## Overview of algorithms for the corners first method, to orient and position the final layer corners

For an explanation of the table below, click here.

code: c1

FR'FR'UR'U'R2F2 (9,11)
F'RU'RU'FUR2F2 (9,11!)

 F F . . B B

code: c2

FU'RU2R'U2R'FRF2 (10,13)
RFRF'U'RU2R'U2R2 (10,13)

 F B . . F B

code: c3

F'RBR'FRB'UR' (9,9)
FR'U'RF'R'UF'R (9,9!)
F'L2F'R2FL2F'R2F2 (9,14*)
R'B'RU2R'BRB'U2B (10,12*)

 F F . . L R

code: c4

R'URU2R2FRF'R (9,11)
FRF'UR2U'RUR2 (9,11!)

 R L . . F F

code: c5

L'U'LUFUF' (7,7)
R'F'RUFUF' (7,7)

 F L . . F R

code: c6

RUR'U'F'U'F (7,7)
B'R'FRBR'F'R (8,8*)
LFL'BLF'L'B' (8,8*)

 R F . . L F

code: c7

RU'FU'FRF2U2R' (9,11)
R'FU'RU'R'U2F2R (9,11!)

 L R . . F F

code: c8

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

 F F . . L R

code: c9

R'UF'RBR'FRB' (9,9)
R'UF'RFU'RUF' (9,9!)
R2F2R'B2RF2R'B2R' (9,14*)
R'U2RF'R'FU2F'RF(10,12*)

 F B . . B F

code: c10

F'U'R'FR2UR'FUF' (10,11)
FURU'R2F'RF'U'F (10,11)
B'UFU'BU2RU'R'F' (10,11*)

 F F . . B B

code: c11

R2D'RU2R'DRU2R (9,12*)
R2U'RUR2UFR2F' (9,12!)

 F R . . L F

code: c12

L2DL'U2LD'L'U2L' (9,12*)
R2UR'F2RF'R'F2R' (9,12!)

 L F . . F R

code: c13

R2U2R'U2R2 (5,9)
R2U2RU2R2 (5,9)

 F B F B . .

code: c14

F2RU2R'L'U2LF2 (8,12)
F2RU2R2F2RF2 (7,12!)
F2R'F2R2U2R'F2 (7,12!)

 F F B B . .

code: c15

R'FRF'U2R2B'R'BR' (10,12*)
R'FRF'U2R2F'U'FR' (10,12!)
FUF'UFUF'LF'L'F (11,11)

 L R F F . .

code: c16

RF2U'R2U'R2UF2R' (9,13)
R'U'F2U'F2UF2U2R (9,13)
LFU2FU2F'U2F2L' (9,13)

 L F R F . .

code: c17

B'UB2U'B2U'B2UB' (9,12)
LUFU'F'UFU'F'L' (10,10*)
FL'U2LU2LF2L'F (9,12*)
BU2B2U'B2U'B2U2B (9,14*)

 F F R L . .

code: c18

F2U'F2RU2R'F2UF2 (9,14)
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*)
FU'FLU2F2LF'U'F (10,12!)
F'UF'L'F2U2L'FUF' (10,12!)

 F F B B . .

code: c20

FR2U2RU2R'U2R'F' (9,13)
F'U2LU2L'U2L'U2F (9,13!)
L'UL'ULU'LF'L2F (10,11!)

 F B B F . .

code: c21

F2URUR'U2F2RU2R' (10,14)
F'U2FL'F2UF'L'F'L (10,12!)
B'U2BU2BL'B2U'BUL (11,14*)
F2U2FU2F'UF'U'L'U'L (11,14)

 R F F L . .

code: c22

F2U'L'U'LU2F2L'U2L (10,14)
FU2F'LU2F'LFUL' (10,12!)
BU2B'U2B'RB2UB'U'R' (11,14*)
F2U2F'U2FU'FURUR' (11,14)

 F L R F . .

code: c23

LU2L'U'LU'L' (7,8*)
RF2R'F'UF'R' (7,8)
RB2L'B'L B'R' (7,8*)

 R F . . L F

code: c24

R2URU2L'UR2U'L (9,12)
R2URU2R'FR2F'R (9,12!)
LF'L2FL'U2LUL2 (9,12!)
F'U'L'ULU'FU'F'U2F (11,12*)

 F R . . F L

code: c25

B'UFU'BUF' (7,7*)
F'RUR'FUF' (7,7!)

 R F . . F L

code: c26

R'URF'R2F'R2F (8,10)
L'BLB'U2B'U2B (8,10*)

 F R . . L F

code: c27

F2RUR2F'R2U'R'F2 (9,13)
F2R'F'R2U'R2FRF2 (9,13)
F2LFL2U'L2F'L'F2 (9,13)
F'LU2L'FLF'U2FL' (10,12*)

 F B . . F B

code: c28

FU2F'U2F'LFL' (8,10*)
FU2F'U2F'RUR' (8,10!)
BR2B'R2B'RUR' (8,10!)

 F B . . B F

code: c29

R'U2RUR'UR (7,8*)
FRF'UFR2F' (7,8!)
BUB'UBU2B' (7,8*)

 F L . . F R

code: c30

L2U'L'U2RU'L2UR' (9,12)
L2U'L'U2LF'L2FL' (9,12!)
R2U'B'R2BU'R2UR' (9,12)
FURU'R'UF'UFU2F' (11,12*)

 L F . . R F

code: c31

BU'F'UB'U'F (7,7*)
FR'F'RF'U'F (7,7)

 F L . . R F

code: c32

LU'L'FL2FL2F' (8,10)
RB'R'BU2BU2B' (8,10*)

 L F . . F R

code: c33

F'U2FU2FR'F'R (8,10*)
F'U2FU2FL'U'L (8,10!)

 F B . . B F

code: c34

F2L'U'L2FL2ULF2 (9,13)
F2R'F'R2UR2FRF2 (9,13)
FR'U2RF'R'FU2F'R (10,12*)

 F B . . F B

code: c35

R2DL'D2RF2R'DR2 (9,13)
B2U'BU2B'U2BU'B2 (9,13!)
L2UL'U2LU2L'UL2 (9,13!)

 . L . F . . . R B

code: c36

RU2R2FRF'RU2R' (9,12*)

 . L . F . . . L F

code: c37

L'ULUFU'F' (7,7)
R'BURUR'B' (7,7!)

 . B . F . . . L F

code: c38

B'R2BUR2URU'R2 (9,12)
RU2RDR'U2RD'R2 (9,12*)
F'U2FUR2URU'R2 (9,12)

 . F . F . . . R B

code: c39

RU2R'U'F2U'F'UF2 (9,12)
F'U2F'D'FU2F'DF2 (9,12*)

 . F . F . . . B L

code: c40

RU'R'U'F'UF (7,7)
BU'B'U'R'UR (7,7)
FR'F'RURU'R' (8,8*)

 . F . B . . . F R

code: c41

F'LF'R2FL'F'R2F2 (9,12*)
F'RU'R2UR'F'R2F2 (9,12)

.

code: c42

R2UF'UFU'R2U'F'U'F (11,13)
F2U'RU'R'UF2URUR' (11,13)
R2DL'BLD'R2U'F'U'F (11,13*)

.

Explanation
Using the algorithms in the table above, you can orient and position all corners of the final layer in one algorithm.

These algorithms may disturb edges in the first two layers.
Algorithms marked with an ! disturb edges in the first and the second layer. Algorithms without a mark disturb edges in the second layer.
Algorithms marked with an * do not disturb edges in the first two layers.
If you want to use algorithms which do not disturb the edges, take a look at the
final layer algorithms.

The table works like this:
First take a look at the orientation of the corners.
• In the situations with code c1 to c6, there are two twisted corners, next to each other, and the corner which needs to be twisted clockwise is on the right.
• In the situations with code c7 to c12, there are two twisted corners, next to each other, and the corner which needs to be twisted clockwise is on the left.
• In the situations with code c13 to c16, there are four twisted corners, and the two corners which need to be twisted clockwise are not next to each other.
Note: Since these situations can be mirrored on the diagonal of the cube, you might need to turn the upper side a half turn to find your situation.
• In the situations with code c17 to c22, there are four twisted corners, and the two corners which need to be twisted clockwise are next to each other.
• In the situations with code c23 to c28, there are three twisted corners, and they need to be twisted counter-clockwise.
• In the situations with code c29 to c34, there are three twisted corners, and they need to be twisted clockwise.
• In the situations with code c35 to c40, there are two twisted corners, and they are not next to each other.
• In the situations with code c41 and 42, there are no two twisted 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 position the corners, using the algorithm LFUF'U'L'.

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

Good luck!