cuBerBruce
Veteran
One thing to remember is that the 6-move edge 3-cycle, if you are fortunate enough to find an insertion point for it, has 4 variations which can be thought of as cyclic shift variations (allowing for switching the order of commuting moves) of the alg in face-turn notation.
For example, M U2 M' U2 translated into face turns is L' R B2 L R' U2. But this can be replaced by any of these other 3 algs:
R B2 L R' U2 L'
L' B2 L R' U2 R
B2 L R' U2 L' R
Considering all four algs doubles your opportunity of getting some cancellation, and also increases your chances of multiple cancellations. If you have to do a setup move in order to use a form of the 6-move alg, the opportunities for cancellations are much reduced, of course.
I also decided to determine all the cube positions having unsolved edges, but all corners solved, up to a distance of 7f*. I provide one maneuver for one element of each symmetry class in the spoiler below. Of course, as the number of unsolved edges goes up, the probability of finding an insertion point matching the configuration goes down, so many of these cases are probably not worth learning.
For 2C,2E positions, I get 10 moves for the minimal alg. The 10f* cases (distinct w.r.t. symmetries of the cube) are:
For pure 2-twist plus pure 2-flip, the minimal alg is 14 moves.
For example, M U2 M' U2 translated into face turns is L' R B2 L R' U2. But this can be replaced by any of these other 3 algs:
R B2 L R' U2 L'
L' B2 L R' U2 R
B2 L R' U2 L' R
Considering all four algs doubles your opportunity of getting some cancellation, and also increases your chances of multiple cancellations. If you have to do a setup move in order to use a form of the 6-move alg, the opportunities for cancellations are much reduced, of course.
I also decided to determine all the cube positions having unsolved edges, but all corners solved, up to a distance of 7f*. I provide one maneuver for one element of each symmetry class in the spoiler below. Of course, as the number of unsolved edges goes up, the probability of finding an insertion point matching the configuration goes down, so many of these cases are probably not worth learning.
Code:
positions requiring 6 moves
---------------------------
3-cycle
B R2 B' F D2 F' (6f*)
5-cycle
B F' R' B' F D (6f*)
U' B D' U R' D (6f*)
B' D' U R D U' (6f*)
U' B' D' U R D (6f*)
pair of 2-cycles
B2 F2 D2 B2 F2 U2 (6f*)
F2 D2 B2 D2 F2 U2 (6f*)
pair of 3-cycles
R D2 U2 L' D2 U2 (6f*)
B2 F2 U' B2 F2 D (6f*)
U2 L' D2 U2 R D2 (6f*)
six 2-cycles
B2 F2 L2 R2 D2 U2 (6f*)
B2 F2 U2 L2 R2 U2 (6f*)
D2 B2 F2 L2 R2 U2 (6f*)
D2 F2 L2 R2 F2 U2 (6f*)
positions requiring 7 moves
---------------------------
3-cycle
D B' F L2 B F' D (7f*)
5-cycle
D' U' B' D' U R D2 (7f*)
D' U' B D' U R' D2 (7f*)
D2 U F D U' R' D (7f*)
D2 U F' D U' R D (7f*)
D R' D U' B D2 U (7f*)
D B F' R B' F D2 (7f*)
D' B' D' U R D2 U' (7f*)
D2 F D U' R' D U (7f*)
U2 B' D' U R D U (7f*)
D2 B F' R B' F D (7f*)
pair of 2-cycles
U' L2 R2 D2 L2 R2 U' (7f*)
D' R2 D2 R2 D2 R2 D' (7f*)
pair of 3-cycles
D U2 L D2 U2 R' D (7f*)
D U2 L' D2 U2 R D (7f*)
U R' D2 U2 L D2 U (7f*)
U R D2 U2 L' D2 U (7f*)
D' B2 F2 U' B2 F2 D2 (7f*)
D2 B2 F2 U B2 F2 D (7f*)
pair of 3-cycles and pair of 2-cycles
L' R2 B2 F2 R' D2 U2 (7f*)
U' L2 R2 D' B2 F2 D2 (7f*)
B2 F2 D' U2 L2 R2 U' (7f*)
U2 R' B2 F2 L' R2 D2 (7f*)
U2 L2 R2 U B2 F2 D (7f*)
six 2-cycles
U' B2 F2 L2 R2 D2 U' (7f*)
U' R2 B2 F2 R2 D2 U' (7f*)
U' B2 F2 U2 L2 R2 U' (7f*)For 2C,2E positions, I get 10 moves for the minimal alg. The 10f* cases (distinct w.r.t. symmetries of the cube) are:
Code:
F R2 D2 L B L' D2 R F' R (10f*)
L' F' L2 D2 R' B' R D2 L' F (10f*)
F2 D' F' D F' R2 B U' B' R2 (10f*)
F2 R2 B' D' B R2 F' U F' U' (10f*)
F R' F R F2 U2 B L B' U2 (10f*)
R B2 L' D L' D' L2 B2 R' U' (10f*)
B2 R2 D' R' D R' B2 L U' L' (10f*)
F' L2 B D' B' L2 F2 U' F' U (10f*)
F R' F' U2 B2 L' B' L B' U2 (10f*)For pure 2-twist plus pure 2-flip, the minimal alg is 14 moves.
Last edited:
