins 30 secs. i had a 4x4 for 2 days now


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## Gordon (Apr 11, 2013)

That is fast for 2 days...


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## qqwref (Apr 11, 2013)

This is not PLL parity, but actually OLL parity - you can see that you only have to switch two edge pieces. The fact that all the yellow stickers on top is actually irrelevant.

PS: Your method is fine, feel free to keep using it if you like it.


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## Kirjava (Apr 11, 2013)

qqwref said:


> This is not PLL parity, but actually OLL parity



it hasn't been reduced to 3x3x3 - this is the edge permutation parity, of which OLL parity is an example.


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## qqwref (Apr 11, 2013)

That's just a difference in terminology. I like to call all wing permutation parities "OLL parity" because it's short without being ambiguous. (Nobody could think I'm talking about PLL parity, which is the important thing to me.)


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## Kirjava (Apr 11, 2013)

qqwref said:


> That's just a difference in terminology. I like to call all wing permutation parities "OLL parity" because it's short without being ambiguous.



Just using 'parity' is non-ambiguous in a non-reduction context and is shorter.

OLL Parity could mean a specific case in this context, and is ambiguous.


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## Christopher Mowla (Apr 11, 2013)

Besides


JasonK said:


> R B (r U2 r U2 F2 r F2 l' U2 l U2 r2) B' R'


, if you want an alternate algorithm, this might be the best I have come up with for speed:
x r U' R' U' r U R U M' U2 r U2 r' U2 l U2 r2 x'

For a large list of algorithms for this case (well the mirror of your specific case), see this.

EDIT:
I just noticed you can insert an R move which could make this faster without adding moves (when applying to the 4x4x4).
x r U' R' U' r U R U (M' *R*) U2 r U2 *R*w' U2 l U2 r2 x'


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## Christopher Mowla (Apr 19, 2013)

cmowla said:


> Besides, if you want an alternate algorithm, this might be the best I have come up with for speed:
> x r U' R' U' r U R U M' U2 r U2 r' U2 l U2 r2 x'


I just found these three which are related algorithms.
x r' U2 r' U2 M U' R' U' r' U R U r U2 l' U2 r2 x'
Lw' U2 r' U2 (M R') U' R U' r' U R' U r U2 l' U2 Rw2 x'
x Rw R U' R U' r U R' U M' U2 r U2 r' U2 l U2 Rw2 x'

I think the first alg listed in this post is even faster than the alg in my previous post (maybe the inverse is faster).


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