Rubik's Cube Solution

My preferred algorithms for solving the cube. Basically a 4-Look CFOP plus some bonus material.

See

Rubik's Cube Solution
Table Of Contents

Notation

Sym	Meaning
U	Up
D	Down
L	Left
R	Right
F	Front
B	Back

CW moves viewing the face are listed directly while CCW face rotations are listed with a "'". E.g. R' Be careful about D and D'. Rotating in direction of right thumb if right palm is on the face is CW.

A "s" postfix means moving the face and the far face in the same direction. So Rs means (R L'). A "a" postfix means moving the face and the far face in opposite directions. So Ra means (R L). A lot of algorithms seem to prefer listing the far face as s rather than s'. E.g., Bs rather than Fs'.

Sym	Name	Meaning
M	Middle	Layer between L and R
E	Equator	Layer between U and D
S	Standing	Layer between F and B

Rotating a face twice uses a "2". E.g., R2 (or R2')

A full cube rotation is noted as

Sym	Meaning
x	Rotate about R
y	Rotate about U
z	rotate about F

A lower case face, e.g., "r", means to rotate 2 layers.

Overview

Cross
F2L
OLL Edges
OLL Corners
2-Look PLL
(Bonus) Rotate Center Face

I'm not going to detail Cross and F2L*. Unless specified the face opposite the cross is UP.

In F2L if you see an edge for which the non-top face matches the L or R center then the edge is oriented and can be placed without a cube rotation and using only turns of the L, R, or U face. See https://www.youtube.com/watch?v=za9RvM1bS0k

Sym	Meaning
*	a face color
o	an opposite side face color
X	a don't know/don't care color
1,2,...	face color in given direction

Triggers

Sexy Move: R U R' U'
Sledgehammer: R' F R F'

Sledgehammer finds a lot of use in F2L.

Undo: U R U' R'
HedgeSlammer: F R' F' R

OLL Edges

Line

XXX
***         F (R U R' U') F'
XXX

L

XXX
X**         f (R U R' U') f'
X*X

Dot

XXX
X*X         F (R U R' U') F' f (R U R' U') f'
XXX         Line then L from above.

OLL Corners (w/ probability)

Sune (4/17)

Twist 3 corners CW.

1
X*X2
***         (R U R') U (R U2 R')
**X
  3

A note on what Sune is doing. It pulls out the F/R F2L, moves them CW to L side of U, then (R U2 R') drops it back into place. In doing so the 3 corners get rotated.

Anti-Sune (4/17)

Twist 3 corners CCW.

   3
 **X
 ***        (R' U' R) U' (R' U2 R)
 X*X2
 1

Note how you are doing a Sune on the B/R F2L with a CCW progression.

Pi (2/17)

   3
1X*X
 ***        f (R U R' U') f' F (R U R' U') F'
2X*X        L then Line from solving cross.
   4

Headlights (2/17)

 ***
 ***        R2' D (R' U2 R) D' (R' U2 R')
 X*X
 1 2

Chameleon (2/17)

 1
 X**
 ***        (r U R' U') (r' F R F')
 X**
 2

Bowtie (2/17)

1X**
 ***        F' (r U R' U') (r' F R)
 **X
   2

H (1/17)

 1 2
 X*X
 ***        F (R U R' U')3 F'
 X*X
 3 4

Just Sune

Note that the non-Sune cases can be reduced to a double application of Sune and Anti-Sune. The two open position cubes can be solved with Sune + Anti-Sune while the four open position cubes can be solved with a double Sune application.

        1
***     X**     **X2
***     ***     ***     Solved with Sune + Anti-Sune.
X*X     X**     X**     Basically: Hold onto a CCW corner.
1 2     2       1

   3
1X*X    1X*X3           Solved with Sune + Sune.
 ***     ***            Basically: Hold onto a CW corner.
2X*X    2X*X4
   4

2-Look PLL

If corners are correct skip to 2.

Find "headlights". A pair of the same color. Move these to B face (LL is still U) and run (the x moves U to B)
```
 A-Perm CCW:     x [(R' U R') D2] [(R U' R') D2] R2
```
If no headlights found run A-Perm CCW anyway and then go back to 1.

To solve directly you can run the following
```
 E-Perm:         x' [(R U' R') D (R U R')] D2 [(L' U L) D (L' U' L)]
```
or alternately
```
 Y-PERM:         (F R U') (R' U' R U) (R' F') (R U R' U') (R' F R F')
```
One of the following is now garaunteed to apply.

A-Perm CW

1*2     3*1
*** ==> ***     x [(R' U R') D2] [(R U' R') D2] R2
**3     **2

E-Perm

1*3     2*4
*** ==> ***     x' [(R U' R') D (R U R')] D2 [(L' U L) D (L' U' L)]
2*4     1*3

Three Edge CCW

Peek the F/R corner and ask if F needs to go to R?

***     ***
3*2 ==> 2*1     (R U') (R U) (R U) (R U') (R' U') R2
*1*     *3*

Three Edge CW

***     ***
2*3 ==> 1*2     (L' U) (L' U') (L' U') (L' U) (L U) L
*1*     *3*

Swap Opposite Edges

*2*     *1*
4*3 ==> 3*4     (M2 U M2) U2 (M2 U M2)
*1*     *2*

Swap Adjacent Edges

I prefer

*2*     *1*
1*4 ==> 2*3     (M2 U M2' U') E2 M' E2 M'
*3*     *4*

to the recommended algorithm

*2*     *1*
1*4 ==> 2*3     (M2' U M2') U M' (U2 M2' U2) M' U2
*3*     *4*

Rotate Center Tile

To rotate a center tile place face with tile as L face and run

(M' E' M) U (M' E M) U'

which will rotate L and U centers by 90 degrees CW.

To rotate a single middle center by 180 degrees run

(U R L U2 R' L')2

M Slice Algorithms

I first learned to solve a cube by solving bottom and top layers and then fixing the middle. I still bump into the need for middle algorithms so here are a few.

Inverted Opposite Edges

An oldy but goody. Here 1 and 2 are the color of the face they are attached to.

*1*
***             (M U' M U' M U2) (M' U M' U M' U2)
*2*

Three Edge Cycle

Hard to describe. Two edges have a proper face color and are out of position by a single side. The third comes from the other side of the cube.

I imagine the very odd was is "the rock" and the other pieces are falling onto it. The rock is M/B and other edges are in U.

M U2 M'

Opposite Color H

*o*
***             D2 M2 D2 M2
*o*

END

TanvirOnGH/rubiks-cube.md