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'U2wL
URF'L'FR'F'LF
B'DBU'B'D'B
L'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'B
R'D'LDRD'L'D
DU'B'D'FDBD'F'
LEF'U'FDF'UFU'F' |
| 4 |
 |
URUR'URUR'U2RU'R'
R'FRF'URU'R'U'F'UF
U'RU'R'U'RU2R'
L'E2LURU'R'L'E2L
URU'R'UR'U'R'U'R'URUR
URU'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'R
RUR'U'F'U'FUR'FRF'
UF'U2FU'F'U'F
U'F'U'FU2F'UFUF'UF
RUR'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'R2
LEF'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'F
UR2UR'URU2R'UR' |
| 13 |
 |
U'F'U'FU2F'U'F
L'E2URU'R'E2L
BE2F'U'FUE2B'
U2RU'R'U2RU2R'U'RU2R'
U2R'FRF'U'RUR'U2F'U'F
R'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'F
RU2R'UR2U2R'U'RU'R2
URU'R'UL'B2D'R'DB2L |
| 18 |
 |
U'RUR'U2RU'R'U2R'U'R'U'R'URUR
U'RUR'U2RU'R2U'R'U'RURUR
L'E2LU2RU2R'U2L'E2L
F'U'FUBL2DFD'L2B'
U2RU2R2U'R'U'RURUR
U2RU2R'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'URUR
U'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 |
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| 29m |
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| 30 |
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| 30m |
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| 31 |
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| 31m |
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| 32 |
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| 32m |
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| 33 |
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| 33m |
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| 34 |
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| 34m |
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| Code | Pattern | Algorithm |
| 35 |
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| 35m |
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| 36 |
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| 37 |
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| 37m |
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| 38 |
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| 39 |
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| 39m |
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| 40 |
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| 40m |
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| 41 |
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| 41m |
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| 42 |
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| 42m |
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