Overview of all algorithms for the final layer,
to orient and permute corners

For an explanation of the table below, click here.


code: c1

FR'FR2U'R'U'RUR'F2 (11,13)
RU2R2F2D'F'DF'R2U2R' (11,16)
F F
. .
B B

code: c2

F2R2FU'L'ULF'R2F2 (10,14)
B2L2BR'U'RUB'L2B2 (10,14)
F B
. .
F B

code: c3

F'L2F'R2FL2F'R2F2 (9,14)
F F
. .
L R

code: c4

R'URU2R'L'URU'L (10,11)
FRF'LFR2FRF2L' (10,12)
R L
. .
F F

code: c5

FUF'U'F'LFL' (8,8)
R'F'RB'R'FRB (8,8)
F L
. .
F R

code: c6

LFL'BLF'L'B' (8,8)
R F
. .
L F

code: c7

L2FU'F'UFUF2L'FL' (11,13)
LU2L2BD'BDB2L2U2L' (11,16)
L R
. .
F F

code: c8

LFUF'U'L' (6,6)
RUBU'B'R' (6,6)
F F
. .
L R

code: c9

R2F2R'B2RF2R'B2R' (9,14)
F B
. .
B F

code: c10

B'UFU'BU2RU'R'F' (10,11)
F F
. .
B B

code: c11

R2D'RU2R'DRU2R (9,12)
F R
. .
L F

code: c12

L2DL'U2LD'L'U2L' (9,12)
L F
. .
F R

code: c13

RU2R'U'RUR'U'RU'R' (11,12)
L'FURU'F'L2FR'F'L' (11,12)
F B
F B
. .

code: c14

B'UR2D'RU2R'DR2U'B (11,14)
F F
B B
. .

code: c15

R'FRF'U2R2B'R'BR' (10,12)
L R
F F
. .

code: c16

F'U'LF'L'F2UFR'F'R (11,12)
L F
R F
. .

code: c17

BU2B2U'B2U'B2U2B (9,14)
LUFU'F'UFU'F'L' (10,10)
F F
R L
. .

code: c18

F'U'FU'F'UL'ULF (10,10)
FUF'UFU'RU'R'F' (10,10)
R L
F F
. .

code: c19

B'RB'R'B2U2L'BLB' (10,12)
F F
B B
. .

code: c20

R'FRF'U'F2LFL'UF (11,12)
F B
B F
. .

code: c21

B'U2BU2BL'B2U'BUL (11,14)
R F
F L
. .

code: c22

BU2B'U2B'RB2UB'U'R' (11,14)
F L
R F
. .

code: c23

LU2L'U'LU'L' (7,8)
RB2L'B'L B'R' (7,8)
R F
. .
L F

code: c24

F'U'L'ULU'FU'F'U2F (11,12)
BU2B'RB'R'BU'BU'B' (11,12)
F R
. .
F L

code: c25

B'UFU'BUF' (7,7)
R F
. .
F L

code: c26

L'BLB'U2B'U2B (8,10)
F R
. .
L F

code: c27

F'LU2L'FLF'U2FL' (10,12)
F B
. .
F B

code: c28

FU2F'U2F'LFL' (8,10)
B F
. .
F B

code: c29

BUB'UBU2B' (7,8)
L'B2RBR'BL (7,8)
F L
. .
F R

code: c30

FURU'R'UF'UFU2F' (11,12)
FUF'UF'LFL'FU2F' (11,12)
L F
. .
R F

code: c31

BU'F'UB'U'F (7,7)
F L
. .
R F

code: c32

RB'R'BU2BU2B' (8,10)
L F
. .
F R

code: c33

F'U2FU2FR'F'R (8,10)
F B
. .
B F

code: c34

FR'U2RF'R'FU2F'R (10,12)
F B
. .
F B

code: c35

LB'D2BL'U2LB'D2BL' (11,14)
. L .
F . .
. R B

code: c36

RU2R2FRF'RU2R' (9,12)
. L .
F . .
. L F

code: c37

BLFL'B'LF'L' (8,8)
. B .
F . .
. L F

code: c38

RU2RDR'U2RD'R2 (9,12)
. F .
F . .
. R B

code: c39

F'U2F'D'FU2F'DF2 (9,12)
. F .
F . .
. B L

code: c40

FR'F'RURU'R' (8,8)
L'B'R'BLB'RB (8,8)
. F .
B . .
. F R

code: c41

F'LF'R2FL'F'R2F2 (9,12)

 .

code: c42

R2DL'BLD'R2U'F'U'F (11,13)

 .


Explanation
Using the algorithms in the table above, you can orient and permute all corners of the final layer in one algorithm.
The table works like this:
First take a look at the orientation of the corners.

Next take a look at the position of the corners.
You can turn the top layer around to find out which corners have to change positions, according to the images.
But there is a better system, so that you do not need to turn the top layer, and can immediately see, which situation the cube is in.
It works like this:

At the right of the cells with the images you see four letters in a certain order. These letters correspond with the following cubies:

For the situations with code c13 to c22.

For the situations with code c1 to c12, and c23 to c34.

For the situations with code c35 to c40.


If two of the designated cubies have the same color, their color becomes the front color (F). If there are two pairs of the same color, then the color of the upper left back is the front color.
Now you know which are the other colors of the cubies, they can be L(eft), R(ight) or B(ack).

Example
Consider the following situation:

The corner at the upper left back needs to be twisted clockwise, and the corner at the upper right back needs to be twisted counter-clockwise.
This corresponds with the situations c7 to c12.
According to the three images above we need to take a look at the color of the cubies at the upper back (blue and blue) and front upper (orange and red).
Since there are two blue cubies, blue becomes the front color. So only situations c8 and c10 remain possible.
Since the other two cubies have different colors, the cube is in situation c8.
Thus we can orient and permute the corners, using the algorithm LFUF'U'L'.

Believe me: after some practice, you can immediately see which algorithm to use.

Good luck!