Optimal Solutions for all 21 PLLs
Recently, I decided to set Kociemba's optimal solver on the PLLs. The results were rather surprisingly shorter in some cases, and I noticed some nice algs.
So here, for reference, are optimal (HTM, ignoring initial U-turns) solutions to all PLLs. The ones in red are equally optimal, from a different U-face start. The ones on the right are the ones I currently use.
| Name | Description | Optimal Algorithm | My Algorithm |
|---|---|---|---|
| Allan | Three-edge cycle, clockwise. | F2 U L R' F2 L' R U F2 (9) |
R2' U R U R' U' R' U' R' U R' |
| Allan | Three-edge cycle, counter-clockwise. | F2 U' L R' F2 L' R U' F2 (9) |
L2 U' L' U' L U L U L U' L |
| (Arne) | Switches edges across LL. | L2 B2 F2 R2 D L2 B2 F2 R2 (9) |
M2' U' M2' U2' M2' U' M2' |
| (Bert) | Figured out my own in Chemistry class. I really should learn the 2-gen for this. | B2 F2 U' L2 R2 D L R' D2 U2 L R' (12) R2 F L F' R L' F' R L F' L' F (12) R2 F2 R2 L2 B2 L2 U' R2 L2 D' R2 L2 (12) |
M2' U' M2' U2' M2' U' M2' |
| Three-Corner Cycle | Three-Corner cycle, counter-clockwise. | R B' R F2 R' B R F2 R2 (9) |
R B' R F2 R' B R F2 R2' |
| Three-Corner Cycle | Three-Corner cycle, clockwise. | R2 F2 R' B' R F2 R' B R' (9) |
L' B L' F2 L B' L' F2' L2 |
| E? | I like that optimal alg... Arthur calls this the "Square Enix". |
L U' R D2 R' U L' R U' L D2 L' U R' (14) R2 U R2 U2 F2 U' F2 U' R2 F2 U2 F2 U' R2 (14) |
L' B L' F2 L B' L' F2' L2 |
| J | The J. | B2 L U L' B2 R D' R D R2 (10) R U' L U2 R' U R U2 R' L' (10) F B U2 B' U' B U2 F' U B' (10) |
L' U R U' L U2' R' U R U2 R' |
| J | It might be better to call this one "L." | B2 R' U' R B2 L' D L' D' L2 (10) L' U R' U2 L U' L' U2 L R (10) F' B' U2 B U B' U2 F U' B (10) |
R U' L' U R' U2 L U' L' U2' L |
| R | Arthur calls this the "Phone." The one I use is also optimal. | R' U2 R U2 R' F R U R' U' R' F' R2 (13) R2 F R U R U' R' F' R U2 R' U2 R (13) B U L' D2 R F' R' D2 L2 U' B' U L' (13) |
R' U2 R U2' R' F R U R' U' R' F' R2 |
| R | Arthur calls this the "British Phone." | L U2 R L' U R' F' L U2 L2 U' L F (13) L2 F' L' U' L' U L F L' U2 L U2 L' (13) B' U' R D2 L' F L D2 R2 U B U' R (13) |
L U2' L' U2 L F' L' U' L U L F L2' |
| T | Too many half-turns in the optimal... | F2 U' F2 D R2 B2 U B2 D' R2 (10) |
R U R' U' R' F R2 U' R' U' R U R' F' |
| V | I once found another nice optimal alg for this. Can't find it... | R U D2 L' U L U2 F2 D R D' F2 D2 R' (14) F2 U F2 U2 R2 D' L2 D' B2 L2 D2 R2 U' F2 (14) L U2 L2 B' U' B L2 F U F2 L' F2 U' F' (14) |
L' U R U' L U L' U R' U' L U2' R U2 R' |
| Y | I once called this the "Psi." Hmm, I think I like that optimal alg... |
F2' U F2' U F2 U' R' U' R F2 R' U R (13) F' L' F R2 F' L F U2 R2 U R2 U R2 (13) |
F R U' R' U' R U R' F' R U R' U' R' F R F' |
| I once called this the "negative T," but I think most people refer to it as the "F." | L R' F2 L D' R F2 L' U L' R2 B2 R2 U' (14) F2 U F2 U2 R2 D' L2 D' B2 L2 D2 R2 U' F2 (14) L U2 L2 B' U' B L2 F U F2 L' F2 U' F' (14) |
R' U R U' R2' F' U' F U x R U R' U' R2 x' =R' U R U' R2' F' U' F U R F R' F' R2 |
|
| N | The annoying one. | F2 R2 U2 R2 U' R2 F2 U2 F2 U' R2 U2 F2 (13) |
R U' L U2 R' U L' R U' L U2 R' U L' |
| N | The other annoying one. | R2 F2 U2 F2 U F2 R2 U2 R2 U F2 U2 R2 (13) |
L' U R' U2' L U' R L' U R' U2' L U' R |
| RL G | I name G's by the edge in the joined block when placed at UFR and the two corners relatively solved. That R U R' F2 D' L U' L' U L' D F2 (12) is really nice; it's the commonly used one:... | F2 R2 D' L2 D L2 U' L2 U L2 R2 F2 (12) R U R' F2 D' L U' L' U L' D F2 (12) L2 D' R2 D' F2 R' D' L D2 R' D L (12) |
R U R' F2 u' F U' F' U F' u F2 |
| RB G | Inverse of the RL G. | F2 R2 L2 U' L2 U L2 D' L2 D R2 F2 (12) F2 D' L U' L U L' D F2 R U' R' (12) F2 D' L U' L U L' D F2 R U' R' (12) R' D' L D2 R' D L B2 D L2 D R2 (12) |
R2 u' R U' R U R' u R2 B U' B' |
| FL G | Inverse of the RL G. | R2 F2 B2 U B2 U' B2 D B2 D' F2 R2 (12) F2 D R' U R' U' R D' F2 L' U L (12) F D B' D2 F D' B' L2 D' B2 D' F2 (12) |
R2' u R' U R' U' R u' R2 F' U F |
| FB G | Inverse of the RL G. | R2 F2 D B2 D' B2 U B2 U' B2 F2 R2 (12) L' U' L F2 D R' U R U' R D' F2 (12) B2 D F2 D R2 F D B' D2 F D' B' (12) |
F' U' F R2' u R' U R U' R u' R2 |