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CLL is the 2nd fastest method for the 2 by 2 Rubik's cube. It is faster than the Ortega Method, but not as fast as the EG Method. The only difference between the EG and CLL methods, is that for CLL, you have to make a first layer. (with EG you don't) There are around 40 algorithms for CLL. (you should learn CLL before EG, and after Ortega). In the CLL method you solve 1 sude and the first layer and then do 1 algorithm to solve the cube.
The cases for CLL are sperated between Ortega cases. (sune, antisune, chameleon, headlights, ect.) In each case, you look at specific pieces and see if they are the same, opposite, or different colors. After you have recognized your case, you do 1 algorithm to solve your cube. IMPORTANT: All cases are shown as if you were solving from the white to yellow sides. Your case might not look exactly like shown. All that matters in the pictures, are if they are the same color, opposite color, or neither. You can look at J Perm's CLL video and he will explain that. (if it doesn't make sense to you) After you have watched that, the cases are written down below.
Sune Case 1:
R, U, R', U, R, U2, R'.
Sune Case 2:
U2, R, U, R', U, R', F, R, F', R, U2, R'.
Sune Case 3:
L, F', L', F, L', U', L.
Sune Case 4:
F, R', F', R, U2, R, U2, R'.
L', U2, L, U2, L, F', L', F.
R, U, R', U', R', F, R, F', R, U, R', U, R, U2, R'.
Anti-Sune Case 1:
L', U', L, U', L', U2, L.
Anti-Sune Case 2:
R', U, R, U', R2, F, R, F', R, U, R', U', R.
Anti-Sune Case 3:
R', F, R, F', R, U, R'.
Anti-Sune Case 4:
F', L, F, L', U2, L', U2, L.
R, U2, R', U2, R', F, R, F'.
L' U' L U L F' L' F L' U' L U' L' U2 L
Car Case 1:
R2, U2, R', U2, R2.
Car Case 2:
x', U2, R, U2, R2, F2, R, F2
Car Case 3:
U', R, U, R', U, R, U, R' F, R', F' R
Car Case 3:
U', F, R2, U', R2, U', R2, U, R2, F'
U, F, R2, U', R2, U, R2, U, R2, F'
R', F2, R, F', U2, R, U', R', U', F
R, U2, R', U', R, U, R', U2, R', F, R, F'
R, U', R2, U, R2, U, R2, U', R
R' U' R' F R F' R U' R' U2 R
R, U', R', F, L' U, L, U, L', U, L
R' U R' U2 R U' R' U R U' R2
R, U2, R2, F, R, F', R, U2, R'
F, R', F', R, U, R, U', R'
F, R, U', R', U', R, U, R', F'
R, U2, R', F, R, U2, R', U, R', F2, R
U, R, U2, R2, F2, R, U, R', F2, R, F'
R', U, R', F, U', R, U, F2, R2.
U, F, R, U, R', U', R, U', R', U', R, U, R', F'.
U', F, U', R, U2, R', U', F2, R, U', R'.
U', R', U, R, U2, R2, F, R, F', R.
U2, R, U, R', U', R', F, R, F'.
L', U', L, U, L, F', L' F
Headlight Case 1:
F, R, U, R', U', F'
Headlight Case: 2
R2 F2 R U R' F R2 U2 R' U' R
Headlight Case: 3
U, R2, F, R, F', R', F2, R, U, R', F, R2
Headlight Case: 4
R U2 R U' R' F R' F2 U' F
U, R, U', R2, F, R, F', R, U, R', U', R, U, R', U'
R' U R' F R F' R U2 R' U R
If you memorized CLL and you want to get even faster at 2 by 2 you want to practice CLL untill you are sub 5 seconds and then you can learn the EG method. In this method you solve 1 side and then do 1 algorithm to solve the cube. The difference between CLL and EG is that in CLL you solve the first layer and in EG you don't. You need to know CLL before you learn EG because if you solve the first layer in EG on accident you need to know what to do. If you are interested in EG press HERE to learn EG.