## Ross Palmer's System For Permuting the Last Layer

 The first algorithm (the algorithm in bold) is the algorithm that I would currently/most likely use to solve that case. Any additional algorithms are ones that I also use, and have found to be very fast as well. The last algorithm in each box is the standard algorithm in standard notation, WITHOUT cube rotations. This is to help set up, and to help people find their own rotations that may be more beneficial than mine. Each box contains an algorithm including the cube rotations that I would make if I were performing the algorithm. The cube rotations are fairly intuitive, and they are marked by LOWERCASE letters within brackets (such as [u]). To make it easy to learn the rotations, all you have to do when you see a lowercase letter in brackets, is turn the ENTIRE cube as if you were turning just that face. The following table relates the bracketed lowercase letters, (using only "u","r", and "f") to the cube rotations that are necessary.
 Rotations of the Cube Move Look at this face: And turn the cube: [r] R Clockwise [r'] R Counter-clockwise [r²] R 1/2 turn [u] U Clockwise [u'] U Counter-clockwise [u²] U 1/2 turn [f] F Clockwise [f'] F Counter-clockwise [f²] F 1/2 turn

 In front of each algorithm, the number contained within the brackets [] is how many moves are in the following algorithm. In the upper right corner of each box, there are two things: a code, which can be used for reference only, and a time. The time is the AVERAGE amount of time that it takes me to perform the move listed below when going top speed. In almost all cases, these moves CAN be performed faster, but the number is merely an average so you can compare your progress/abilities to mine, and so you can know what is possible for each algorithm. The algorithms are also divided into finger shortcuts, and each shortcut is a few moves that are contained within the parenthesis. If a cube rotation and a regular move are located within the parenthesis, this means that you should rotate the cube WHILE you perform the regular face turn. To show how the half turns are performed, I extended that part of the notation slightly. R²' means turn the R face 180 degrees as a COUNTER-CLOCKWISE turn, R² means turn the R face 180 degrees as a CLOCKWISE turn. Any lowercase letters by themselves represent turning 2 layers. This means that u by itself is the equivalent of turning the top 2 layers in a clockwise fashion, as if turning the u face. Any time you see a lower case letter, turn that face and the one behind it in the same direction. Hopefully, this will make sense.

 code: P1Time(sec): 1.91 [9] [r] ((R'UR')D²) (RU'R') [f'] (R²U²')R'FR'B²RF'R'B²R² code: P2Time(sec): 1.85 [9] [r] (R²D²') ((RUR')D²) (RU'R)R²B²RFR'B²RF'R code: P3Time(sec): 2.94 [9] [r'] (RU'R'D) (RUR') (D²) [f] (U'RU) (LU') (R'U)RB'R'FRBR'F²L'BLFL'B'L code: P4Time(sec): 2.24 [13] [r'] (RU'R'U) (DR'DU') (R'UR) [f'] (rR²'U)RB'R'BFR'B'FR'BRF2U code: P5Time(sec): 2.81 [10] L'(R'U²) (RL) [u'] L(RU²') (R'L')[11] (R²'M²') (R²U') (R²M²) (R²'U²) (R²'M²') (R²U') ((R²M²)(R²'))L'R'U2LRFBU2F'B' code: P6Time(sec): 1.66 [7] (R²U') S' (U²S) (U'R²)[9] (R²U') [u'] (r'L') (RU²') (L[r]) ((R')(U'[u]R²))R²US'R²SUR² Right click here to download a video of this algorithm to your harddisk. code: P7Time(sec): 1.75 [7] (R²'U) S' (U²S) (UR²')[9] (R²'U) [u'] ([r']L')(RU²') (L[r]) (R'U) [u] (R²)R²U'S'R²SU'R² code: P8Time(sec): 2.49 [10] [r'] U² (R'F'R) (D²'E²') [r] ((R'UR')(U'R²)[10] [r'] U² (R'F'R) U²' [r'] (L'UL') (U'L²)B2R'U'RB2L'DL'D'L2 code: P9Time(sec): 2.89 [10] B² (LUL') [r'] U² [r'] (RU'R) (UR²')B2LUL'B2RD'RDR2 code: P10Time(sec): 2.47 [15] F (RU'R'U) (RUR²') (F'RU) (RU'R')FRU'R'URUR²F'RURU'R' code: P11Time(sec): 2.51 [14] ((R'U²)(RU')) [u'] (R'FRB') (R'F'RU') [u] (RU')R'U2RU'F'LFR'F'L'FU'RU' code: P12Time(sec): 2.72 [14] [f] (U(R²U'R)) [f'][u'][r'] (RU'R'D)(RUR'F) [f'] (R'F)[14] [u²] ((RU²)(R'U)) [u] (RB') (R'F) (RBR') [f][r] (RU'R)LU2L'UFR'F'LFRF'UL'U code: P13Time(sec): 2.86 [15] ((R'U)(RU'R²)) [u'] (R'U'RU) [u][r] (RUR'U'R²B')[14] [u'] ((R²FR')(D²)) [r'] ((LU'L')(B²)) (R'U'R') [f'] (R'UL)R'URU'R2F'U'FURFR'F'R2U' code: P14Time(sec): 2.47 [12] ((RUR')[u']) (R²u') (RU') (R'UR') (uR²)RUR'F²D'LU'L'ULDF² code: P15Time(sec): 2.41 [12] (R²u') ((RU'R)(UR')) (uR²') [u] (RU'R')L²D'BU'BUB'DL²FU'F' code: P16Time(sec): 2.56 [12] (R'U'R) [u] (R²'u) (R'URU'R) (u'R²)R'U'RB²DL'ULU'LD'B² code: P17Time(sec): 2.31 [12] (R²'u) (R'UR'U'R) (u'R²) [u'] (R'UR)R²DB'UB'U'BD'R²F'UF code: P18Time(sec): 2.50 [14] (R'UR'U') [u] (R'F'R²U') ((R'UR')F)) (RF)[14] (R'UR'U') [u][f'] (U'RU')(R'U²) [f][r] ((U'R'U)(RU)R'UR'U'B'DB'D'B²RB'RBR code: P19Time(sec): 2.80 [15] [f] (UR'D)(R²U'[r']RB') [r] (UR'D)(R²U'r'R) [f'] (R'U)LU'RU2L'UR'LU'RU2L'UR'U code: P20Time(sec): 2.8 [15] [f] (U'R[r']B')(R²'[r]UR'D) (U'R[r']B')(R²[r]R') [f'] (RU')R'UL'U2RU'LR'UL'U2RU'LU' code: P21Time(sec): 2.78 [13] F (RU') (R'F) (DR') [u][r] (R'U'R) [f] (R²'F'U²)[13] [r'][f'] (U'R'FRU') ([f']B) (URU'R'U²) (([f']B')(U²))FRU'R'FDR'B'R'BR2D'F2