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### 3ELL

3ELL, three cycle edges of the last layer, solves any 3-cycle of edges in LL, both EO and EP, using algorithms that preserves all the rest.

Keywords:
• AAO, (short only A), adjacent-adjacent-opposite, the order for one type of cycle, (Mushroom)
• AOO, (short only O), adjacent-opposite-opposite, the order for the other type of cycle, (Horseface)
Cases:

EO and EP correct:

 GD o 1:12
Good Godsh!
Getting a skip, occurrences at this page are calculated from assuming we already solved any two LL-edges and all the corners in some previous steps. We got two groups of a total of 24 cases but the groups are equal to each other, you may get one or the other configuration for the 3-cycle, each are having a skip case of 1:12 probability.

Orientation only (EO) :

 A o 1:8
 D o 1:8
(L F R' F' L') U2' (R U R U' R2' U2 R) (13 RULF) R' U' R (L F R' F' L') U2' (R U R U' R2' U2' R) (16 RULF)

The first alg is the Bruno based 3x3 2-flip, the second about the same alg but with setup and the last U2 in opposite direction (that ends the alg and luckily also cancles the setup).

Three cycles :

Dark yellow edges are in solved position, the other three needs a fix...

Permutation only (EPLL) :

AAO Cases
 MS + 1:24
 MS - 1:24
[y] F' U' L' U L F (y2') F R U R' U' F' (12 RULF) [y'] F U R U' R' F' (y2) F' L' U' L U F (12 RULF)

AOO cases
 HF + 1:24
 HF- 1:24
F' U2' L' U L F (y2') F R U R' U' F' (y) R' U R (15 RULF) F U2 R U' R' F' (y2) F' L' U' L U F (y') L U' L' (15 RULF)

Name:

AAO Cases
 MA + 1:24
 MA - 1:24
L F U F' U' (R' L') U' F' U F R  (12 RULF) R' F' U' F U (L R) U F U' F' L' (12 RULF)

AOO cases
 MD + 1:24
 MD - 1:24
[y2] R' U' F' L U2 F U' F' U' L' F R U (13 RULF) [y] R' F' L U F U F' U2' L' F U R U' (13 RULF)

Name:

AAO Cases
 NA a+ 1:24
 NA d- 1:24
[y] F' U2' L' F U R U' R' F' L U F U (13 RULF) F' U' L' F R U R' U' F' L U2 F U' (13 RULF)
 NA a- 1:24
 MA d+ 1:24
[y'] F U2 R F' U' L' U L F R' U' F' U' (13 RULF) F U R F' L' U' L U F R' U2' F' U (13 RULF)

AOO cases
 ND a+ 1:24
 ND d- 1:24
(y2') (R' L2) U2 (R L') F (R' L) U2' (R L') F' L' (13 RULF) (y2') L F (L R') U2 (L' R) F' (L R') U2' (L2' R) (13 RULF)
 ND a- 1:24
 ND d+ 1:24
(y2) (L R2') U2' (L' R) F' (L R') U2 (L' R) F R (13 RULF) (y2) R' F' (R' L) U2' (R L') F (R' L) U2 (R2 L') (13 RULF)

Average number of moves : 295/24 = 12.29 ... all RULF algs, also RUF works but is pretty much longer in most cases.