# 22LL - a last layer subset



## aronpm (Jan 5, 2012)

*Link*: 22LL page

*What is 22LL?*

22LL is a subset of last layer algorithms. Each case consists of a 2-cycle of corners and a 2-cycle of edges. So, some PLLs such as T perm are 22LL cases. Z perm is not a 22LL case because while it has 2 2-cycles, they are both edge cycles.

*How many cases are in 22LL?*

22LL is only 56 cases. There are 5 sets, based on the corner 2-cycle, each of which represents a separate CLL case. The A and D sets contain adjacent and diagonal corner swap PLLs, respectively. The A set contains T, J, L, F, and both R perms, and the D set contains Y, V, and both N perms. The D set contains less algorithms than the other 4 sets because there were 4 cases which were reducible by AUF, which I didn’t notice until I made the case pictures for them. Additionally, there is no F set ( for the 2-cycle (UBR LUF) ) because it is identical to the I set with a U2 AUF.

*Why make 22LL?*

Originally, I planned to learn how to solve each 2x2-cycle for (UBR x) (DF y), where x is an edge and y is a corner, by using setups to PLLs or ZBLLs. I soon realised that it would be much simpler if I allowed edges to be unoriented.

_You can read more about it on my blog._

If you have any better algs, or see any errors, post them here or send me a message.

*Example Solves*:


Spoiler



Speedsolve:


Spoiler



U' B' R' D B R' D2 B2 L' F U' F2 U B2 D F2 U2 L2 U L2 D' F2

z2 y // inspection
U2 L R U R F B' D // cross
U' R' U' R // F2L #1
U' R U' R' U' L' U' L // F2L #2
R U' R' U y' R' U' R // F2L #3
y' R U2 R' // F2L #4
U F U R' U' R D' R2 U R' U' R2 D F' U' // 22LL


BLD:


Spoiler



F' R' D' L D' F' R' L B D F2 U R2 U2 L2 U B2 F2 D2 F' 

y // memo

// corners
D L' U2 L D' L' U2 L // UBR->LDB->FDL
R' U2 R' D' R U2 R' D R2 // UBR->URF->ULB
y' R2 D2 R U2 R' D2 R U2 R y // UBR->RBD->RFU
U2 L D' L' U2 L D L' // UBR->ULF->RDF

// edges
U2 M' U L U' M U L' U // DF->BU->LB
M U2 M U M' U2 M' U' // DF->UF->UR
R2 u M' U L U' M U L' U' u' R2 // DF->RD->FL
z L' U M' U' L U M U' z' // DF->DL->LU

(M2) R2 U R U R' U' R2 F' U F R' F' U' F R2 U' R2 (M2) // 22LL parity

z2 M' U M' U M' U2 M U M U M U2 // flip edges


----------



## AJ Blair (Jan 5, 2012)

IAB - y' U' R' U' R U R' F' R U R' U' R' F R2

I like these...I use a few already, but I could always use a few more tricks for last layer!


----------



## aronpm (Jan 5, 2012)

AJ Blair said:


> IAB - y' U' R' U' R U R' F' R U R' U' R' F R2
> 
> I like these...I use a few already, but I could always use a few more tricks for last layer!


 
Thanks, that's a nice cancellation/cyclic shift. I've added it.


----------



## PandaCuber (Jan 5, 2012)

Can I see an example solve? Im a visual person...


----------



## irontwig (Jan 5, 2012)

Tbh I'm kinda surprised that someone hasn't done this earlier, especially considering that a lot of BLD prås seem to be pretty insane.


----------



## AJ Blair (Jan 5, 2012)

aronpm said:


> Thanks, that's a nice cancellation/cyclic shift. I've added it.


 
Being the noob I am...I really have no clue what that means...it's just an Old Pochman alg with an R cancellation...if that's what you said...then oops...


----------



## irontwig (Jan 5, 2012)

Cyclic shifts is e.g: ABC => BCA => CAB.


----------



## AJ Blair (Jan 5, 2012)

irontwig said:


> Cyclic shifts is e.g: ABC => BCA => CAB.


 
Gotcha!



ABI - M' U R U R' F' R U R' U' R' F R2 U' R' U2 M
EAE - B' U R' U' R' F R2 U' R' U' R U R' F' R B

Two more...just turned them into a J perm or a T perm...not sure if that's what we're looking for here...but it's fast


----------



## aronpm (Jan 5, 2012)

PandaCuber said:


> Can I see an example solve? Im a visual person...


Sure. (I made the speedsolve scramble using Cube Explorer, based on F2L from a qqtimer scramble and a random 22LL case):

Speedsolve:


Spoiler



U' B' R' D B R' D2 B2 L' F U' F2 U B2 D F2 U2 L2 U L2 D' F2

z2 y // inspection
U2 L R U R F B' D // cross
U' R' U' R // F2L #1
U' R U' R' U' L' U' L // F2L #2
R U' R' U y' R' U' R // F2L #3
y' R U2 R' // F2L #4
U F U R' U' R D' R2 U R' U' R2 D F' U' // 22LL


BLD:


Spoiler



F' R' D' L D' F' R' L B D F2 U R2 U2 L2 U B2 F2 D2 F' 

y // memo

// corners
D L' U2 L D' L' U2 L // UBR->LDB->FDL
R' U2 R' D' R U2 R' D R2 // UBR->URF->ULB
y' R2 D2 R U2 R' D2 R U2 R y // UBR->RBD->RFU
U2 L D' L' U2 L D L' // UBR->ULF->RDF

// edges
U2 M' U L U' M U L' U // DF->BU->LB
M U2 M U M' U2 M' U' // DF->UF->UR
R2 u M' U L U' M U L' U' u' R2 // DF->RD->FL
z L' U M' U' L U M U' z' // DF->DL->LU

(M2) R2 U R U R' U' R2 F' U F R' F' U' F R2 U' R2 (M2) // 22LL parity

z2 M' U M' U M' U2 M U M U M U2 // flip edges


Excuse my terribly inefficient CFOP...

It's not like ZBLL, where you use ZBF2L to orient edges; there's no extra step before 22LL to setup a case. You just do it whenever it comes up. 



AJ Blair said:


> Being the noob I am...I really have no clue what that means...it's just an Old Pochman alg with an R cancellation...if that's what you said...then oops...


 
Cyclic shift of an algorithm is when you take moves from one side of an algorithm and moving them to the other. J perm is a cyclic shift of T perm, by moving R U R' F' from the end of T perm to the start. The alg you gave moves the U' R' U' from the end of J perm and takes it to the front.



AJ Blair said:


> ABI - M' U R U R' F' R U R' U' R' F R2 U' R' U2 M
> EAE - B' U R' U' R' F R2 U' R' U' R U R' F' R B
> 
> Two more...just turned them into a J perm or a T perm...not sure if that's what we're looking for here...but it's fast


Originally I had that for ABI, but I still think there _might_ be a direct alg that faster than both of them. That's a good EAE though, I'll add that one.


----------



## PandaCuber (Jan 5, 2012)

thats really cool.


----------



## gyc6001 (Jan 5, 2012)

example solve ftw.


----------



## cubersmith (Jan 5, 2012)

Thats beautiful.


----------



## StachuK1992 (Jan 5, 2012)

I already gave this to him, but
F2 r U r' F R U R' F' U' F might interest some others.


----------



## Athefre (Jan 5, 2012)

I once considered this as a direct solve LL method. The first step being to solve two corners and two edges. I stopped when I realized that the first step has the same "problem" as CLL+1 and Snyder LL. Start mixing corners with edges in a direct solve and the two piece types' orientations and positions relative to each other create a large number of cases.

I didn't consider if the second step has potential for BLD.


----------



## Egide (Jan 5, 2012)

an alternative for AAD that l find faster is y L U' R' U L' U2 R U' R' U2 R y'


----------



## y235 (Jan 5, 2012)

If using it in a solve, how do you recognize if this a 22LL case or not?
I think that start checking the cycles isn't good, because if it's not a 22LL case you just wasted a lot of time.


----------



## Kirjava (Jan 5, 2012)

PandaCuber said:


> Can I see an example solve? Im a visual person...


 
22LL isn't an LL system.


----------



## bamilan (Jan 5, 2012)

Kirjava said:


> 22LL isn't an LL system.


 
But it can easily be. If reducing all other LL cases to 22LL takes only low-number-move algorithms(6-9) we should give it a try.
Just think about that. For every LL case you should solve "only" any 2 corners and 2 edges.


----------



## Kirjava (Jan 5, 2012)

bamilan said:


> But it can easily be. If reducing all other LL cases to 22LL takes only low-number-move algorithms(6-9) we should give it a try.


 
ahahahaha the best part was when you said 'easily'


----------



## riffz (Jan 5, 2012)

bamilan said:


> But it can easily be. If reducing all other LL cases to 22LL takes only low-number-move algorithms(6-9) we should give it a try.
> Just think about that. For every LL case you should solve "only" any 2 corners and 2 edges.


 
Awesome. So you'll have a LL system with terrible recognition and step 2/2 will require one more algorithm than simply OLL/PLL.


----------



## chris w (Jan 5, 2012)

Aron, good work on finishing the page, it looks good. I'd been on your site earlier on and had learnt a few, now thats its complete I'l try and get through more of it.


----------



## bamilan (Jan 6, 2012)

riffz said:


> Awesome. So you'll have a LL system with terrible recognition and step 2/2 will require one more algorithm than simply OLL/PLL.


 
Recognition is faster than recognition of PLLs when you are used to it(I basically know the place of remaining cubies after step 1, and what is needed only the orientation of 1 corner)
Step 2 requires a lot of moves, but can be done around 1.5 sec with speed optimal algorithms.
There are many ways to reduce the number of cases in step 1(or skip it).

"step 2/2 will require one more algorithm than simply OLL/PLL" <= what do you mean?


----------



## oll+phase+sync (Jan 9, 2012)

What's th probability for a random LL case to be 22LL? ... quite low I suppose?

More difficult might be the question: how much can it be increased be doing some trivial Last-Slot modifications? (partial edgecontrol / partial corner control)


----------



## Kirjava (Jan 9, 2012)

Anyone suggesting this as a last layer method needs to read Athefre's post.

Once you have read that you can start working on a system that will solve this problem. Then you can tell us how to do CLL+1 easily, too.


----------



## Egide (Jan 21, 2012)

For EBE l found this one U' R U2 R' U F U' F' U' R U' R' F R U' R' F'


----------



## bobthegiraffemonkey (Jan 30, 2012)

So, finally getting some time to have a look at this and learn some. I'm learning by PLL sets, and I'm not learning all of it. I don't see why I should, I can setup to one of a few PLL shapes easily then solve any orientation of the pieces within that shape. I decided to use T, Jb, Rb and Y. I didn't like some of the algs, so I made what I believe to be better ones for some cases, sometimes copying/modifying the ones from the site. Here's my full alg list for what I'm learning, bear in mind that it's not in Aron's notation, but by edge orientation and the "shape" of the corner orientation. Also that I sometimes do crazy stuff like R3 , adjust to your style as necessary.

T
PLL: R U R' U' R' F R2 U' R' U' R U R' F'
T: r' U r' U2 R B' R' U2 r2 B'
U: U R' z R2 U R' U' D R D' R2' U R' D R3 U'
Flip: R2 B' R' B R' F' U' F R U R' U'
T Flip: F U R' U' R D' R2 U R' U' R2 D F'
U Flip: r' R2 U' R' U F' r U' L' U2 L R2 F R F' U' 

Jb
PLL: R U R' F' R U R' U' R' F R2 U' R' U'
T: r U R2' F R F' R U2' r' U r U r'
U: F2 R' F R2 U' R' U' R U R' F' R U R' U' F2
Flip: R r U R' U l' U2 L F' R U2 r2' F2
T Flip: R U2 R' U' F' U R U R' U' R' F R2 U' R' U2
U Flip: r' R U R U' L U L' U R' U' r B2 R B2 R2'

Rb
PLL: R' U2 R' D' R U' R' D R U R U' R' U' R U'
T: R U2 R' U' R' F R2 U' R' U' R U R' F' R U' R'
U: U R U' L U L' U R' U' L2' R' F2 l D2 L r
Flip: L2 l' U' R U2' L' U R' U' R r B2 r2'
T Flip: R U R' U R U2' B' R' U' R U B U' R' U2
U Flip: R' F U' F R' F' R2 U' R' U2 r U' r' F' R

Y
PLL: F R' F R2 U' R' U' R U R' F' R U R' U' F'
L1: U r U2' R2' F R F' R U2' r'
L2: l' U L2 F' L' F L' U2 l U'
Flip: R2 U R2' F' U F R F' U' F R2 U R U' R' U' R2
L1 Flip: M' U L' U' L r U2 R' F' R U2 R r2
L2 Flip: R' U' R U' B2 r' U' r B2 R' U' R U B 

Enjoy 

Matt

Edit: Fixed some and improved some, still a couple I don't like (Y flip, T U) but I'll work on it.


----------



## Cubeur-manchot (May 12, 2018)

Hi everyone, don't know if it's ok to reply here but anyway...

I generated my own set of 22LL, taking algs from http://aronpm.cubing.net/22ll/, from http://algdb.net/puzzle/333/zbll for those which are ZBLL, and I worked a lot with http://birdflu.lar5.com/?pos=Ar6i for the bad cases.
Even if it has a part of subjectivity, I consider my algs to be *near of* speed-optimal.

My 22LL set is available on my website : https://cubeur-manchot.github.io/Les-Algos-d-un-Manchot/22ll.html
(if you remove the /22ll.html in the url you get the home page of my website, some people might be interested)


----------

