Orienting The Last Layer

The graphics show the top view of the last unsolved layer (the U side). The black squares and the short line segments at the sides show the color of the last layer (the U side). For some positions, there are several algorithms, all doing the same thing. Choose among them according to your preference. The numbers in brackets show the number of moves for each algorithm in four different countings (face moves, quarter moves, slice moves, and antislice moves). More details and notation explanation can be found in the legend or at the bottom of this page.

Pattern Algorithm(s) Probability
of Occurrence		 

 O1a) (11,14,11,3) R U²R²F R F'U²R'F R F'
 O1b) (11,12,11,4) R U B'R B R²U'R'F R F'
 1/108

 O2a) (11,14,11,3) F R'F'R U²F R'F'R²U²R'
 02b) (11,12,11,4) F R'F'R U R²B'R'B U'R'
1/54

 O3a) (12,12,12,4) R  U B U'B'R'F R U R'U'F'
 03b) (11,13,10,4) Rs B'L U²L'B'R B'R²L
 03c) (12,13,12,3) F' U²F'L F L'U'L'U'L U'F
1/27

 O4a) (12,12,10,5) R'F R F'U'Ls D'F D Rs
 04b) (11,12,11,4) L F'L'F U²F  U'R U'R'F'
 04c) (11,14,11,3) R B U²B²U'R' U R B U²R'
1/54

 O5a) (11,14,11,4) L F R U²R'U²R U²R'F'L'
 05b) (11,12,11,4) B L U L'U B'U²B'R B R'
 05c) (13,15,13,3) B L'B'L U²L'U'B'U B L²U'L'
1/54

 O6a) (12,12,10,5) Rs D'B'D Ls U B L'B'L
 O6b) (11,12,11,4) R  B²U L'U' B'U L B'U'R'
 06c) (11,14,11,3) L  U²F'L'U' L U F²U²F'L'
1/54

 O7a) (13,13,11,4) Rs U'B'U B U B U B'U'Ls
 07b) (12,18,9,6)  R² U²B F'L'B²F²R'D²R²B F'
1/216

 O8a) (11,12,11,4) L F U'R U R²F'L'F R F'
 O8b) (11,14,11,4) R U'B²D B'U²B D'B²U R'
 08c) (11,14,11,3) R'U²R²U R'U R U²B'R'B
1/108

 O9a) (12,12,12,4) R B U B'U'B R'F R B'R'F'
 09b) (11,12,11,4) B L F L'B²L U F'U'L'B
 09c) (13,15,13,3) R'U'F U²F U'F U F'U²F'U'R
1/108

 O10) (10,10,10,3) L U F U'F'U F U'F'L'
1/54

 O11a) (10,10,10,4) R U B U'B L'B'L B'R'
 011b) (12,13,12,3) L U F'U'F L'F²L F L'U F
1/54

 O12a) (10,12,10,4) F R'F'R U²F²L F L'F
 012b) (11,12,11,3) R B L'B L B'L'B L B²R'
1/27

 O13a) (9,12,9,3)  R F'U²F U²F R²F'R
 O13b) (10,12,10,4)L'B L'B'L²U²F'L F L'
1/27

 O14) (10,10,10,3) R B U B'U'B U B'U'R'
1/27

 O15a) (7,8,7,3)  R B L'B L B²R'
 O15b) (8,10,8,3) L'B²R B²L B'R'B
1/27

 O16a) (11,13,10,3) B F²L'F L'F'L²F L'B'F
 016b) (11,12,11,4) F'L'B L'B D'B'D B'L²F
1/27

 O17a) (10,10,10,3) L'U'L B L' B'U B L B'
 O17b) (11,12,9,5)  B U²B'U'Rs D B'D'Ls
1/27

 O18a) (7,8,7,3)  L'B²R B R'B L
 018b) (8,10,8,3) L'U'L²F'L'F²U'F'
1/27

 O19) (10,10,10,3) R B'R'U'R B R'B'U B
1/27

 O20a) (10,10,9,4)  L F L'R U R'U'L F'L'
 O20b) (11,15,11,3) B'U²B²U B²R'U R B²U'B'
 020c) (12,12,12,3) F'U'L'U L F L U F U'F'L'
1/27

 O21a) (10,11,9,4)  R L²D'B'D B L B'Ls
 021b) (11,12,11,3) R U'R'U²R U B U'B'U'R'
1/27

 O22a) (10,10,10,4) B U L U'F L'B'L F'L'
 O22b) (10,12,10,3) B L B'R B L²B L B²R'
1/27

 O23) (9,9,9,3) R  U B'U'R'U R B R'
 023b)(9,9,8,4) Rs U'B'U B L U R'
1/27

 O24a) (8,8,8,3)  B L'B'L U L U'L'
 025b) (9,12,9,3) L'U²L F'L F L²U²L
1/54

 O25a) (6,6,6,3) B U L U'L'B'
 025b) (8,8,8,4) F'U'F R B U B'R'
1/27

 O26) (9,12,9,3) F'U²F²R'F'R F'U²F
1/54

 O27) (6,6,6,3) R B U B'U'R'
1/54

 O28) (8,8,8,3) B'U'B U B L'B'L
1/54

 O29) (9,9,9,3) R B'R'U'R U B U'R'
1/27

 O30a) (10,10,9,4)  L U L'U'F'L'B L Fs
 030b) (11,15,11,3) B U²B²U'R'U R²B R²U R
 030c) (12,12,12,3) L U L'U B'U B U L'B L B'
1/54

 O31a) (8,8,8,4) F R U'B U B'R'F'
 O31b) (8,8,8,3) F U F R'F'R U'F'
1/54

 O32a) (10,11,10,3) R B U B²U'R'U R B R'
 O32b) (10,14,10,4) L'U²L²F²R'F L'F²R F'
1/27

 O33a) (11,12,11,2) F U²F' U'F U F'U'F U'F'
 033b) (11,11,11,3) L U L' U L U R'U L'U'R
 033c) (11,15,10,5) B'U²Bs D F²U F²D'L²F
1/108

 O34a) (9,14,9,2)   R U²R²U'R²U'R²U²R
 034b) (11,11,11,3) R'U L U'R U'L'U'L U'L'
1/54

 O35a) (9,12,9,3)   F²D'F U²F'D F U²F
 035b) (10,11,10,3) F'U²F L U'F'U'F U L'
1/54
 O36) R'F'L F R F'L'F
1/54

 O37) (8,8,8,3) R'F'L'F R F'L F
1/54

 O38a) (7,7,7,3) B'U F U'B U F'
 038b) (7,8,7,2) L U²L'U'L U'L'
1/27

 O39a) (11,12,7)   Rs B Ls U²Rs B Ls
 039b) (9,12,9,3)  L  F'L  F²R' F R F²L²
 039c) (10,10,8,4) F  R'F' R L' U R U'R'L
1/54

 O40a) (10,10,8,4)  Fs U F'U'Fs'L F L'
 040b) (12,14,12,3) B' U'B'R'U' R U B²U²B'U'B
1/108



Legend:

U = Top(Up) D = Down (Bottom)
R = Right   L = Left
B = Back    F = Front

Ls = LR'   Rs = RL'   Ra = RL = La
Ds = DU'   Us = UD'   Da = DU = Ua
Fs = FB'   Bs = BF'   Fa = FB = Ba

Ls' = Rs   Rs' = Ls   Ra' = R'L' = La'
Ds' = Us   Us' = Ds   Da' = D'U' = Ua'
Fs' = Bs   Bs' = Fs   Fa' = F'B' = Ba'

Inverting:  Read backwards and negate everything.

Reflecting: 
  over x axis replace
      B  - F'  F  - B'  R  - R'  L  - L'  D  - D'  U  - U'
      B' - F   F' - B   R' - R   L' - L   D' - D   U' - U
      B2 - F2  F2 - B2  R2 - R2  L2 - L2  D2 - D2  U2 - U2
      Bs - Bs  Fs - Fs  Rs - Ls  Ls - Rs  Ds - Us  Us - Ds
      Ba - Ba' Fa - Fa' Ra - Ra' La - La' Da - Da' Ua - Ua'

  over y axis replace
      R  - L'  L  - R'  F  - F'  B  - B'  D  - D'  U  - U'
      R' - L   L' - R   F' - F   B' - B   D' - D   U' - U
      R2 - L2  L2 - R2  F2 - F2  B2 - B2  D2 - D2  U2 - U2
      Rs - Rs  Ls - Ls  Fs - Bs  Bs - Fs  Ds - Ts  Us - Ds
      Ra - Ra' La - La' Fa - Fa' Ba - Ba' Da - Da' Ua - Ua'

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