Orientation of the Last Layer (OLL)
This page is written for people that want to learn all 57 algorithms to orientate the last layer pieces in one algorithm. If you don't know a very fast system to solve the F2L (First 2 Layers) yet, the easiest way to improve your times is to learn a good F2L system. This website has a nice section where you can view all the F2L algorithms on java applets (Click on "Solve First Two Layers" on the left). Also, learning all these algorithms is not nessesary for reaching sub-20 times. It's not very hard to average sub-20 with a system that uses fewer algorithms, like a three look last layer (for example: orientate edges, orientate corners, PLL). It will take a lot of practice, though.
But if you really want to learn all the algorithms, don't fear the big number of 57 algorithms. A lot of algorithms have the same kind of moves, with only small differences. Most OLL-pages just group all the OLL-cases by their shapes, for example, there are two 'T-shapes', four 'knight move-shapes'. For recognition, grouping the cases by their shape is pretty usefull. But when it comes to memorising the algorithms, it's maybe better to group the cases by their algorithm structure. So, on this page, I will try to do a little bit of both. For some OLL-cases, I will give you multiple algorithms to solve them, just to show the connections between the algorithms. I added a few comments to show the relation between the algorithms, but it's not always easy to tell you in words how the algorithms are connected, so you should also look at the relations between the algorithms that are placed close to each other yourself.
Also note that this page requires the knowledge of the standard notation of moves. This means you should know that the moves R and r are two different moves. R means rotating the right layer clockwise, while r means rotation the right layer and the middle layer next to it clockwise. If you are not sure what I mean by this, look at this notation glossary (thanks to Dan Harris).
Group 1: The Sune Family
The first group of algorithms, is a group that uses 'Sune' algorithms. The basic Sune move twists three corners. For the first two cases, there are four different Sunes. All of them put one corner edge pair in the U layer, reposition it with a U move, and then insert it in the F2L again. The other moves are just variations and combinations of those four algorithms. Also note that when I say '1a executed twice', I mean '1a executed twice, with cancelation of moves'.
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| 1a. (R'U2) (RUR'UR) (the inverse of 2a) |
2a. (R'U'RU') (R'U2R) (the inverse of 1a) |
1b. (RUR'U) (RU2R') (the inverse of 2b) |
2b. (RU2) (R'U'RU') R' (the inverse of 1b) |
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| 3. (r'U2) (RUR'Ur) (variation of 1a) |
5. (r'U'RU') (R'U2r) (variation of 2a) |
6. (rUR'U) (RU2r') (variation of 1b) |
4. (rU2) (R'U'RU') r' (variation of 2b) |
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| 7. (R'U2) (RUR'U') (RUR'UR) (1a executed twice) |
7. (RUR'U) (RU'R'U) (RU2R') (1b executed twice) |
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| 8. (r'U2) (RUR'U') (RUR'Ur) (variation of 7) |
9. (rUR'U) (RU'R'U) (RU2r') (variation of 7) |
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10. (RUR'U) (RU'R'U) (RU'R'U) (RU2R') |
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| 11. (r'U2) (RUR'U) (r2 U2) (R'U'RU') r' or (R'U2) F (RUR'U') y' (R2U2RB) (combination of 3 and 4) |
12. (rUR'U) (RU2) (r2'U'RU')(R'U2r) or y2 F (RUR'U) y' (R'U2) (R'FRF') (combination of 5 and 6) |
Group 2: The RUR'U' Family
This group of algorithms, is a group that uses the basic moves RUR'U' or L'U'LU and their inverses.
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| 13a. F (RUR'U') F' (the inverse of 14) |
14. FU (RU'R') F' (the inverse of 13a) |
13b. F' (L'U'LU) F or f (URU'R') f' |
15. F'U' (L'UL) F or y L' d' (R'UR) B (the inverse of 13b) |
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| 16. F (RUR'U') (RUR'U') F' (1a executed twice) |
18. FU (RU'R'U) (RU'R') F' or y2 f (RUR'U') (RUR'U') f' (1a executed twice) |
17. F' (L'U'LU) (L'U'LU) F or z F'U' (R'URU'R'U) R b |
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| 19. (rUr') (RUR'U') (rU'r') (mirror of 20) |
21. (r'U'r) U' (R'URU') (R'UR) (r'Ur) | 20. (R'F'R) (L'U'LU) (R'FR) (mirror of 19) |
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| 22. F (RUR'U') F' f (RUR'U') f' (combination of 13a) |
23. f (RUR'U') f' U F (RUR'U') F' or y l (L2U'LU') (l'U2l) U' M' (combination of 13a) |
24. f (RUR'U') f' U' F (RUR'U') F' or y r' (R2UR'U) (rU2r') UM' (combination of 13a) |
Group 3: Combinations of Sune's and RUR'U' moves
Maybe it's a bit weird to call this a group, because there are just two algorithms, but their place after the first and second group makes sense, because the algorithms are combinations of algorithm 1, 13 and 14.
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| 25. FU (RU'R') F' (R'U2) (RUR'UR) (combination of 1 and 14) |
26. (R'U2) (RUR'UR2) y (RUR'U') F' (combination of 1 and 13) |
Group 4: Removing and inserting a corner-edge pair
The connections in the stucture of these algorithms are not as straigtforward as in the previous groups. But all these algorithms remove a corner edge pair from the first two layers, then do something useful, and then insert the pair again. To make memorization easier, just look where the F2L pieces are going, especially the corner edge pair.
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| 27. (RUR'U') (R'FRF') | 28. (FR'F'R) (URU'R') or y' x' (RU'R'U) y' (RUR'U')yx (the inverse of 27) |
32. x' (RU'R'F') (RUR') x y (R'UR) (the inverse of 33) |
33. (R'U'R) y' x' (RU'R'F) (RUR')x (the inverse of 32) |
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| 29. (RUR'U') r (R'URU') r' (variation of 27) |
30. (r UR'U') r' R U (RU'R') (the inverse of 29) |
34.(R'FRU) (R'F'R) y' (RU'R') (mirror of 32) |
35. (RUR') y (R'FRU') (R'F'R) (mirror of 33) |
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| 31. (RUR'U') x D' (R'URU') D x' (variation of 27) |
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| 36. (RUR'U) RU'R'U' (R'FRF') (mirror of 37) |
37. (R'U'RU') R'URU x' (RU'R'U) x (mirror of 36) |
38. (RU2') (R2'FRF') U2 (R'FRF') | 39. (RU2') (R2'FRF') (RU2'R') |
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| 40. (RUR'U) R d' (RU'R') F' | 41. (RUR'U) (R'FRF') U2 (R'FRF') | 42. (rUR'U) (R'FRF') (RU2'r') (variation of 41) |
43. (r'U'RU') x' (RU'R'U) x (R'U2r) (mirror of 42) |
Group 5: Not categorized
This group of algorithms is not really easy to put in a group according to their algorithms. I tried to order them, so cases that are each others inverses, and cases that have similar patterns are next to each other.
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| 44. R'F(RUR'U') F'UR (the inverse of 45) |
45. R'U'FU (RU'R') F'R (the inverse of 44) |
46. LF' (L'U'LU) FU'L' (mirror of 44) |
47. LUF'U' (L'UL) FL' or R'FRF' d' L'U'LU L'UL (mirror of 45) |
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| 48. (R'FRF') (RU2'R') d' (L'U'L) | 48. (R2'UR'B') RU' (R2'URBR') | ||
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| 50. R B' R2' F R2 B R2 F' R (mirror of 51) |
51. R' F R2 B' R2' F' R2 B R' (mirror of 50) |
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| 52. (R'U2) (R2'U) (R'U) (RU2') x' U' (R'U)x | 53.r'RU (RUR'U') r2R2'U (RU'r') | 54. x' (RUR') D (RU'R') D' x | 55. (RU2') (R2'U') (R2U') (R2'U2R) |
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| 56. (R2D') (RU2') (R'D) (RU2'R) | 57. RU x' (RU'R'U) x U'R' |