View source for Rubik PLL

This page is dedicated to permute correctly the last layer of the [[Rubik's cube]].

== The 21 PLL cases ==
Source:
* '''BB''': [http://www.cubewhiz.com/pll.php Bob Burton's - cubewhiz.com] (including original pictures and comments),
* '''BM''': [http://www.badmephisto.com/pll.php Badmephisto's algo],
* '''AK''': [http://www.kungfoomanchu.com/home.html Andy Klise's algo],
* '''VC''': [https://www.youtube.com/channel/UCVkyHhB6spac596jVclMtQw Victor Colin's algo].

Moves in '''BOLD''' are my current favorites.

Probabilities:
* {{blue|1=BLUE &mdash; p=1/18}}
* {{green|1=GREEN &mdash; p=1/36}}
* {{red|1=RED &mdash; p=1/72}}

=== Permutations of edges or corners only ===

{|
|- valign=top
|width=5% align=center|[[File:pllUa-180.gif]]<br/>'''{{blue|Ua}}'''
|width=45%|
{{rubik|[y2] (R U' R U) (R U) (R U') (R' U' R2)}} (BB)
:BB:''This is just a simple 3-edge cycle. It is almost as fast as the corner cycles. I solve this case with the bar at the front or the back.''
'''{{rubik|(R2 U' (R' U' R U) (R U) (R U' R)}}''' ([https://www.youtube.com/watch?v=esuH74SGe0Q VC,video])
|
|width=45%|
{{rubik|[y2] (R2 U) (R U R' U') (R' U') (R' U R')}} (BB)<br/>
:BB:''This is the inverse of the other U perm. I place my hands slightly differently for this algorithm. I solve this case with the bar at the front or the back.''
'''{{rubik|(R' U R' U') (R' U') (R' U) (R U R2)}}''' ([https://www.youtube.com/watch?v=96PG84UQ8x4 VC,video])
|width=5% align=center|[[File:pllUb-180.gif]]<br/>'''{{blue|Ub}}'''
|-
|
:
|- valign=top
|width=5% align=center|[[File:pllZ-90.gif]]<br/>'''{{green|Z}}'''
|width=45%|
{{rubik|(M2' U) (M2' U) (M' U2) (M2' U2) (M' U2)}}<br/>	
'''{{rubik|(M2' U') (M2' U') (M' U2') (M2' U2') (M' U2')}}'''
:BB:''The Z permutation is performed very similarly to the H perm. The last U2 is not necessary if you account for it before the algorithm.''
|
|width=45%|{{rubik|(M2' U) (M2' U2) (M2' U) M2'}}<br/>	
'''{{rubik|(M2' U') (M2' U2') (M2' U') M2'}}'''	
:BB:''This is extremely easy to recognize and can be performed VERY quickly. The M'2 is actually performed as (M'M') with rapid pushing at the back face of the M layer with the ring and then middle fingers.''
|width=5% align=center|[[File:pllH.gif]]<br/>'''{{red|H}}'''
|-
|
:
|- valign=top
|width=5% align=center|[[File:pllAa.gif]]<br/>'''{{blue|Aa}}'''
|width=45%|'''{{rubik|x (R' U R') D2 (R U' R') D2 R2}} (VC,BB,[https://www.youtube.com/watch?v=-YrtxKcg7m0 video])'''<br/>
:BB:''This is a basic corner 3-cycle. It is one of my favorite and fastest algorithms. Perform the D2s with the left hand and everything else with the right.''
|
|width=45%|'''{{rubik|x R2 D2 (R U R') D2 (R U' R)}} (BB,VC)'''
:BB:''This is just the inverse of the other A perm.  It is performed in a very similar manner.''
{{rubik|[y'] x (L U' L) D2 (L' U L) D2 L2}}
|width=5% align=center|[[File:pllAb.gif]]<br/>'''{{blue|Ab}}'''
|-
|
:
|- valign=top
|width=5% align=center|[[File:pllE.gif]]<br/>'''{{green|E}}'''
|width=45%|'''{{rubik|x' (R U') (R' D) (R U R' D') (R U R' D) (R U') (R' D')}} (BB)'''<br/>
:BB:''This alg is just two orientations performed consecutively.''
:Note:''The algo are OCLL5 OCCL4''.
|
|width=45%|
|width=5% align=center|<br/>'''{{red|solved}}'''
|}

=== Swap one set of adjacent corners ===

{|
|- valign=top
|width=5% align=center|[[File:pllRa.gif]]<br/>'''{{blue|Ra}}'''
|width=45%|{{rubik|R U R' F' R U2 R' U2 R' F R U R U2 R' U'}}<br/>
'''{{rubik|(R U' R' U') (R U R) D (R' U' R) D' (R' U² R')}}''' ([https://www.youtube.com/watch?v=RcHXkA8KCvs video])
:BB:''You could also just mirror Rb, but this alg is more right and friendly. Notice the similarity with the Jb permutation.''
:VC:NO AUF if front right corner correct.
|
|width=45%|'''{{rubik|(R' U2) (R U2) (R' F R U R' U') (R' F' R2 U')}} ([https://www.youtube.com/watch?v=rqh9FMqr4hA video])'''<br/>
:BB:''This is a pretty straightforward alg that flows pretty nicely.''
|width=5% align=center|[[File:pllRb.gif]]<br/>'''{{blue|Rb}}'''
|-
|
:
|- valign=top
|width=5% align=center|[[File:pllJa-90.gif]]<br/>'''{{blue|Ja}}'''
|width=45%|{{rubik|(R' U L') U2 (R U' R') U2 (L R U')}}<br/>
{{rubik|z (D' R U') R2 (D R' D') R2 (U D R')}} (same but different grip)<br/>
'''{{rubik|(L' U' L F) (L' U' L U) (L F' L²' U L)}}''' (VC,[https://www.youtube.com/watch?v=tGiOoJww-0s video VC])<br/>
:BB:''I perform the R of the [R L] a split second after I start the L so that I can immediately perform the U' to AUF when the L face has been moved to where it belongs.''
:VC: NO AUF if left front block is correct.
|
|width=45%|{{rubik|(R U R' F') (R U R' U') (R' F) (R2 U') (R' U')}} (BB)<br/>
:BB:''This is the same as the T perm with the last four moves instead performed at the beginning.''
|width=5% align=center|[[File:pllJb.gif]]<br/>'''{{blue|Jb}}'''
|-
|
:
|- valign=top
|width=5% align=center|[[File:pllT.gif]]<br/>'''{{blue|T}}'''
|width=45%|'''{{rubik|(R U R' U') (R' F) (R2 U') (R' U' R U) (R' F')}} (BB)'''<br/>
:BB:''This is the T permuation. It is long but definitely very fast and easy. It can be performed in almost one swift motion without any readjusting of the fingers. Note that it is a combination of two easy orientations.''
|
|width=45%|'''{{rubik|R' U' F' (R U R' U') (R' F) (R2 U') (R' U' R U) (R' U R)}}'''<br/>
:BB:''This is a T permutation with a 3 move setup in the beginning and a cancellation of one of those moves at the end.''
|width=5% align=center|[[File:pllF.gif]]<br/>'''{{blue|F}}'''
|}

=== Swap one set of corners diagonally ===
The Na / Nb permutation variants come from [https://www.youtube.com/watch?v=Grl4ELs_vk4 Finger Trick - How to Execute the N Perms Like a Pro (cyotheking)].

{|
|- valign=top
|width=5% align=center|[[File:pllV.gif]]<br/>'''{{blue|V}}'''
|width=45%|'''{{rubik|(R' U R' Dw') (R' F' R2 U') (R' U R' F) (R F)}} ([https://www.youtube.com/watch?v=YB7VufuoOgc video VC])'''<br/>
:BB:''This is one of my least favorite permutations because the flow just isn't there.''
|
|width=45%|'''{{rubik|(F R U') (R' U' R U) (R' F') (R U R' U') (R' F R F')}} (BB)'''<br/>
:BB:''This is very quick and can be performed without any adjustments of where the fingers are. It is just a combination of two quick orientations.''
|width=5% align=center|[[File:pllY.gif]]<br/>'''{{blue|Y}}'''
|-
|
:
|- valign=top
|width=5% align=center|[[File:pllNa.gif]]<br/>'''{{red|Na}}'''
|width=45%|{{rubik|(z) D (R' U) (R2 D' R D U') (R' U) (R2 D' R U' R)}} (BB)
'''{{rubik|z U _(R' D)_ (R2 U' R U D') _(R' D)_ (R2 U' R D' [R])}}'''
:BB:''This alg could also be performed using <R,U,L> if you don't do the rotation, but this way is faster with practice.''
For the 2nd variant:
* Use {{blue|normal grip}} after {{rubik|z}}
* {{blue|RH sexy regrip}} during the first and second {{rubik|U'}}
|
|width=45%|{{rubik|(z) U' (R D') (R2' U R' D U') (R D') (R2' U R' D R')}} (BB)
{{rubik|z U' (R D') (R2 U R' D U') (R D') R2 U R' D [R]}}<br/>
'''{{red|NEW}} {{rubik|(R' U R U') (R' F' U' F) (R U R' F) (R' F' R U' R)}}''' ([https://www.youtube.com/watch?v=CjSYvNKkums video VC])
:BB:''This is just the mirror of the other N permutation.''
For the 2nd variant:
* Use {{blue|normal LH grip, RH sexy grip}} after {{rubik|z}}
* {{blue|RH sexy regrip}} for both {{rubik|R2}}. All {{rubik|U}}, {{rubik|D'}} done with RH.
* The new 3rd variant from Victor Colin is much better. Watch the video.
|width=5% align=center|[[File:pllNb.gif]]<br/>'''{{red|Nb}}'''
|}

=== Double spins ===

To recognize these PLLs:
* Put the HEADLIGHT on the left
* Observe the position of the BLOCK: if it is as the FRONT (resp. FAR RIGHT, BACK and CLOSE RIGHT), then it is a '''Ga''' (resp. '''Gb''', '''Gc''' and '''Gd''') permutation.

To remember the algorithms, observe the sequence of RIGHT face versus sequence of UP face:
* '''Ga''': {{rubik|R2 R' R' R}} vs {{rubik|Uw U U' Uw'}}
* '''Gb''': {{rubik|R2 R' R  R}} vs {{rubik|Uw U U' Uw'}} &mdash; Quick recognition: BLOCK is on the RIGHT on the face and next to OPPOSITE color!
* '''Gc''': {{rubik|R2' R R R'}} vs {{rubik|Uw' U' U Uw}}
* '''Gd''': {{rubik|R2' R R' R'}} vs {{rubik|Uw' U' U Uw}} &mdash; Quick recognition: BLOCK is on the LEFT on the face and next to OPPOSITE color! Also, the middle color in the PHARE is opposite (like for the Gb)

{|
|- valign=top
|width=5% align=center|[[File:pllGa.gif]]<br/>'''{{blue|Ga}}'''
|width=45%|'''{{rubik|(R2' u) (R' U R' U' R u') R2' y' (R' U R)}}'''<br/>
:BB:''This alg has a pretty decent flow to it and can be performed almost in one motion until the rotation.''
|
|width=45%|{{rubik|(R2' u' R U') (R U R' u R2) (f R' f')}} ({{blue|Start with thumb on U face}})<br/>
'''{{rubik|[y2] R2' F2' R U2 R U2') (R' F R U) (R' U' R' F) R2}} (VC,[https://www.youtube.com/watch?v=63jenxhu9Mg&t=10m15s video])''' ({{blue|Start with RH under D face, {{rubik|F2'}} and {{rubik|U2}} with RH index+middle, {{rubik|U2'}} with LH}}<br/>
:BB:''You could rotate and insert the pair instead of performing the last three moves as shown.''
|width=5% align=center|[[File:pllGc.gif]]<br/>'''{{blue|Gc}}'''
|- valign=top
|width=5% align=center|[[File:pllGd.gif]]<br/>'''{{blue|Gd}}'''
|width=45%|'''{{rubik|(R U R') y' (R2' u' R U') (R' U R' u R2)}}'''<br/>
:BB:''This is just the inverse of Gc. I execute it very similarly because most of the moves overlap in the same manner.''
|
|width=45%|'''{{rubik|(R' U' R) y (R2' u R' U) (R U' R u' R2')}}'''<br/>
:BB:''This is the inverse of Ga. Note how similar they look. I perform this one almost exactly the same way.''
|width=5% align=center|[[File:pllGb.gif]]<br/>'''{{blue|Gb}}'''
|}

== Recognizing the PLL cases ==
=== Links ===
* [http://youtu.be/lPvF21KeAPE Recognizing the PLLs, from Badmephisto]
:A *must* see video on how to quickly recognizes the PLL based on features like ''headlights'', ''bar'', ''pairs''...
* [http://www.cubewhiz.com/pllrecognition.php Recognizing the PLLs, from Bob Burton]

=== Color cases ===
{| class=wikitable
|-
|
{|
|- 
| style="background: orange; border:none; margin:0px; padding:0px;" width=20px |   
| style="background: orange; border:none; margin:0px; padding:0px;" width=20px |   
| style="background: orange; border:none; margin:0px; padding:0px;" width=20px |   
| width=1px style="border:none"|   
| style="background: blue; border:none; margin:0px; padding:0px;" width=20px |   
| style="background: blue; border:none; margin:0px; padding:0px;" width=20px |   
| style="background: blue; border:none; margin:0px; padding:0px;" width=20px |   
| width=1px style="border:none"|   
| style="background: red; border:none; margin:0px; padding:0px;" width=20px height=20px|   
| style="background: red; border:none; margin:0px; padding:0px;" width=20px |   
| style="background: red; border:none; margin:0px; padding:0px;" width=20px |   
| width=1px style="border:none"|   
| style="background: green; border:none; margin:0px; padding:0px;" width=20px |   
| style="background: green; border:none; margin:0px; padding:0px;" width=20px |   
| style="background: green; border:none; margin:0px; padding:0px;" width=20px |   
|}
|Solved.
|-
|
{|
|- 
| style="background: green; border:none; margin:0px; padding:0px;" width=20px |   
| style="background: orange; border:none; margin:0px; padding:0px;" width=20px |   
| style="background: orange; border:none; margin:0px; padding:0px;" width=20px |   
| width=1px style="border:none"|   
| style="background: blue; border:none; margin:0px; padding:0px;" width=20px |   
| style="background: blue; border:none; margin:0px; padding:0px;" width=20px |   
| style="background: green; border:none; margin:0px; padding:0px;" width=20px |   
| width=1px style="border:none"|   
| style="background: red; border:none; margin:0px; padding:0px;" width=20px height=20px|   
| style="background: red; border:none; margin:0px; padding:0px;" width=20px |   
| style="background: blue; border:none; margin:0px; padding:0px;" width=20px |   
| width=1px style="border:none"|   
| style="background: red; border:none; margin:0px; padding:0px;" width=20px |   
| style="background: green; border:none; margin:0px; padding:0px;" width=20px |   
| style="background: red; border:none; margin:0px; padding:0px;" width=20px |   
|}
|Aa. The corner block + headlight, or corner block + opposite color on same face (telling where the headlights are)
|-
|
{|
|- 
| style="background: red; border:none; margin:0px; padding:0px;" width=20px |   
| style="background: orange; border:none; margin:0px; padding:0px;" width=20px |   
| style="background: orange; border:none; margin:0px; padding:0px;" width=20px |   
| width=1px style="border:none"|   
| style="background: blue; border:none; margin:0px; padding:0px;" width=20px |   
| style="background: blue; border:none; margin:0px; padding:0px;" width=20px |   
| style="background: red; border:none; margin:0px; padding:0px;" width=20px |   
| width=1px style="border:none"|   
| style="background: green; border:none; margin:0px; padding:0px;" width=20px height=20px|   
| style="background: red; border:none; margin:0px; padding:0px;" width=20px |   
| style="background: green; border:none; margin:0px; padding:0px;" width=20px |   
| width=1px style="border:none"|   
| style="background: orange; border:none; margin:0px; padding:0px;" width=20px |   
| style="background: green; border:none; margin:0px; padding:0px;" width=20px |   
| style="background: blue; border:none; margin:0px; padding:0px;" width=20px |   
|}
|Ab. The corner block + headlight, or corner block + opposite color on same face (telling where the headlights are)
|-
|
{|
|- 
| style="background: blue; border:none; margin:0px; padding:0px;" width=20px |   
| style="background: orange; border:none; margin:0px; padding:0px;" width=20px |   
| style="background: green; border:none; margin:0px; padding:0px;" width=20px |   
| width=1px style="border:none"|   
| style="background: orange; border:none; margin:0px; padding:0px;" width=20px |   
| style="background: blue; border:none; margin:0px; padding:0px;" width=20px |   
| style="background: red; border:none; margin:0px; padding:0px;" width=20px |   
| width=1px style="border:none"|   
| style="background: green; border:none; margin:0px; padding:0px;" width=20px height=20px|   
| style="background: red; border:none; margin:0px; padding:0px;" width=20px |   
| style="background: blue; border:none; margin:0px; padding:0px;" width=20px |   
| width=1px style="border:none"|   
| style="background: red; border:none; margin:0px; padding:0px;" width=20px |   
| style="background: green; border:none; margin:0px; padding:0px;" width=20px |   
| style="background: orange; border:none; margin:0px; padding:0px;" width=20px |   
|}
|E. No blocks. We see: orange green - orange blue on the corner &rarr; orange face must be on the left.
|-
|
{|
|- 
| style="background: orange; border:none; margin:0px; padding:0px;" width=20px |   
| style="background: red; border:none; margin:0px; padding:0px;" width=20px |   
| style="background: orange; border:none; margin:0px; padding:0px;" width=20px |   
| width=1px style="border:none"|   
| style="background: blue; border:none; margin:0px; padding:0px;" width=20px |   
| style="background: blue; border:none; margin:0px; padding:0px;" width=20px |   
| style="background: blue; border:none; margin:0px; padding:0px;" width=20px |   
| width=1px style="border:none"|   
| style="background: red; border:none; margin:0px; padding:0px;" width=20px height=20px|   
| style="background: green; border:none; margin:0px; padding:0px;" width=20px |   
| style="background: red; border:none; margin:0px; padding:0px;" width=20px |   
| width=1px style="border:none"|   
| style="background: green; border:none; margin:0px; padding:0px;" width=20px |   
| style="background: orange; border:none; margin:0px; padding:0px;" width=20px |   
| style="background: green; border:none; margin:0px; padding:0px;" width=20px |   
|}
|Ua
|}

=== Recognition ===
It's very easy to observe two sides. Depending on what you see, it will quickly narrow down the possible cases. The features to observe are:
* The '''bar''': A side with 3 identical color.
* The '''corner''': A corner with 2 adjacent edges of same color.
* The '''pair''': A corner and an adjacent edge of same color.
* The '''headlight''': Two corners of same color.

;Two bars
* The cube is solved. Just AUL as necessary.

;Bar + headlight
* Possible cases are: '''Ua''' or '''Ub'''
* Ua: if headlight on the right (resp. left) contains adjacent (resp. opposite) colors
* Ub: if headlight on the right (resp. left) contains opposite (resp. right) colors

;Bar + pair
* Possible cases are: '''Ja''' or '''Jb'''.
* Ja: if bar and pair "connected", and pair on the right, OR bar and pair of different color, and pair on the left
* Jb: if bar and pair "connected", and pair on the left, OR bar and pair of different color, and pair on the right

;A bar only
* One possible case: '''F'''.

;A corner
* Possible cases are: '''Aa''', '''Ab''', or '''V'''.
* V: the opposite corners adjacent to the corner are of DIFFERENT color:
* Aa: The opposite corners have same color, and the one of the RIGHT is of opposite color compared to adjacent pair.
* Ab: The opposite corners have same color, and the one of the LEFT is of opposite color compared to adjacent pair.

;Two pairs (without corner)
* Possible cases: '''Ja''', '''Jb''', '''Na''', '''Nb''', or '''Y''''
:In all cases but Y, we have either two RIGHT/LEFT stickers of same color + left/right sticker of either OPPOSITE or DIFFERENT color.
* Na: The stickers of same color are on the RIGHT, and the left sticker has the OPPOSITE color on EACH face.
* Nb: The stickers of same color are on the LEFT, and the left sticker has the OPPOSITE color on EACH face.
* Ja: The RIGHT sticker on the right face has a DIFFERENT color.
* Jb: The LEFT sticker on the left face has a DIFFERENT color.
* Y: Easily recognizable since both pairs are adjacent to a same corner.

;Pair + headlight
* Possible cases: '''Aa''', '''Ab''', '''T''', '''Ra''', '''Rb''', '''Ga''', or '''Gc'''.
* Aa: Pair is on the RIGHT, and headlight has OPPOSITE color.
* Ab: Pair is on the LEFT, and headlight has OPPOSITE color.
* T: headlight and pair have a common corner, and the edge adjacent to headlight corner is OPPOSITE color.
* 

TBC

;A pair only

;Two headlights

;One headlight only

;Nothing
* '''E''' perm if ''corner has one color identical to one side and one color opposite to the other side''. Set up the case by moving the corner and side with identical color on the left or right side.