# Square-1 Parity Algs



## blade740 (Feb 13, 2009)

I'm really just posting this so that I can link to it instead of emailing the algs to everyone. 

O: opposite
A: adjacent
N: no swap


AA: /(-3,0)/(-3,0)/(-5,0)/(-2,0)/(4,0)/(-4,0)/(-2,0)/(5,0)/(-3,0)/ (matching bars at UR and DL)
AN: /(3,3)/(-1,0)/(2,0)/(-4,0)/(4,0)/(2,0)/(1,0)/(-3,-3)/ (matching bar at UR)
AO: /(3,3)/(-1,0)/(2,0)/(-4,0)/(4,0)/(2,0)/(-5,0)/(-3,-3)/ (matching bar at UL)
NA: /(-3,-3)/(0,-5)/(-4,-2)/(-4,0)/(-4,0)/(2,-4)/(5,0)/(-3,-3)/ (matching bar at DR)
OA: /(-3,-3)/(0,-5)/(-4,-2)/(-4,0)/(-4,0)/(2,-4)/(-1,0)/(-3,-3)/ (matching bar at DL)
OO: /(3,3)/(1,0)/(4,-2)/(2,-4)/(0,-4)/(3,3)/(3,0)/(3,3)/
ON: /(3,3)/(-1,0)/(-4,2)/(-2,4)/(0,1)/(3,3)/
NO: /(3,3)/(-1,0)/-4,2)/(-2,4))/(0,-5)/(3,3)/

Basically, I recognize parity and corner permutation at the same time. If there is no parity, I do a standard corner permutation alg and continue with a normal vandenbergh solution. If there IS parity, I do the parity alg that corresponds with the corner permutation and then continue with a normal vandenbergh solution. Basically, this means that by learning a few extra CP algs, I can save myself from having to learn half of the EP algs (and the worse half, at that).

Algs generated with Jaap's wonderful sq1optim program.


Oh, bonus: the AA alg is 2gen, and was half of the secret to solving the bandaged square-1.


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## Robert-Y (Feb 14, 2009)

Although I don't solve square-1s, let me be the first to say thanks as no-one has bothered so far .


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## Hakan (Feb 15, 2009)

Thank you very much.


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## AvGalen (Feb 15, 2009)

I don't know any algs for Square-1, except for the regular parity-alg. This is now on my to-learn-list


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## byu (Feb 15, 2009)

I'm going to have to actually use a square-1 to figure out these. I ordered mine off PuzzleProz a few days ago, and I'm still waiting for it to come. Do I need to memorize all of these to solve the Square-1?


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## DavidWoner (Feb 15, 2009)

byu said:


> I'm going to have to actually use a square-1 to figure out these. I ordered mine off PuzzleProz a few days ago, and I'm still waiting for it to come. Do I need to memorize all of these to solve the Square-1?



No, you only need one parity alg.


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## Vig (Feb 16, 2009)

Wow this is great insight thanks a bunch!


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## Sebastian-1 (May 27, 2009)

I don't understand how this works. I mean, first alg changes parity on D but not on U.



Help me please


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## Jokerman5656 (May 27, 2009)

the first letter stands for the top layer and the second for the bottom, at least i think thats how it works. time to experiment.


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## Jason (May 27, 2009)

I love a bit of square-1 action, and this seems really interesting although I don't quite understand the notation. When referring to Opposite, Adjacent, No Swap, what does it mean? And what does "matching bars" mean? Is a bar a solid colour of 2 corners and an edge aligned on a side? Are matching bars of the same colour?
This method has got me really interested in square-1 again, any help would be great


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## blade740 (May 27, 2009)

Recognition for this method is essentially twofold (though you can do both together with practice) First, determine whether or not you have parity. Then, you recognize a corner permutation case (essentially an ortega/guimond PBL case) A is an adjacent swap (like a J perm) O is an opposite corner swap (like a Y perm) N is no swap (like a U perm). Matching bar refers to the 2 corners that are paired up on an adj swap.


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## Jason (May 27, 2009)

Sweet, thank you very much Blade. I think I'm going to have a lot of fun this evening


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## blade740 (May 27, 2009)

Be safe. Don't forget to wear your helmet


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## blade740 (Sep 6, 2009)

Bump. I updated a few of the algorithms in the original post (namely AO, AN, NO, ON) Thanks to dan and dene for those algs. As a byproduct of generating algs with a solver that can't ignore pieces, I have large lists of algorithms for every case (directly output from jaap's solver) hosted here: http://dl.getdropbox.com/u/1186263/cpparity.rar
They're just text files, open them with notepad or whatever. If you find any algs that are more fingertrick-friendly than the ones I have posted here, let me know. I didn't really try very hard when I picked the original algs, so not all of them are that great.


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## deepSubDiver (Aug 31, 2010)

Sorry for this bump.

I have problems detecting whether I have parity or not. I usually try to visualize the permutations I get but it fails when it comes to O-perms (which seem to have the correct order of the edges in their respective layer but actually are parity cases). How do you go around that?


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## Forte (Aug 31, 2010)

deepSubDiver said:


> Sorry for this bump.
> 
> I have problems detecting whether I have parity or not. I usually try to visualize the permutations I get but it fails when it comes to O-perms (which seem to have the correct order of the edges in their respective layer but actually are parity cases). How do you go around that?



Do you do lots of 3x3? If you have four edges wrong and it's not a Z or H perm, then it's an O or W perm (W perm has some opposite edges)


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## hawkmp4 (Aug 31, 2010)

I don't know if this is really effective at speed (I'm not fast at sq1 at all) but I recognise the permutation case like a 3x3 case. If the perm on top is a 3x3 perm and the one on bottom is not (or vice versa) then I know I have parity. If both top and bottom have 3x3 perms or neither top nor bottom have 3x3 perms I know I don't have parity.


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## Forte (Aug 31, 2010)

hawkmp4 said:


> I don't know if this is really effective at speed (I'm not fast at sq1 at all) but I recognise the permutation case like a 3x3 case. If the perm on top is a 3x3 perm and the one on bottom is not (or vice versa) then I know I have parity. If both top and bottom have 3x3 perms or neither top nor bottom have 3x3 perms I know I don't have parity.



That's like, the only way to do it


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## masterofthebass (Aug 31, 2010)

Forte said:


> hawkmp4 said:
> 
> 
> > I don't know if this is really effective at speed (I'm not fast at sq1 at all) but I recognise the permutation case like a 3x3 case. If the perm on top is a 3x3 perm and the one on bottom is not (or vice versa) then I know I have parity. If both top and bottom have 3x3 perms or neither top nor bottom have 3x3 perms I know I don't have parity.
> ...



I do that in a different way than I do on 3x3 though. I usually do it by looking at blocks. For example, if there is a CEC block, I know that there cannot be another block (except for a j perm) for it not to have parity. On the same note, if there are 2 adj EC blocks, then unless there its a Jperm or Nperm (easy to detect) it has parity. Tricks like this really help me since you don't actually have to see the PLL (although I end up knowing what they are).


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## Dene (Aug 31, 2010)

Yea I use some tricks like masterofthebass said. Basically, with time you just get the hang of recognising parity cases just like you recognise PLLs. For some of them you will have heuristics, for others you will have to figure it out with brute force. For example, I have particular trouble distinguishing E perm from what I will call "E parity"; I have to line up the edges to make sure it is one or the other.


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## blade740 (Sep 1, 2010)

masterofthebass said:


> I do that in a different way than I do on 3x3 though. I usually do it by looking at blocks. For example, if there is a CEC block, I know that there cannot be another block (except for a j perm) for it not to have parity.



I'm not sure if you're mistaken or just disregarding a horrible parity case.



Dene said:


> For example, I have particular trouble distinguishing E perm from what I will call "E parity"; I have to line up the edges to make sure it is one or the other.



Have you ever heard of the "three-color rule"?

http://www.cubestation.co.uk/cs2/index.php?page=3x3x3/cfop/cross/cross

Scroll about 2/3 of the way down.


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## Dene (Sep 1, 2010)

Actually I have heard of it, but too much work  . I prefer to be CN and go for easy cross than actually think about it.


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## deepSubDiver (Sep 1, 2010)

Forte said:


> Do you do lots of 3x3? If you have four edges wrong and it's not a Z or H perm, then it's an O or W perm (W perm has some opposite edges)


This is not exactly true. When I have an O-perm, they are in correct relation to each other. This means, I will have to add corners into my recognition. Detecting "3x3 PLLs" isn't the best method, I guess.

I also tried to detect patterns like Dan does but I have a weird system which doesnt work well, at least for me.

Any other ideas?


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## blade740 (Sep 1, 2010)

deepSubDiver said:


> Forte said:
> 
> 
> > Do you do lots of 3x3? If you have four edges wrong and it's not a Z or H perm, then it's an O or W perm (W perm has some opposite edges)
> ...



If the corners are solved and the edges are correct in relation to each other, there are only 3 possibilities: solved, H perm, and O perm. You should be able to tell those three apart.


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## TobiasD (Nov 25, 2010)

(Sorry for my English )

By Reason of the terrible ([-]x, -x) move (for me), I used the method in this thread.
I found 2 more algs (Inverted), which don't use this move, except of the last move.

NA: / (3, 3) / (1, 0) / (-2, 0) / (4, 0) / (-4, 0) / (-2, 0) / (-1, 0) / (-3, -3) (matching bar at *DL*)
OA: / (3, 3) / (1, 0) / (-2, 0) / (4, 0) / (-4, 0) / (-2, 0) / (5, 0) / (-3, -3) (matching bar at *DR*)


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## Dene (Nov 25, 2010)

Oh nice! Those algs are sooo much better than the other ones!

Now we just need good N/N or O/O whatever you want to call it.


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## TobiasD (Nov 25, 2010)

For NN I use the Adj-Alg (I do a normal Vandenbergh Solution at CP-Skip). I'm able to execute that algorithm in 4 Seconds.
For OO I currently use the "normal" Alg and then the Adj-Alg.


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## CubingBanana (Feb 20, 2017)

I'm so sorry. This hasn't been replied to for 6 1/2 years, but I need to know:

Is this for corner or edge? Because the edges don't seem to move, only the corners


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## DGCubes (Feb 20, 2017)

CubingBanana said:


> I'm so sorry. This hasn't been replied to for 6 1/2 years, but I need to know:
> 
> Is this for corner or edge? Because the edges don't seem to move, only the corners



This solves parity during corner permutation instead of during edge permutation. The main pro to it is that it has less algs to learn, but now that cubeshape parity is a thing, this should probably be disregarded if you want to get world class.


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## Thomas Figura (Jun 12, 2017)

I have two adjacent edges that need to be swapped. Do I do AN or NA?


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## xyzzy (Jun 12, 2017)

Thomas Figura said:


> I have two adjacent edges that need to be swapped. Do I do AN or NA?



The list of algs in the OP doesn't include the NN case, which is what you're looking for. Just use any parity EP alg instead.


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## Thomas Figura (Jun 12, 2017)

xyzzy said:


> The list of algs in the OP doesn't include the NN case, which is what you're looking for. Just use any parity EP alg instead.


 Thanks that helped!


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## wearephamily1719 (Jul 14, 2019)

What does UR, DL, and UL mean?


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## Filipe Teixeira (Jul 15, 2019)

wearephamily1719 said:


> What does UR, DL, and UL mean?


UR: Up/Right
DL: Down/Left
UL: Up/Left 

etc


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## Cuz Red (Mar 22, 2022)

blade740 said:


> I'm really just posting this so that I can link to it instead of emailing the algs to everyone.
> 
> O: opposite
> A: adjacent
> ...


doesn’t even tell you how to hold it


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## Thom S. (Mar 22, 2022)

Cuz Red said:


> doesn’t even tell you how to hold it


You know, due to reasons, CPP isn't really used anymore.


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## Cuz Red (Mar 22, 2022)

Thom S. said:


> You know, due to reasons, CPP isn't really used anymore.


what do we use now? so we just do parity?


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## OreKehStrah (Mar 22, 2022)

Cuz Red said:


> what do we use now? so we just do parity?


Solve parity during cube shape


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## Cuz Red (Mar 22, 2022)

OreKehStrah said:


> Solve parity during cube shape


hahaha yeah right CSP is CANCER


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## Thom S. (Mar 23, 2022)

Cuz Red said:


> hahaha yeah right CSP is CANCER


It used to be with tracing but it's not anymore.


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