F2L Last Corner + LLCO

These algorithms simultaneously fix the last F2L corner and correct the orientation of the last layer corners without disturbing the orientation of the last layer edges. I started generating these algorithms around US National 2004 in the hope of using the following as an alternative to the Fridrich Method:

 Steps Algorithms Moves on avg. (FTM) Step 1: Cross Intuitive 6 Step 2: F2Lx3 Not considered algs 7x3 = 21 Step 3: F2Le+LLEO Intuitive 5.71 Step 4: F2Lc+LLCO 27+15+? x Step 5: PLL 21 11.21 Total 43.92+x

This method is the same as Ryan Heise's up to Step 3, but by fixing the orientation of the corners, it makes the last step PLL, which Fridrich cubers are already familiar with. For this method to have an average of moves less than that of Fridrich (54.43), Step 4 must be done in less than 10.51 moves on average. The advantage of this method is that it cuts the memorization of the numerous OLL algorithms completely and replaces them with easier algorithms.

At this point, I have only memorized a few cases that I use when those pattern come up during normal Fridrich solves. Since most patterns have quick 2-generator solutions, taking advantage of certain cases results in considerably easier solve.

Thanks to Andy Camann for his help with generating these algorithms (10, 14, 16, 22, 26, and 27), and to Ron van Bruchem for his Cube Solver. Algorithms using R and U only can be found: here.

Corner on Top - Facing Front

 Code Pattern Algorithm 1 L'U2wRU2R'U2wLURF'L'FR'F'LFB'DBU'B'D'BL'D2LU2L'D2L 2 RUR'U'RU'R'URU'R'U2F'U2FU2F'U'FUF'U'FU 3 ULU'RUL'U'R'U'F'U'B'UFU'BR'D'LDRD'L'DDU'B'D'FDBD'F'LEF'U'FDF'UFU'F' 4 URUR'URUR'U2RU'R'R'FRF'URU'R'U'F'UFU'RU'R'U'RU2R'L'E2LURU'R'L'E2LURU'R'UR'U'R'U'R'URURURU'R'U'R'U'R'U'RURUR 5 U2F2UBU'F2UB'U'RU'R'U2RUR'U'RUR'U'RU'R'U'RU'R'U'F'UFU'F2LFL'F 6 U2R'FRF'URU'R'UF'U'F 7 y'R'U'RURURURU'R'U'R'y'RURURU'R'U'R'U'R'U'RRUR'U'F'U'FUR'FRF'UF'U2FU'F'U'FU'F'U'FU2F'UFUF'UFRUR'U'RU'R'U2RU2R' 8 U'RU'R'U2RUR'U'RU'R'RU'RU'L'UR'U'LU'R'U2RUR' 9 RU'RU2R'U'RU'R2LEF'U'FUwL'U2LU2L' 10 (R U2 R2 U R')(U2 R' U' R U')(R U' R) 11 U'RU'R'U2RU'R'R'U2RUwRU'R'U'wUB2L'B'LB' 12 FR'F'R2U'R'U2F2LFL'FUR2UR'URU2R'UR' 13 U'F'U'FU2F'U'FL'E2URU'R'E2LBE2F'U'FUE2B'U2RU'R'U2RU2R'U'RU2R'U2R'FRF'U'RUR'U2F'U'FR'U'RU'DR'U'RD'R'U'R
 Code Pattern Algorithm 14 (R2 U R' U)(R2 U' R2 U R')(U2 R2) 15 F'UFU2R2B'DB'D'B2R2 16 (R U2 R' U2)(R' U' R U' R')(U2 R2 U' R') 17 U'F'UFU'F'U'FUF'U'FRU2R'UR2U2R'U'RU'R2URU'R'UL'B2D'R'DB2L 18 U'RUR'U2RU'R'U2R'U'R'U'R'URURU'RUR'U2RU'R2U'R'U'RURURL'E2LU2RU2R'U2L'E2LF'U'FUBL2DFD'L2B'U2RU2R2U'R'U'RURURU2RU2R'U2R'U'R'U'R'URUR 19 F'U2FUR2B'DB'D'B2R2 20 U'RU'R'U'RU'R'URU2R'RUR'URU'R'URU'R'U'R'U'R'U'R'URUR 21 URUR'URUR'U'RU2R' 22 (R2 U2)(R U' R' U)(R2 U')(R U' R' U R') 23 U'RUR'U'RU2R2U'R'U'R'URURU'RUR'U'RU2R'U2R'U'R'U'RURUR 24 U'RU'R'U'RU'R'URU'R'URU2R' 25 U2RU'R'U2RU2R'U2RU'R'U'F'U'FU2F'U2FU'F'U2F 26 (R U' R' U)(R' U' R U' R')(U2 R2 U' R') 27 (U2 R U R')(U2 R' U' R U' R')(U2 R2 U R')

Corner on Top - Facing Up

 Code Pattern Algorithm 28 [R'FRF']x3 29 29m 30 30m 31 31m 32 32m 33 33m 34 34m
 Code Pattern Algorithm 35 35m 36 37 37m 38 39 39m 40 40m 41 41m 42 42m