Rubik PLL

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

The 21 PLL cases

Source:

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

PllUa-180.gif
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.
 PllUb-180.gif
Ub
PllZ-90.gif
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.
 PllH.gif
H
PllAa.gif
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

PllAb.gif
Ab
PllE.gif
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

PllRa.gif
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.
 PllRb.gif
Rb
PllJa-90.gif
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.
 PllJb.gif
Jb
PllT.gif
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.
 PllF.gif
F

Swap one set of corners diagonally

PllV.gif
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.
 PllY.gif
Y
PllNa.gif
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.
 PllNb-90.gif
Nb

Double spins

PllGa.gif
Ga
  • Recognition: HEADLIGHT left face, BLOCK front face (i.e. on ADJ faces)
  • Note: HEADLIGHT face has ADJ colors, BLOCK face has ADJ colors.
  • Note: Ga / Gd = Aa + Ua. Corners move CLOCKwise, edges moves ANTI-clockwise.
(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.
  • Recognition: HEADLIGHT left face, BLOCK right-back corner (i.e. on OPP faces)
  • Note: HEADLIGHT face has OPP colors, BLOCK face has OPP colors.
  • Note: Gb / Gc = Ab + Ub. Corners move ANTI-clockwise, edges moves CLOCKwise.

[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.
 PllGb-270.gif
Gb
PllGc.gif
Gc
  • Recognition: HEADLIGHT left face, BLOCK back face (i.e. on ADJ faces)
  • Note: HEADLIGHT face has ADJ colors, BLOCK face has ADJ colors.
  • Note: Gb / Gc = Ab + Ub. Corners move ANTI-clockwise, edges moves CLOCKwise.

(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.
  • Recognition: HEADLIGHT left face, BLOCK right-front corner (i.e. on OPP faces)
  • Note: HEADLIGHT face has OPP colors, BLOCK face has OPP colors.
  • Note: Ga / Gd = Aa + Ua. Corners move CLOCKwise, edges moves ANTI-clockwise.

[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.
 PllGd-90.gif
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

Links to reference guides and methods, and a nice 2-page PDF with easy method (File Pll2side-20140531.pdf)
Another two side method. See these videos (part 1, part 2), or excellent video from Sarah herself.
A quite clear video on PLL recognition, almost only two sides.
Yet another guide video on 2-side PLL recognition.
Nice app to train PLL recognition from 2 sides only!
All cases listed by PLL cases instead of the two visible edges.
A *must* see video on how to quickly recognizes the PLL based on features like headlights, bar, pairs...
Reddit post, with many links (reported above).
Advanced stuff
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.

Corner analysis

We number the corners with 1 2 3 4, and looking at the cube from 2 sides, we assume corner 1 is always on the left. We have the 6 following possible cases. We look at features like:

  • Headlights (HL)
  • Bookend (BE)
Case State Obtained by Visible features Hidden features
4 3
1 2
Solved HL (2x) HL (2x)
2 3
1 4
(1,3) or (2,4) relatively solved Swap 2-4 or swap 1-3 no BE, no HL
3 4
1 2
(1,2) relatively solved (3,4) swap / (1,2,3) cycle / (1,2,4) cycle HL BE
2 4
1 3
(3,4) relatively solved (1,2) swap / (1,3,4) cycle / (2,3,4) cycle HL BE
4 2
1 3
(1,4) relatively solved (2,3) swap / (1,2,4) cycle / (1,3,4) cycle BE HL
3 2
1 4
(2,3) relatively solved (1,4) swap / (1,2,3) cycle / (2,3,4) cycle BE HL

Conclusions:

  • If we see TWO HEADLIGHTS, then ALL corners are SOLVED.
  • If we see ONE HEADLIGHT, then TWO corners are SOLVED.
  • If we see BOOKEND (hence no headlight), then TWO corners are SOLVED on non-visible side (-> HIDDEN HEADLIGHTS)
  • If we don't see any bookend (nor headlights), then TWO OPPOSITE corners are SOLVED.

Notes:

  • HEADLIGHT and BOOKEND (as visible features) are mutually exclusive.
  • Any permutation with HEADLIGHT will exhibit the HEADLIGHT on two cube orientations, and BOOKEND on the two others.

2-face recognition

Reference:

  • Mark49152's two-sided PLL Recognition Guide (pll2side-20150531.pdf)
  • ALT: alternate detection way that I use personally.
Front Right
pattern = perm (AUF)
BAR

headights = Ua (-)
headights = Ub (-)
headights = Ub (U)
headights = Ua (U)

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 (OPP) = Ua (U2)
2:1 pattern & 3 colors (no OPP) = Ua (U')
2:1 pattern & 3 colors (OPP) = Ub (U2)
2:1 pattern & 3 colors (no OPP) = Ub (U')

  • Odd edge opp/adj col -> bar adj/opp
  • 2:1 moves ANTI-clockwise -> Ua
  • 2:1 moves CLOCKwise -> 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 (U)

outer block & 4 color = Gc (U)

LONE LIGHTS
5-checker = Ra (U2)

5-checker = Rb (-)

4-checker = Ga (U'2)

4-checker = Gc (-)

  • BLOCK always next to checker
 lights enclose adj (but no checker) = Aa (U')

lights enclose adj (but no checker) = Ab (U')

  • Note Aa/Ab also have a 2:1 pattern

lights enclose opp + 2:1 left = Gb (U')
lights enclose opp + no 2:1 left = Gd (U)
lights enclose opp + 2:1 right = Gd (-)
lights enclose opp + no 2:1 right = Gb (U2)

  • Block touches side with 2:1 pattern
  • ... i.e. mirror of sq. w/ opp colors.
  • last corner always same as opp
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 = Ja (U2)
same side & bookends = Jb (-)
same side & bookends = Jb (U')

  • Bar adjacent to side with ADJ colors.
  • ... shorter AUF when blocks ADJ colors
 same side & no bookends = Na (-)

same side & no bookends = Nb (-)

  • All sides have OPP colors.
OUTSIDE BLOCK
no bookends = V (-)
adj appears twice = Ra (-)

adj appears twice = Rb (U2)

opp appears twice = Gb (U)
opp appears twice = Gd (U2)

adj by block & 4 colors = T (-)
adj by block & 4 colors = T (U2)

opp by block & 4 colors = Aa (-)

opp by block & 4 colors = Ab (U2)

INSIDE BLOCK
no bookends = Y (U')

ALT: same color around block

bookends adj color = Ga (-)
bookends adj color = Gc (U')

bookends opp color = Gb (-)
bookends opp color = Gd (U')

BOOKENDS NO BLOCK

enclosed 4-checker = F (U')
enclosed 4-checker = F (-)

  • Bar adjacent to OPP color pair
 adj appears twice = Ra (U')

adj appears twice = Rb (U')

  • HEADLIGHTS further from test pair
  • ... or OPP to OPP HEADLIGHTS

opp appears twice = Ga (U')
opp appears twice = Gc (-)

  • HEADLIGHTS nearer to test pair
  • ... or OPP to OPP HEADLIGHTS
NO BOOKENDS
inner 4-checker = V (U')
outer 4-checker = Y (U2)

5-checker w/opp middle = E (U'/U)
5-checker w/opp middle = E (-)

Notes:

=>

OPP HEADLIGHT trick: if perm must have an HEADLIGHT, it is always OPPOSITE to side with the OPP HEADLIGHT."
Also, there is always a BOOKEND (and vice-versa).

Predicting PLL cases

  • Look blocks on the cube.
  • Tracking a corner (the one in the "branching" motion of the algorithm, usually the first corner that).
  • G perms are the most common.

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.
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