# 2 PLLs faster than 1?



## cuBerBruce (Nov 26, 2011)

On Square-1, it is easy to do U-perms simultaneously on both layers. This got me thinking about seeing how many moves it takes to do PLLs on a Rubik's Cube simultaneously on both the U and D layers. One might think the move count would be higher for doing such a "double PLL" than for a regular PLL on one layer. I found that in most cases (at least when the same letter PLL is done both layers), the opposite to be true. Only two of the 13 letter categories take more moves to do on both layers, assuming we can choose any subcategory (i.e. "a"/"b"/"c"/"d" variants), AUF case, and angle case for each layer. Also, for one letter, the two optimal cases are equal in length. I note that I used face-turn metric in my comparisons.

Before opening the spoiler, perhaps you might try to guess which two double PLLs take more moves than the corresponding regular PLL. In the spoiler, I give examples of optimal algs for each PLL letter. If you're constrained to solving the same variant on both layers (e.g. Jb on both layers), the optimal move count increases, and a third letter requires more move than the plain PLL (and two more become equal to the plain PLL). An example of one variant of each relevant PLL is also given in the spoiler. I note that here I am only comparing the best cases with respect to each double and regular PLL.



Spoiler



A: R B' R F2 R' B R F2 R2 (9f*)
A/A: R2 U R2 U' R2 F2 R2 U R2 U' F2 R2 (12f*) 

E: R U' L D2 L' U R' L U' R D2 R' U L' (14f*)
E/E: F2 U2 L2 B2 D2 R2 F2 D B2 F2 L2 R2 U' R2 (14f*) 

F: F2 L2 B' F2 U B' R2 F D' B R2 B F' (13f*)
F/F: B2 U2 L2 U' L2 B2 R2 F2 D F2 D2 R2 (12f*) 

G: R' U' R B2 D L' U L U' L D' B2 (12f*)
G/G: B2 D L2 U' B2 L2 D B2 U' L2 (10f*) 

H: R2 F2 B2 L2 D' R2 F2 B2 L2 (9f*)
H/H: B2 L2 B2 D U' R2 F2 R2 (8f*) 

J: B2 L U L' B2 R D' R D R2 (10f*)
J/J: F2 D' F2 U2 L2 U' L2 (7f*) 

N: R U' R2 F2 U' R F2 R' U F2 R2 U R' (13f*) 
N/N: L2 B' D2 L2 R2 U2 F' R2 (8f*) 

R: R' U2 R U2 R' F R U R' U' R' F' R2 (13f*)
R/R: F2 L2 D' F2 D U F2 U' L2 F2 (10f*) 

T: R2 U R2 D' F2 L2 U' L2 D F2 (10f*)
T/T: B2 U2 L2 U L2 B2 R2 F2 D' F2 D2 R2 (12f*) 

U: R2 U' B' F R2 B F' U' R2 (9f*)
U/U: F2 L2 U' L2 R2 D R2 F2 (8f*) 

V: R U' R U F D' F D F2 R F R' F' R' (14f*)
V/V: L2 U2 L2 F2 D' L2 R2 U' B2 R2 U2 L2 (12f*) 

Y: L' U' L F2 R' D R U R2 D' R2 U' F2 (13f*)
Y/Y: B2 D' R2 D2 B2 L2 U2 F2 U L2 (10f*) 

Z: R2 L2 U F2 B2 D' F' B U2 D2 F' B (12f*)
Z/Z: L2 R2 U2 B2 F2 D' B2 F2 L2 R2 (10f*) 

Ab/Ab: B2 L' R' F L R B2 D2 B F R' B' F' (13f*) 
Gb/Gb: F2 L2 U' L2 D L2 R2 D L2 U' R2 F2 (12f*) 
Jb/Jb: F2 U' R2 U R2 F2 U' R2 U R2 (10f*) 
Nb/Nb: B' F' D2 L2 U2 R2 B' F' L2 D2 R2 (11f*) 
Rb/Rb : B2 D R2 D' L2 U' R2 U F2 L2 B2 R2 (12f*) 
Ua/Ua: R2 D L2 R2 U' B2 L2 D R2 F2 R2 (11f*)


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## oll+phase+sync (Jan 2, 2012)

cuBerBruce said:


> Before opening the spoiler, perhaps you might try to guess which two double PLLs take more moves than the corresponding regular PLL...


Did you find any logic that could tell you wich double PLLs take more moves?


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