Rubik PLL

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

The 21 PLL cases

Source:

• BB: Bob Burton's - cubewhiz.com (including original pictures and comments),
• BM: Badmephisto's algo,
• AK: Andy Klise's algo,
• VC: Victor Colin's algo.

Moves in BOLD are my current favorites.

Probabilities:

• BLUE — p=1/18
• GREEN — p=1/36
• RED — p=1/72

Permutations of edges or corners only

Ua	(R2 U') (R' U' R U) (R U) (R U' R) (VC video) [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. No AUF if front bar matches F face.		(R' U R' U') (R' U') (R' U) (R U R2) (VC video) [y2] (R2 U) (R U R' U') (R' U') (R' U R') (BB) 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. No AUF if front bar matches F face.	Ub
Z	(M2' U) (M2' U) (M' U2) (M2' U2) (M' [U2]) (BB, VC Video) (M2' U') (M2' U') (M' U2') (M2' U2') (M' [U2']) (BB,VC,mirror) 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. No AUF if front headlight is OPPOSITE to F face.		(M2' U) (M2' U2) (M2' U) M2' (BB, VC Video) (M2' U') (M2' U2') (M2' U') M2' (BB,VC,mirror) 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. No AUF if front headlight matches F face.	H
Aa	x (R' U R') D2 (R U' R') D2 R2 (BB,VC video) 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. To avoid a parasitic move of the L face after D2 (R ... that would block the U' move, the key is to twist slightly the right wrist such that to make a small D' move that would block the L face, hence stabilizing the cube. No AUF if front block matches F face.		x R2 D2 (R U R') D2 (R U' R) (BB,VC Video) BB:This is just the inverse of the other A perm. It is performed in a very similar manner. Same remark as for Aa. No AUF if front block matches F face. [y'] x (L U' L) D2 (L' U L) D2 L2	Ab
E	x' (R U') (R' D) (R U R' D') (R U R' D) (R U') (R' D') (BB, VC Video) BB:This alg is just two orientations performed consecutively. Note:The algo are OCLL5 OCCL4. No AUF if edge centers match their face.			solved

Swap one set of adjacent corners

Ra	R U R' F' R U2 R' U2 R' F R U R U2 R' [U'] (BB) BB:You could also just mirror Rb, but this alg is more right and friendly. Notice the similarity with the Jb permutation. (R U' R' U') (R U R) D (R' U' R) D' (R' U² R') (VC video) No AUF if front RIGHT CORNER matches F face.		(R' U2) (R U2) (R' F R U R' U') (R' F' R2 [U']) (BB, VC video) BB:This is a pretty straightforward alg that flows pretty nicely. No AUF if front EDGE CENTER matches F face.	Rb
Ja	(R' U L') U2 (R U' R') U2 (L R U') (BB) z (D' R U') R2 (D R' D') R2 (U D R') (BB,same with z setup) 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. (L' U' L F) (L' U' L U) (L F' L2' U L) (VC video VC) First F with RH index. No AUF if front FRONT BLOCK matches F face.		(R U R' F') (R U R' U') (R' F) (R2 U') (R' [U']) (BB) BB:This is the same as the T perm with the last four moves instead performed at the beginning. (R U R' F') (R U R' U') (R' F R2 U' R') (VC, edited from Ja perm) First F with LH index. No AUF if front FRONT BLOCK matches F face.	Jb
T	(R U R' U') (R' F) (R2 U' R' U') (R U R' F') (BB,edited) 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. No AUF if front FRONT BLOCK matches F face.		(R' U' F') (R U R' U') (R' F) (R2 U' R' U') (R U R' U R) (BB,edited) 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. No AUF if front LEFT CORNER matches F face.	F

Swap one set of corners diagonally

V	(R' U R' d') (R' F' R2 U') (R' U R' F) (R F) (video VC) BB:This is one of my least favorite permutations because the flow just isn't there. No AUF if front block matches F face.		(F R U' R' U') (R U R' F') (R U R' U') (R' F R F') (BB) 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. First F' with the LH index (as for Jb perm). No AUF if front block matches F face.	Y
Na	(z) D (R' U) (R2 D' R D U') (R' U) (R2 D' R U' R) (BB) 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. z U (R' D) (R2 U' R U D') (R' D) (R2 U' R D' [R]) (cyotheking video) Normal grip after z. RH sexy regrip during the first and second U'. No AUF (last R if blocks on F and L faces are swapped. Otherwise, AUF taking in account that F and L blocks are swapped. (R U R' U) (R U R' F') (R U R' U') (R' F R2 U' R') (U2 R U' R) (VC, from youtube chat) Sexy grip star, with two variants: either second U with RH like a Sune, or pushed with LH index. No AUF if front block matches the F face.		(z) U' (R D') (R2' U R' D U') (R D') (R2' U R' D R') (BB) BB:This is just the mirror of the other N permutation. z U' (R D') (R2 U R' D U') (R D') R2 U R' D [R] (cyotheking video) Normal LH grip, RH sexy grip z. RH sexy regrip for both R2. All U, D' done with RH. (R' U R U') (R' F' U' F) (R U R' F) (R' F' R U' R) (VC video) Note:Looks easier to fingertrick. Always AUF FIRST, such that front block matches F face.	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: R2 R' R' R vs u U U' u'
• Gb: R2 R' R R vs u U U' u' — Quick recognition: BLOCK is on the RIGHT on the face and next to OPPOSITE color!
• Gc: R2' R R R' vs u' U' U u
• Gd: R2' R R' R' vs u' U' U u — 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)

Ga	(R2 u) (R' U R' U' R u') R2' y' (R' U R) (BB,VC video) BB:This alg has a pretty decent flow to it and can be performed almost in one motion until the rotation. Right thumb on URB corner and right ring/major on F face. First u with RH index, and U with major/ring fingers. Then U' and u' with LH. No AUF if front block matches the F face.		[y'] (R' U' R) y (R2' u R' U) (R U' R u' R2') (BB) BB:This is the inverse of Ga. Note how similar they look. I perform this one almost exactly the same way. (F' U' F) (R2' u R' U) (R U' R u' R2') (VC, from an example solve) F' and F with RH thumb and index, then similar to Ga.	Gb
Gc	(R2' u' R U') (R U R' u R2) (f R' f') (bB) BB:You could rotate and insert the pair instead of performing the last three moves as shown. Start with RH thumb and index pinching RU corner-edge-corner (such that to be out of the way for the first u'), and RH ring finger under RD edge, and LH in standard grip. First u' with LH index or ring, which requires lifting slightly the RH index and ring fingers. During U' R, the RH thumb must move down such that not to block the U move done with RH index. The last u is done with the RH ring finger that was prepared from the beginning.) [y2] R2' F2' R U2 R U2') (R' F R U) (R' U' R' F) R2 (VC,example solve) Start with RH under D face and RH thumb on RU edge, F2' and U2 with RH index+middle, U2' with LH. No AUF if front block matches the F face.		[y] (R U R') y' (R2' u' R U') (R' U R' u R2) (BB) BB:This is just the inverse of Gc. I execute it very similarly because most of the moves overlap in the same manner. (f R f') (R2' u' R U') (R' U R' u R2) (VC video) Careful with regrip after R2' move. The RH ring finger must be under RD edge, and thumb on the FRD corner, such that at the u move the slice is pushed by the RH ring finger, and the thumb is holding the BRD corner and not the RD edge with a risk of lock because it would push the RD edge upwards.	Gd

PLL training sequence

From Victor Colin:

Ga	(R2 u) ...
Nb	(R' U R U') ...
Gb	(F' U' F) ...
Gd	(f R f') ...
Gc	(R2' u' R U') ...
Y	(F R U') ...
Ra	(R U' R' U') ...
Ua	(R2 U') ...
Rb	(R' U2) (R U2) ...
Ub	(R' U R' U') ...
Jb	(R U R' F') ...
F	(R' U' F') ...
V	(R' U R' d') ...
Na	(R U R' U) ...
Aa	x (R' U R') ...
Ab	x R2 ...
H	(M2' U') (M2' U2') ...
Z	(M2' U') (M2' U') ...
E	x' (R U') ...
T	(R U R' U') ...
Ja	(L' U' L F) ...

Recognizing the PLL cases

Links

• Mark49152's Two-sided PLL recognition guide

Links to reference guides and methods, and a nice 2-page PDF with easy method (File Pll2side-20140531.pdf)

• Sarah's PLL recognition guide

Another two side method. See these videos (part 1, part 2), or excellent video from Sarah herself.

• CrazyBadCuber - Ultimate PLL Recognition Guide

A quite clear video on PLL recognition, almost only two sides.

• Improve Rubik's Cube Last Layer: 2 Sided PLL Recognition [CFOP [Tutorial/Guide]]

Yet another guide video on 2-side PLL recognition.

• Android trainer - Advance Cube | PLL Recognition and Timer

Nice app to train PLL recognition from 2 sides only!

• Andy Klise's 2 Sided PLL Recognition

All cases listed by PLL cases instead of the two visible edges.

• 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
• When learning 1 look PLL how do you recognize so fast

Reddit post, with many links (reported above).

Advanced stuff

• J Perm - How I Recognize PLL Fast (Recognition Method)

An advanced method to predict in OLL where headlights are going to be, and adapt PLL recognition accordingly, and even influence where the headlights are going to be. Lot of nice tips though.

2-face recognition

Reference:

• Mark49152's two-sided PLL Recognition Guide (pll2side-20150531.pdf)

Front Right

pattern = perm (AUF)

BAR headights adj edge = Ua (-) headights opp edge = Ub (-) block = Ja (U') block = Jb (U) 4 colors = F (U)	DOUBLE LIGHTS 2-color 6-checker = Z (U) adj edges & 4 colors = Z (-) opp edges = H (-) 2:1 pattern & 3 colors = Ua (?) 2:1 pattern & 3 colors = Ub (?)	LIGHTS + BLOCK inside block & 3 colors / opp edge = T (U) inside block & 3 colors / opp edge = T (U2) inside block & 4 colors / adj edge = Ra (U) inside block & 4 colors / adj edge = Rb (U) outer block & 3 colors / 4-checker = Aa (U2) outer block & 3 colors / 4-checker = Ab (U2) outer block & 4 color = Ga (?) outer block & 4 color = Gc (?)
LONE LIGHTS 5-checker = Ra (U2) 5-checker = Rb (-) 4-checker = Ga (U2) 4-checker = Gc (-) lights enclose opp = Gb (U') lights enclose opp = Gd (U') lights enclose adj (but no checker) = Aa (U') lights enclose adj (but no checker) = Ab (U')	DOUBLE BLOCKS both outside = Y (-) both inside & bookends = Aa (U) both inside & bookends = Ab (U) both inside & no bookends = V same side & bookends = Ja (U) same side & bookends = Jb (-) same side & no bookends = Na (-) same side & no bookends = Nb (-)	OUTSIDE BLOCK no bookends = V (-) adj appears twice = Ra (-) adj appears twice = Rb (U2) opp appears twice = Gb/d (?) adj by block & 4 colors = T (-) opp by block & 4 colors = Aa (-) opp by block & 4 colors = Ab (U2)
INSIDE BLOCK no bookends = Y (U') bookends adj color = Ga/c (?) bookends opp color = Gb/d (?)	BOOKENDS NO BLOCK enclosed 4-checker = F (?) adj appears twice = Ra (U') adj appears twice = Rb (U') opp appears twice = Ga/c (?)	NO BOOKENDS inner 4-checker = V (U') outer 4-checker = Y (U2) 5-checker w/opp middle = E (?)

Note:

• To find orientation, use OPP HEADLIGHT trick. If perm has 2 adj solved corner (ie. HEADLIGHT), they are necessarily opposite to the side with the OPP. HEADLIGHT (e.g. a side with a BLUE and GREEN corner).

• Double lights

• 2:1 pattern & 3 colors = U

• The single edge of 2:1 pattern gives the position of the side with opposite colors in U perm. Ua perm if that edge on the left, and Ub perm if that edge on the right.
• However it is better to look at the headlight of the 2:1 pattern, and in particular the edge of that side, because it also gives the position of the bar on the U perm. If the edge is adj. color, the bar is on the opposite side; if edge is opp. color, the bar is on adj. side. Moreover if the headlight we're looking is on the right, it's a Ua perm; if it's on the left it is a Ub perm.
• So, in fact, if the 2:1 HEADLIGHT is on the LEFT, we use the LEFT hand for ONE (if OPP. colors) or TWO (if ADJ colors) U', and we do Ub perm. To remember that, we think that we want to put that side on the RIGHT as fast as possible (hence the U' moves), and we want that side to have opposite colors, so necessarily Ub perm.
• And if the 2:1 HEADLIGHT is on the RIGHT, we use the LEFT hand for TWO (if OPP. color) or ONE (if ADJ. colors) U', and we do Ua perm. To remember that, we think that we want to put that side on the LEFT as fast as possible (hence the U' moves), and we want that side to have opposite colors, so necessarily Ua perm.

• Lone lights

• 4-checker

• 2-BAR is always close to 4-checker.
• If 4-checker on the LEFT, 2-BAR on the LEFT, so U with RIGHT hand, and Gc.
• If 4-checker on the RIGHT, 2-BAR on the BACK, so 2U' with LEFT hand, and Ga.

Facts

• Look at corners first, because they give the most information at first.
• When 2 corners are solved, we see one headlight. In that case, the opposite side will have an headlight of opposite color.

This is particularly interesting when having A perm, to identify where are the headlights.