Permutation of Last Layer (PLL)
PLL, the last step of CFOP, permutes all last-layer pieces while preserving their orientation.
Also see other cubers' lists to find your favorite algorithms. Even for the same algorithm, try chunking into different substeps or changing the grips. Keep in mind that you don't need to worry about cube turns and that you need to put down the cube to stop the timer.
(You might be thinking, "aren't you then allowing the method of timing to influence, if only slightly, the method?" Yes! The 100-meter dash analogy shows why this is reasonable: here, here, and here.)
Recognition and AUF
Recognition takes longer for PLL than for OLL because we often need to adjust the U face (AUF) before we can determine the case. Rather than systematically matching corners or edges, I recommend using "blocks" for recognition. Refer to your keyboard's numpad for the following description (props to Timothy Wang for the idea). Cycles describe the permutation.
Two adjacent top-layer pieces are connected if they have the same color on the same side. Each permutation has a unique pattern of connected pieces that form blocks. For example, (46)(39), the T permutation, has blocks 12 and 78. (37)(48), the Y permutation, has blocks 12 and 69--also two 2x1 blocks, but in a different arrangement. We recognize each case by its particular pattern of blocks.
Learning the block pattern for each permutation allows us to do recognition often from two adjacent sides. For instance, if you see the block 1236 (not connected to 9), the only possible case is (79)(48), a J-perm. Sometimes, we need more information. Say you see the block 236 (not connected to either 1 or 9). There are three possible permutations: (19)(48), (179), and (197). We can distinguish between these patterns by inspecting one of the two remaining sides. Note: It is always possible to do recognition from two adjacent sides. Take the same block 236. With (19)(48), the colors of 1 and 23 and those of 9 and 63 are opposite. For the three cycle, only one set is opposite and the other is adjacent, on F or on R depending on the direction. I personally find this too cumbersome.
If there is only one block, consisting of a corner and an edge, you have a G-perm. Match this block with the first two layers to determine which of the four you have. If there is no block at all, you have the E-perm, and matching any edge (which automatically matches all the edges) shows which corner pair need to be switched.
An advantage of this recognition method is that you can sometimes see blocks coming together during OLL. When this happens, by slowing down slightly towards the end of OLL, you can predict the PLL and reduce the pause between the two last layer steps.
If you're sub-15, see Sébastien Felix's R-OLL for a much more sophisticated PLL-prediction method.
Learning PLL
Start by learning two-step PLL, which is a subset of the complete PLL. There are two algorithms for corners (n3 and n15) and four for edges (n1, n2, n5, n6). Learn n4, the reflection of n3. Of the algorithms above, n15, which is used to swap corners across a diagonal, takes the longest. For this reason, the next PLL cases to learn are the other cases with a diagonal corner swap: n7, n9, n20, n21. From there, it's all preference. The intimidating G permutations are actually not any more difficult to recognize than the other cases.
Algorithms
Only Edges
- PLL n1a (U): 1/18
- R'UR'U'-R'U'-R'URUR2
- zU2'RURU'R'U'R'U'RU'z'
- For OH. Mirror of n2a.
- PLL n2a (U): 1/18
- R2U'R'U'RU-RURU'R
- Inverse of n1a, first algorithm.
- PLL n1b (U): 1/18
- RU'RU-RURU'R'U'R2
- Mirror of n1a. First-timers can ignore n1b/n2b, but they help since AUF and cube rotation are relatively significant for easy PLLs.
- PLL n2b (U): 1/18
- R2U-RUR'U'-R'U'-R'UR'
- Mirror
- zU'RU'R'U'R'U'RURU2z'
- For OH. Mirror of n1b, first algorithm.
- PLL n5 (Z): 1/36
- UR'U'RU'RURU'R'URUR2U'R'U
- Fast two-gen. For OH, replace first and last U with U'.
- (y)R'U'RU'RURU'R'URUR2U'R'U2
- U cycled to the end
- U'M'UM2UM2UM'U2M2
- Fast slices. Saw this credited to fanwuq. Can also cycle U'.
- PLL n6 (H): 1/72
- M2'UM2'U2M2'UM2'
- Several possible M2' fingerings: the Bob Burton double trigger (left-hand ring middle), Rw2(R'M') with. Or R2'Rw2U'L2Lw2'U2R2'Rw2U'L2Lw2'.
- R2U2'RU2'R2U2'R2U2'RU2'R2
- For OH. Reduction to R2U2'R2U2'R2U2'.
Adjacent Corners (Except Gs)
- PLL n4 (Acw): 1/18
- xR'UR'DDRU'R'DDR2x'
- The Rowe Hessler Acw. No regrip, DD as left ring twice.
- (y)x'R2DDR'U'RDDR'UR'x
- (y')RUR'F'*RwUR'-U'Rw'FR2U'R'
- Thick J
- PLL n3 (Accw): 1/18
- xR2'DDRUR'DDRU'Rx'
- The Rowe Hessler Accw.
- PLL n8 (T): 1/18
- RU*R'U'R'FR2-U'R'U'RUR'F'*
- Left thumb on F throughout
- (y2)U2'RU*R'U'R'FR2U'R'U-F'L'UL
- Left-handed T.
- RUR'U'R2z'RU'zU'R'U'RUR2z'R'Dw
- The Robert Yau OH T
- PLL n10 (F): 1/18
- R'U'F'*RUR'-U'R'FR2-U'R'U'RUR'UR
- F en T
- (y)R'U2R'Dw'-R'F'R2U'R'UR'FRU'F
- F en V
- (y')R'URU'R2'F'U'F-URU'x'R2U'R'U
- Old F, but with less rotation
- PLL n11 (Ra): 1/18
- PLL n12 (Rb): 1/18
- U'RU'R'U'RURD-R'U'RD'R'U2'R'
- Also good for OH, but as -R'U'RUw'zx'-U'R2U' after the hyphen.
- PLL n13 (Ja): 1/18
- RU2'R'U'RU2'-L'UR'U'L
- RUR'F'*RUR'-U'R'FR2U'R'U'
- T-perm like. With right-index push for F', faster than the first alg. Cycle U' to beginning for another angle.
- PLL n14 (Jb): 1/18
- R'U2'RUR'U2'-LU'RUL'
- Mirror of n13
- R'U2RUR'z-R2'UR'DRU'
- Same, but with a funky fingering
- xU2'Rw'U'RwU2'-Lw'UR'U'R2x2
- Optimal.
Opposite Corners
These cases tend to be more difficult.
- PLL n9 (V): 1/18
- R'UR'Dw'-R'F'R2U'R'UR'FRF
- By Stefan Pochmann. Keep the thumb on F center except at the hyphen, where you need to move it from L to F.
- (y)zU'RDR'URU'Rz'-R'U'LU2'RU2'R'
- Great for OH.
- R'Uz'RU'RU2R'U'R2U'zU'Rz'R'U'R2U
- For OH.
- R'UR'Dw'z-U'RU'R'-Dw2R'URUR
- Old. Still good for OH.
- PLL n15 (Y): 1/18
- R2U'R'U(RU'x')z'-L'U'RU'R'U'LU
- Also definitely (y2)L2U'L'ULU'x'z-L'U'RU'R'U'LU (same ending), maybe R2'URU'R'Ux'z-RUL'ULUR'U'.
- R2U'R'URU'x'-U'R'DR'D'R'UR
- Same algorithm. For OH.
- FRU'R'U'RUR'F'*RUR'U'-R'FRF'
- Two OLLs.
- U'x'-U'RUR'x'z'-R'U'RU2'RU'R'y-U'RUR'
- Jeremy Fleischman's OH
- PLL n20 (Nb): 1/72
- R'UR'FRF'RU'R'F'UF-RUR'U'R
- Inverse of Stefan Pochmann's (his is also nice).
- U'R'UL'U2'RU'R'LUL'U2'RU'L
- Variat of (R'UL'U2RU'L)*2U. For OH.
- PLL n21 (Na): 1/72
- U-LU'R-U2'L'ULR'U'RU2'L'UR'
- Also for OH.
- RUR'URUR'F'RUR'U'R'FR2U'R'U2RU'R'
- Conjugated J (set-up RUR'U). 21 moves.
- PLL n7 (E): 1/36
- x'RU'R'DRUR'D'RUR'DRU'R'D'x
- The Rowe Hessler E. Left ring for D, keep it in place, push back for D'!
- x'U'RU'Rz'RU'Rwxz'-RU'RURDR'U'R
- Robert Yau OH E
- (y)x'RU'RU'zU'RUw'zx'-U'RU'R'U'zU'RDR'
- Robert Yau OH E
G perms
Yeah, G perms look scary. Each one has a single 1x1x2 block. Tell them apart by looking at the location of this block relative to the two correctly permuted corners. Another recognition method is to use the side sticker of the unique edge that extends this block to a 1x2x2. For example, for n16 in the figure below, the FU and FUR stickers are opposite in color, while in n17, RU and RUB are adjacent.
The French Gs (see Sébastien Felix's PLL) all start with the two good corners on the left and use singe instead of double layer turns (but essentially the same algorithms). Some of them are worth learning, especially when the two corners on the left are in the right place (i.e. no AUF).
- PLL n16 (Ga): 1/18
- RUR'y'-R2Uw'RU'R'U-R'UwR2
- The second regrip can be omitted, but David Gomes calls the resulting right-index push for Uw "The Elbow" for its (lack of) accuracy.
- PLL n18 (Gb): 1/18
- R'U'R(UD')R2U*-R'URU'RU'R2'D(U')
- French G
- R'U'Ry-R2UwR'URU'RUw'R2
- Mirror of n16. Best for OH. For 2H, use R2' as appropriate. The first three moves can also be done as x'Uw'R'Uwx.
- PLL n17 (Gc): 1/18
- R2'Uw'RU'RUR'-Uw-R2'FwR'Fw'
- (y2)R2'F2RU2'RU2'R'FRUR'U'R'FR2
- From Erik Akkersdijk.
- PLL n19 (Gd): 1/18
- R2Uw-R'UR'U'RUw'-(R2x')-Uw'RUw
- Mirror of n17
- (y'U)D'R2U*R'UR'U'RU'R2-(DU')R'UR
- French G. Only from this direction and AUF.
Other PLL Pages
- Algobase by Jai Gambhir, John Tamanas, Jun Hyuk Kim, and Harris Chan
- kora's blog
- Cube Core 909 (Gungz's blog)
- Erik Akkersdijk's flying colours
- Katsuyuki Konishi's Planet Puzzle
- Lars Vandenbergh's CubeZone
- Dan's Cube Station
- Bob Burton's Rubik's Cube Page
- Leyan's Stuff
- Speedsolving.com wiki algorithms list
Older PLL
These pages contain many algorithms that have since fallen out of use. It's interesting to see how PLL algorithms have changed just in the law few years. The 2-gen U-perms, for example, only became popular from Peter Jansen's site shortly after World Championship 2003.