Rubik PLL

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

The 21 PLL cases

Credits

• Original comments and pictures from http://www.cubewhiz.com/pll.php

Moves in BOLD are my current favorites.

Corners Only

Name	Diagram	Algorithm	Comments
Aa		x (R' U R') D2 (R U' R') D2 R2 (video)	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.
Ab		x R2 D2 (R U R') D2 (R U' R) [y'] x (L U' L) D2 (L' U L) D2 L2	This is just the inverse of the other A perm. It is performed in a very similar manner.
E		x' (R U') (R' D) (R U R' D') (R U R' D) (R U') (R' D')	This alg is just two orientations performed consecutively.

Edges Only

Name	Diagram	Algorithm	Comments
Ua		(R U' R U) (R U) (R U') (R' U' R2) [y2] (R2 U' (R' U' R U) (R U) (R U' R) (video)	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.
Ub		(R2 U) (R U R' U') (R' U') (R' U R') [y2] (R' U R' U') (R' U') (R' U) (R U R2) (video)	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.
H		(M2' U) (M2' U2) (M2' U) M2' (M2' U') (M2' U2') (M2' U') M2'	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.
Z		(M2' U) (M2' U) (M' U2) (M2' U2) (M' U2) (M2' U') (M2' U') (M' U2') (M2' U2') (M' U2')	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.

Swapping Two Adjacent Corners & Two Edges

Name	Diagram	Algorithm	Comments
Ja		(R' U L') U2 (R U' R') U2 (L R U') z (D' R U') R2 (D R' D') R2 (U D R') (same but different grip)	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.
Jb		(R U R' F') (R U R' U') (R' F) (R2 U') (R' U')	This is the same as the T perm with the last four moves instead performed at the beginning.
T		(R U R' U') (R' F) (R2 U') (R' U' R U) (R' F')	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.
Rb		(R' U2) (R U2) (R' F R U R' U') (R' F' R2 U') (video)	This is a pretty straightforward alg that flows pretty nicely.
Ra		R U R' F' R U2 R' U2 R' F R U R U2 R' U' (video)	You could also just mirror Rb, but this alg is more right hand friendly. Notice the similarity with the Jb permutation.
F		R' U' F' (R U R' U') (R' F) (R2 U') (R' U' R U) (R' U R)	This is a T permutation with a 3 move setup in the beginning and a cancellation of one of those moves at the end.

Cycling Three Corners & Three Edges

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: R2 R' R' R vs Uw U U' Uw'
• Gb: R2 R' R R vs Uw U U' Uw'
• Gc: R2' R R R' vs Uw' U' U Uw
• Gd: R2' R R' R' vs Uw' U' U Uw

Name	Diagram	Algorithm	Comments
Ga		(R2' Uw) (R' U R' U' R Uw') R2' y' (R' U R)	This alg has a pretty decent flow to it and can be performed almost in one motion until the rotation.
Gb		(R' U' R) y (R2' Uw R' U) (R U' R Uw' R2')	This is the inverse of Ga. Note how similar they look. I perform this one almost exactly the same way.
Gc		(R2' Uw' R U') (R U R' Uw R2) (Fw R' Fw') (Start with thumb on U face)	You could rotate and insert the pair instead of performing the last three moves as shown.
Gd		(R U R') y' (R2' Uw' R U') (R' U R' Uw R2)	This is just the inverse of Gc. I execute it very similarly because most of the moves overlap in the same manner.

Permutations Of Two Diagonal Corners & Two Edges

The Na / Nb permutation variants come from Finger Trick - How to Execute the N Perms Like a Pro (cyotheking).

Name	Diagram	Algorithm	Comments
V		(R' U R' Dw') (R' F' R2 U') (R' U R' F) (R F) (video VC)	This is one of my least favorite permutations because the flow just isn't there.
Na		(z) D (R' U) (R2 D' R D U') (R' U) (R2 D' R U' R) z U _(R' D)_ (R2 U' R U D') _(R' D)_ (R2 U' R D' [R])	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 normal grip after z RH sexy regrip during the first and second U' Last R assumes following start position (X means cube at correct position) (B) . . X (L) X X X (R) X . . (F) After z U face must have the following pattern: X X . X X X X X X
Nb		(z) U' (R D') (R2' U R' D U') (R D') (R2' U R' D R') z U' (R D') (R2 U R' D U') (R D') R2 U R' D [R]	This is just the mirror of the other N permutation. For the 2nd variant: Use normal LH grip, RH sexy grip after z RH sexy regrip for both R2. All U, D' done with RH. Last R assumes following start position (X means cube at correct position) (B) . X X (L) . X . (R) X X . (F) After z U face must have the following pattern: X X . X X . X X X
Y		(F R U') (R' U' R U) (R' F') (R U R' U') (R' F R F')	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.

Recognizing the PLL cases

Links

• Recognizing the PLLs, from Badmephisto

A *must* see video on how to quickly recognizes the PLL based on features like headlights, bar, pairs...

• Recognizing the PLLs, from Bob Burton

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