05/17/2004 Sequences to place LF edge to UR position and to orient UFL corner and orient FU, FR, and FD edges

created by Josef Jelinek (gloom@email.cz) using ACube 3.1 beta solver by Josef Jelinek and AnimCube applet by Josef Jelinek

sequences generated on request from Duncan Dicks for his new method (currently in progress).



























The inputs and outputs of the ACube follows (the cube is oriented in a different way - the F face is facing up, the L and R faces are in their positions, all other faces are oriented accordingly to the U face)

  ~U  ?  ?  ? RB !  !  !  !  !  !  @? !  @?  @?   ?  @?  !   !   !   !
  B R U B' U' B R' B' (8q, 8f*, 8s)
  B R U R' B' R U' R' (8q, 8f*, 8s)
  R' B U B' U' B' R B (8q, 8f*, 8s)

  ~U -?  ?  ? RB !  !  !  !  !  !  @? !  @?  @?   ?  @?  !   !   !   !
  R' U' R U B U B' (7q, 7f*, 7s)

  ~U  ? -?  ? RB !  !  !  !  !  !  @? !  @?  @?   ?  @?  !   !   !   !
  R' U R B' R B R' (7q, 7f*, 7s)

  ~U -? -?  ? RB !  !  !  !  !  !  @? !  @?  @?   ?  @?  !   !   !   !
  U2 L' B2 U' B U B2 L (11q, 8f*, 8s)

  ~U  ?  ? -? RB !  !  !  !  !  !  @? !  @?  @?   ?  @?  !   !   !   !
  R' U R U B U' B' (7q, 7f*, 7s)

  ~U -?  ? -? RB !  !  !  !  !  !  @? !  @?  @?   ?  @?  !   !   !   !
  U L' B2 U' B' U B2 L (10q, 8f*, 8s)

  ~U  ? -? -? RB !  !  !  !  !  !  @? !  @?  @?   ?  @?  !   !   !   !
  L' U' L' D' B D L U L (9q, 9f*, 9s)
  L' D' R D B D' R' D L (9q, 9f*, 9s)
  L' B R B R' U' B' U L (9q, 9f*, 9s)
  L' B' U' L' B L B U L (9q, 9f*, 9s)

  ~U -? -? -? RB !  !  !  !  !  !  @? !  @?  @?   ?  @?  !   !   !   !
  R' U' L R' D' F D L' R2 (10q, 9f*, 9s)
  R' U' R' D' L F L' D R2 (10q, 9f*, 9s)
  R' U' M' F' U F L' R2 (10q, 9f*, 8s)

  ~U  ?  ?  ? RB !  !  !  !  !  !  @? !  @?  @?  +?  @?  !   !   !   !
  F' L2 D' B D L2 F (9q, 7f*, 7s)

  ~U -?  ?  ? RB !  !  !  !  !  !  @? !  @?  @?  +?  @?  !   !   !   !
  U L' D' B' D L B' U B (9q, 9f*, 9s)
  L R' U' R U L' B U B' (9q, 9f*, 9s)
  M' B' R B L' D B D' (9q, 9f*, 8s)

  ~U  ? -?  ? RB !  !  !  !  !  !  @? !  @?  @?  +?  @?  !   !   !   !
  B' R B R' B U B' (7q, 7f*, 7s)

  ~U -? -?  ? RB !  !  !  !  !  !  @? !  @?  @?  +?  @?  !   !   !   !
  U' B' U2 L' B2 L U2 B (11q, 8f*, 8s)

  ~U  ?  ? -? RB !  !  !  !  !  !  @? !  @?  @?  +?  @?  !   !   !   !
  B L R U' L' U R' B' (8q, 8f*, 8s)

  ~U -?  ? -? RB !  !  !  !  !  !  @? !  @?  @?  +?  @?  !   !   !   !
  B' R' U L' R B2 L U B (10q, 9f*, 9s)
  B' R' U M U2 L F U (10q, 9f*, 8s)

  ~U  ? -? -? RB !  !  !  !  !  !  @? !  @?  @?  +?  @?  !   !   !   !
  U' B U2 L U2 L' U2 B' (11q, 8f*, 8s)

  ~U -? -? -? RB !  !  !  !  !  !  @? !  @?  @?  +?  @?  !   !   !   !
  R' U' R U B U2 L U' L' B' (11q, 10f*, 10s)

  ~U  ?  ?  ? RB !  !  !  !  !  !  @? !  @?  @?  -?  @?  !   !   !   !
  U' F D R2 D' F2 U F (10q, 8f*, 8s)
  F U F' L2 D' B' D L2 (10q, 8f*, 8s)
  F' D2 B U B' U' D2 F (10q, 8f*, 8s)

  ~U -?  ?  ? RB !  !  !  !  !  !  @? !  @?  @?  -?  @?  !   !   !   !
  R' U' F' L' U L F U R (9q, 9f*, 9s)

  ~U  ? -?  ? RB !  !  !  !  !  !  @? !  @?  @?  -?  @?  !   !   !   !
  L2 D' B R B' R' D L2 (10q, 8f*, 8s)
  R2 U' F R F' R' U R2 (10q, 8f*, 8s)

  ~U -? -?  ? RB !  !  !  !  !  !  @? !  @?  @?  -?  @?  !   !   !   !
  U L' F' D' B' L' D F U L2 (11q, 10f*, 10s)
  U L' B' U B L' D' B' D L2 (11q, 10f*, 10s)
  U2 L' U' B U R B' R' B' L (11q, 10f*, 10s)
  U2 L' U' B' L' B' L U B L (11q, 10f*, 10s)

  ~U  ?  ? -? RB !  !  !  !  !  !  @? !  @?  @?  -?  @?  !   !   !   !
  B U2 L U L' U2 B' (9q, 7f*, 7s)
  R' U R U2 B U2 B' (9q, 7f*, 7s)

  ~U -?  ? -? RB !  !  !  !  !  !  @? !  @?  @?  -?  @?  !   !   !   !
  U L' D' B' D L2 F U F' L' (11q, 10f*, 10s)

  ~U  ? -? -? RB !  !  !  !  !  !  @? !  @?  @?  -?  @?  !   !   !   !
  B U2 R B L' B' L R' U' B' (11q, 10f*, 10s)
  B U2 R B L' B' M' B' D' (11q, 10f*, 9s)
  L' U' L' D' B L U L' D L2 (11q, 10f*, 10s)

  ~U -? -? -? RB !  !  !  !  !  !  @? !  @?  @?  -?  @?  !   !   !   !
  R' U F' U' F U R U' B U B' (11q, 11f*, 11s)


03/01/2004 Sequences to place LF edge to UR position and to orient UFL corner and orient and move FR and FU edges to FL and FU positions

created by Josef Jelinek (gloom@email.cz) using ACube 3.0 beta solver by Josef Jelinek and AnimCube applet by Josef Jelinek

sequences generated on request from Duncan Dicks for his new method (currently in progress).


The last layer is the front one. The last edge of the first two layers is at left-front and should go to the up-right position. The corner at up-front-left is to be oriented as well as edges at front-up and front-right. These edges are to be moved next to the up-front-left corner (the front-up and front-left positions).

The following sequences are optimal in face-turn metric and sequences in one row are different variants for the same situation. The color of the last face is white. Flipped edges (at FU and FR) can recognized by their white facelets facing away from the white front face. Corner orientation (UFL) is similar. You can ignore all other cubies of the last layer (FD, UFR, DFR, DFL)


oriented UFL corner




clock-wise twisted UFL corner




counter clock-wise twisted UFL corner




Improvement summary

The lines marked '#' are taken from the original mail, other lines are my results.

#    UFL           UF        RF
#  1 Untwisted     Unflipped Unflipped
#   R'F'RFUFU' (7,7)
    R'F'RFUFU' (7,7) ... no change

#  2 Untwisted     Unflipped Flipped
#   R'FRU'RUR' (7,7)
    R'FRU'RUR' (7,7) ... no change

#  3 Untwisted     Flipped   Unflipped
#   L'UB'R'URBLU' (9,9)
    L2B'UBULU'F'L (9,10) ... worse in quarter-turn metric
    if I optimized for quarter turns it would be the same
    (note: my sequence keeps UFL corner in place)

#  4 Untwisted     Flipped   Flipped
#   L'URUR'F'U'FL (9,9)
    L'URUR'F'U'FL (9,9) ... no change
    L'U'F'L'ULUFL (9,9) ... alternative

#  5 Clockwise     Unflipped Unflipped
#   D'L2B'UBL2D (7,9)
    D'L2B'UBL2D (7,9) ... no change

#  6 Clockwise     Unflipped Flipped
#   L2B'UBL2DF'D' (8,10)
   It seems to be "Clockwise Unflipped Unflipped" instead!
   My version for "Clockwise Unflipped Flipped":
    FD'F'L'FL'B'UBL2D (11,12) ... solution!
    FD'LB'U'BULU'L2D (11,12) ... #2
    FU'FL'U'LUFU'F2U (11,12) ... #3

#  7 Clockwise     Flipped   Unflipped
#   No solution yet
    F2U'RUR2D'L'FLDR (11,13) ... solution :)
    UF2LFL'F'U'FUF2U' (11,13) ... #2
    R'FRF2UF'U'FUF2U' (11,13) ... #3

#  8 Clockwise     Flipped   Flipped
#   No solution yet
    UFU2L2R'F'RFL2U (9,12) ... solution :)
    UL2DR'DRD2L2FU' (9,12) ... alternative

#  9 AntiClockwise Unflipped Unflipped
#   R2FL'F2RF'LR'FL'F2RF'LFR (16,19) !!! too long!
    FL'B'U'BLF'U'F2U (10,11) ... big improvement

# 10 AntiClockwise Unflipped Flipped
#   No solution yet
    F'DR2FR2F'U'R'UR'D' (11,13) ... solution :)
    D'F'DR2FR2F'U'R'UR' (11,13) ... alternative

# 11 AntiClockwise Flipped   Unflipped
#   FRFR'DBR'B'D' (9,9)
    FRFR'DBR'B'D' (9,9) ... no change

# 12 AntiClockwise Flipped   Flipped
#   R'F'RUF'U'F2R'FRF'UFU' (14,15) also too long
    UF2RUL'U'LR'F'U' (10,11) ... big improvement
    RU'R'UR2D'F'DFR2 (10,12) ... alternative

To be complete, all obtained sequences are also included. The cube is oriented in a different way. To be compatible with the previous sequences translate U to F, D to B, F to D, and B to U. 'U'-turns at the end of some seuences can be removed, and thus one turn can be saved in these cases. The different optimal lengths for one case are not an error (contact me if you want an explanation).

   R' U' R U B U B' (7q, 7f*, 7s)
   U' R' B' R' F R F' B R (9q, 9f*, 9s)
   U' R' B' R' F R S D (9q, 9f*, 8s)

   R' U R B' R B R' U' (8q, 8f*, 8s)
   L U L' B' U L' B2 L U B (11q, 10f*, 10s)

   U2 R2 F R U F' U F U2 F' R (14q, 11f*, 11s)
   F' L2 D' B L' D L' F2 U' F' U' (13q, 11f*, 11s)
   F' L2 D' B L' D2 F' D' F2 L' U2 (15q, 11f*, 11s)
   F' L2 D' B2 D' B' D2 L' F L' U2 (15q, 11f*, 11s)
   L' U2 L U B L' B U L U' B2 (13q, 11f*, 11s)
   L2 D' B D B L B' U' L (10q, 9f*, 9s)

   U B2 U2 B' U B L' D' B D L B (14q, 12f*, 12s)
   U L F R2 F R2 F2 L' B' R B R' (15q, 12f*, 12s)
   U L F' L' B2 L2 F L2 B R B R' (15q, 12f*, 12s)
   U' B' U' R' U2 R U' L' B2 L U B (14q, 12f*, 12s)
   U' L D2 F' U2 R2 F2 R2 U2 F D2 L' (19q, 12f*, 12s)
   U' L D2 F' D2 L2 B2 L2 D2 F D2 L' (19q, 12f*, 12s)
   U' L D2 B' L2 U2 B2 U2 L2 B D2 L' (19q, 12f*, 12s)
   U' L D2 B' R2 D2 F2 D2 R2 B D2 L' (19q, 12f*, 12s)
   U' L' B' L R' U2 R F' L2 B' L2 F (15q, 12f*, 12s)
   U' L' B' L R' U2 R B' U2 B' U2 B (15q, 12f*, 12s)
   U' L' B' M' B2 R U' L2 D' L2 U (15q, 12f*, 11s)
   U' L' B' M' B2 R D' B2 D' B2 D (15q, 12f*, 11s)
   B' U' B2 L U F U2 F' U' L2 B' L (15q, 12f*, 12s)
   L' B R B R' U' B' U L (9q, 9f*, 9s)
   L' B' U' L' B L B U L (9q, 9f*, 9s)

   F' L2 D' B D L2 F U2 (11q, 8f*, 8s)
   U B R B' U B U' R' B' U2 (11q, 10f*, 10s)
   U2 F D B U' B' U D' F' U (11q, 10f*, 10s)
   U2 F D B U' B' E R' U (11q, 10f*, 9s)
   U' L U' D2 B U' B' U2 D2 L' (13q, 10f*, 10s)
   U' L U' D2 B U' B' E2 R' (13q, 10f*, 9s)

   U' B R U' B2 U' B2 U B2 R' B' U2 (16q, 12f*, 12s)
   U' B R D' R2 U' R2 D B2 R' B' U2 (16q, 12f*, 12s)
   B2 L2 B R B' L2 B2 R' B U B' U' (16q, 12f*, 12s)
   L U F U' L D2 R B R2 B' D2 L2 (16q, 12f*, 12s)
   L R2 F' L F D' F' D' R' D2 L2 R' (15q, 12f*, 12s)
   L2 D' B D L2 F2 R' F' R U' F' U2 (16q, 12f*, 12s)
   L2 D' R B R' B' R B R' B' D L2 (14q, 12f*, 12s)
   R2 U' F U2 F2 U' F2 U' R F' R U (16q, 12f*, 12s)
   R2 U' R F R' F' R F R' F' U R2 (14q, 12f*, 12s)
   R' U R U2 R2 F' L F' L' F2 R2 U (16q, 12f*, 12s)
   R' U2 F' U F L' U2 L F2 R' F2 R2 (17q, 12f*, 12s)
   U F' U' L' U L' D' B D L2 F U2 (14q, 12f*, 12s)
   U F' L D' B' D B L B' L2 F U2 (14q, 12f*, 12s)
   U B' U L' B' L B U B' U2 B U2 (14q, 12f*, 12s)
   B R B2 D' R2 F' U F R2 D R' B' (15q, 12f*, 12s)
   L F2 R F2 L' U F U R2 U' F' U2 (16q, 12f*, 12s)
   R U2 R U2 R' U F U R2 U' F' U2 (16q, 12f*, 12s)

   U2 B' R B R2 F' L' U L F R (13q, 11f*, 11s)
   U' L U L' U L' D' B D L2 U2 L' (14q, 12f*, 12s)
   B U2 L U L' U' B' U B U2 B' U' (14q, 12f*, 12s)
   R' U R U2 B U' B' U B U2 B' U' (14q, 12f*, 12s)

   U F2 D2 L B L' D2 F' R' F' U2 (15q, 11f*, 11s)
   B U B2 L2 R' U' R U L2 B U' (14q, 11f*, 11s)
   B L2 F R' F R F2 L2 U B' U (14q, 11f*, 11s)

   U L' D' B' D L U' B' U2 B (11q, 10f*, 10s)
   U' L2 F' D' L2 B2 L2 D F L2 (15q, 10f*, 10s)
   U' L D2 R2 F R F' R D2 L' (13q, 10f*, 10s)

   L' U' B' U L' D2 F' R F D2 L2 (14q, 11f*, 11s)
   U' F R2 U R2 U' B' R' B R' F' (13q, 11f*, 11s)
   F' U' F R2 U R2 U' B' R' B R' (13q, 11f*, 11s)
   L2 D F' R' F D2 L B2 L' D L2 (15q, 11f*, 11s)

   U L' D' B' D L2 F U F' L' U (12q, 11f*, 11s)
   U R U R' F D R' D' F' U (10q, 10f*, 10s)
   R' F2 D' B L' B' D F2 U R (12q, 10f*, 10s)

   U' L2 B' L U2 B2 U2 L' B L2 (15q, 10f*, 10s)
   B U2 R B L' B' L R' U' B' U (12q, 11f*, 11s)
   B U2 R B L' B' M' B' D' B (12q, 11f*, 10s)
   R B' R' B R2 F' U' F U R2 U2 (14q, 11f*, 11s)

To get other optimal sequences for specific situations, send me an e-mail.