This guide is NOT about speed. It's about understanding and building your own formulas from scratch.
There are many methods to solve the cube: Layer-by-Layer, CFOP (Cross, F2L, OLL, PLL), Corners First, Edges First, Columns First, 8355, and many more.
While these methods can solve the cube, they require learning many formulas. Unfortunately, most of these formulas are not intuitive or easy to understand.
For example, consider the popular CFOP method. The Cross and F2L (First Two Layers) are often intuitive, and many people can solve the first two layers without memorizing algorithms.
However, the OLL (Orientation of the Last Layer) and PLL (Permutation of the Last Layer) formulas are difficult to grasp. I often forget them after just a few months.
I searched for a long time and eventually found a different method (though I lost the original bookmark). I forgot some of its specific formulas, but I remembered the core concept and was able to rebuild them.
X (Slice): L M R (Left, Middle, Right layers)
Y (Slice): U E D (Up, Equator, Down layers)
Z (Slice): F S B (Front, Standing, Back layers)
Core Method Concept:
The method is based on a simple 4-step sequence:
Step 1 (Setup): Make a change on one side of the cube (e.g., swap two edges on the U face with the sequence S M D' M' D2 S').
Step 2 (Target Adjustment): Turn the side you are working on (e.g., U).
Step 3 (Reverse Setup): Reverse the change from Step 1 (e.g., S D2 M D M' S').
Step 4 (Reverse Adjustment): Reverse the turn from Step 2 (e.g., U').
|
vs |
|
| S M D' M' D2 S' | S D2 M D M' S' | |
| Demo | Demo |
Why This Works:
Any sequence of moves can be undone by its exact reverse (e.g., the reverse of S M D' M' D2 S' is S D2 M D M' S'; the reverse of L R U D F B is B' F' D' U' R' L').
By inserting a turn of one side (Step 2) between the setup and its reverse, the effects of the setup are applied to different pieces on that specific side.
Think of it this way: if Step 1 swaps two corners, then after turning that side (Step 2), Step 3 will swap two different corners. This creates a useful algorithm that only affects the side you turned.
Building and Finding Formulas:
First, working on the same side (U): Use other sides as a "working area" to manipulate pieces.
Swap two edges on side U:
Concept: Disconnect, then reconnect.
Sequence: S M D' M' D2 S'
Explanation:
S disconnects the S layer from U.
M disconnects the M layer from U
D' disconnects an edge (white X) from the S layer and connects it to the M layer.
M' reconnects the M layer to U
D2 connects another edge (black X) to the S layer.
S' reconnects the S layer to U
Demo (S M D' M' D2 S') U (S D2 M D M' S') U'
Demo (S M D' M' D2 S') U' (S D2 M D M' S') U
Demo (S M D' M' D2 S') U2 (S D2 M D M' S') U2
Swap two corners on side U:
Sequence: F D F' L D2 L' F D' F'
Explanation:
F disconnects the F layer from U
D disconnect corner(black X)
F disconnects the F layer from U
D disconnect corner(black X)
F' reconnects the F layer to U
L disconnects the L layer from U
D2 swap corner (white X/black X) on layer D
L' reconnects the L layer to U
F disconnect the F layer from U
D' reconnects corner (black X)
F' reconnects the F Layer to U
Demo F D F' L D2 L' F D' F'
Demo (F D F' L D2 L' F D' F') U (F D F' L D2 L' F D' F') U'
Demo (F D F' L D2 L' F D' F') U' (F D F' L D2 L' F D' F') U
Demo (F D F' L D2 L' F D' F') U2 (F D F' L D2 L' F D' F') U2
Using two formulas together (swap edges & corners):
Demo (S M D' M' D2 S') (F D F' L D2 L' F D' F') U (F D F' L D2 L' F D' F') (S D2 M D M' S') U'
Demo F D F' L D2 L' F D' F'
Demo (F D F' L D2 L' F D' F') U (F D F' L D2 L' F D' F') U'
Demo (F D F' L D2 L' F D' F') U' (F D F' L D2 L' F D' F') U
Demo (F D F' L D2 L' F D' F') U2 (F D F' L D2 L' F D' F') U2
Using two formulas together (swap edges & corners):
Demo (S M D' M' D2 S') (F D F' L D2 L' F D' F') U (F D F' L D2 L' F D' F') (S D2 M D M' S') U'
Adjusting the edge formula to swap a different set of edges:
Demo (S M' D M D2 S') (F D F' L D2 L' F D' F') U (F D F' L D2 L' F D' F') (S D2 M' D' M S') U'
(just for fun)
Swap two opposite corners on side U:
Demo (S M' D M D2 S') (F D F' L D2 L' F D' F') U (F D F' L D2 L' F D' F') (S D2 M' D' M S') U'
(just for fun)
Using D2 / E2 for 180-degree turns:
A half-turn of a middle layer (D2 or E2) can be very useful for swapping pieces.
Concept: L R moves two corners from U to D, D2 swaps them, L' R' moves them back.
Sequence: L R D2 R' L'
Demo
Demo
Demo
Demo
Swap two adjacent corners on side U:
like above sample, before R use U' to move another corner to swap
Demo L U' R D2 R' U L'
Demo (L U' R D2 R' U L') U (L U' R D2 R' U L') U' exchange three corners
Demo (L U' R D2 R' U L') U' (L U' R D2 R' U L') U exchange three corners
Demo (L U' R D2 R' U L') U2 (L U' R D2 R' U L') U2 exchange two beside corners
Swap two opposite edges on side U (using E2):
like above sample, use E2 to swap edge
Demo L R E2 R' L'
Demo (L R E2 R' L') U (L R E2 R' L') U'
Swap two adjacent edges on side U:
Demo L U' R E2 R' U L'
Demo (L U' R E2 R' U L') U (L U' R E2 R' U L') U'
Demo (L U' R E2 R' U L') U' (L U2 R E2 R' U L') U
Demo (L U' R E2 R' U L') U2 (L U2 R E2 R' U L') U2
Swap two adjacent corners & edges on side U:
Demo L U' R E2 D2 R' U L'
Demo L U' R E2 D2 R' U L' U L U' R D2 E2 R' U L' U'
Turning (Rotating) Pieces:
L R D2 R' L'
Demo
(L R D2 R' L') U (L R D2 R' L') U'swap two opposite corners
Demo
(L R D2 R' L') U' (L R D2 R' L') Uswap two opposite corners
Demo
(L R D2 R' L') U2 (L R D2 R' L') U2No change, as expected
Swap two adjacent corners on side U:
like above sample, before R use U' to move another corner to swap
Demo L U' R D2 R' U L'
Demo (L U' R D2 R' U L') U (L U' R D2 R' U L') U' exchange three corners
Demo (L U' R D2 R' U L') U' (L U' R D2 R' U L') U exchange three corners
Demo (L U' R D2 R' U L') U2 (L U' R D2 R' U L') U2 exchange two beside corners
Swap two opposite edges on side U (using E2):
like above sample, use E2 to swap edge
Demo L R E2 R' L'
Demo (L R E2 R' L') U (L R E2 R' L') U'
Swap two adjacent edges on side U:
Demo L U' R E2 R' U L'
Demo (L U' R E2 R' U L') U (L U' R E2 R' U L') U'
Demo (L U' R E2 R' U L') U' (L U2 R E2 R' U L') U
Demo (L U' R E2 R' U L') U2 (L U2 R E2 R' U L') U2
Swap two adjacent corners & edges on side U:
Demo L U' R E2 D2 R' U L'
Demo L U' R E2 D2 R' U L' U L U' R D2 E2 R' U L' U'
Turning (Rotating) Pieces:
Rotate one corner on side U (#1):
Concept: Use the R side to isolate and turn the corner.
Sequence: R' D R D' R' D R
R' move the corner from side U to D
D disconnect the corner & edge and move the corner from side F to B
R turn the corner and move from side B to F
D' move the corner from R to L wait for the edge
R' move the edge to wait for the corner
D move the corner to reconnect the edge
R move the corner back to side U
Demo R' D R D' R' D R
Demo (R' D R D' R' D R) U (R' D' R D R' D' R) U'
Demo (R' D R D' R' D R) U' (R' D' R D R' D' R) U
Demo (R' D R D' R' D R) U2 (R' D' R D R' D' R) U2
Rotate one corner on side U (#2) - like a Megaminx corner twist:
Demo R' D R F D F'
Demo (R' D R F D F') U (F D' F' R' D' R) U'
Rotate one corner on side U (#3) - like a Pyraminx edge or Megaminx corner twist:
Demo R' D2 R F D2 F'
Demo (R' D2 R F D2 F') U (F D2 F' R' D2 R) U'
F D' R F2 R' F'
Rotate two corners on side U (#1):
Demo (F D B' D2 F' D B) U2 (B' D' F D2 B D' F') U2
Rotate two corners on side U (#2):
Demo (F D B' D2 F' B D B' D' B) U' (B' D B D' B' F D2 B D' F') U
Demo (F D B' D2 F' B D B' D' B) U (B' D B D' B' F D2 B D' F') U'
Demo (F D B' D2 F' B D B' D' B) U2 (B' D B D' B' F D2 B D' F') U2
Rotate two corners on side U (#3):
Demo F D' F' D B' F D2 F' D B
Demo (F D' F' D B' F D2 F' D B) U' (B' D' F D2 F' B D' F D F') U
Demo (F D' F' D B' F D2 F' D B) U (B' D' F D2 F' B D' F D F') U'
Demo (F D' F' D B' F D2 F' D B) U2 (B' D' F D2 F' B D' F D F') U2
Flip one edge on side U (#1):
Demo S D2 S' D' S D S'
Demo (S D2 S' D' S D S') U' (S D' S' D S D2 S') U
Flip one edge on side U (#2):
Demo (S D2 S' R' E' R) U' (R' E R S D2 S') U
Flip one edge on side U (#3):
Demo R E2 R2 E R
Demo (R E2 R2 E R) U' (R' E' R2 E2 R') U
R2 F B' D F' S D' S' D2 B
Flip one edge on side E (the equator):
Demo R F' U R' F
Demo (R F' U R' F) E (F' R U' F R') E'
Summary:
The formulas above can be used to solve 2x2x2 and 3x3x3 cubes. These are just basic building blocks—try experimenting to find more!
All the examples above change only one side (e.g. the U face).
Advanced Technique: Using Setup Moves
The power of this method grows when you add setup moves. The general sequence becomes:
Step 0 (Global Setup): Make a temporary change to the cube (e.g., R D).
Step 1 (Local Setup): Make a change on one side.
Step 2 (Target Adjustment): Turn that side.
Step 3 (Reverse Local Setup): Reverse Step 1.
Step 4 (Reverse Adjustment): Reverse Step 2.
Step 5 (Reverse Global Setup): Reverse Step 0 (e.g., D' R').
This allows you to apply a basic formula to different pieces.
Example: Swapping corners (with setup moves):
Demo B' ( (L U' R D2 R' U L') U (L U' R D2 R' U L') U' ) B
Demo B ( (L U' R D2 R' U L') U (L U' R D2 R' U L') U' ) B'
Demo D' R' ( (L U' R D2 R' U L') U (L U' R D2 R' U L') U' ) R D
Example: Swapping edges (with setup moves):
Example: Rotating a corner (with setup moves):
Demo B' ( (R' D R F D F') U2 (F D' F' R' D' R) U2 ) B
Example: Flipping an edge (with setup moves):
try to find more setup moves...
Working on Two Sides Simultaneously:
Sometimes you can create even shorter algorithms by making an adjustment that affects the target side in a helpful way.
Swap corners (shorter sequence):
Demo R D2 R'
Demo (R D2 R') U' (R D2 R') U
Demo L ( (R D2 R') U' (R D2 R') U ) L'
* with setup move L: L helps set up the swap on the same side with fewer moves
Swap edges (shorter sequence):
Demo R E2 R'
Demo (R E2 R') U' (R E2 R') U
Demo L ( (R E2 R') U' (R E2 R') U ) L'
Swap corners & edges (shorter sequence):
Demo R E2 D2 R'
Demo (R E2 D2 R') U' (R E2 D2 R') U
Demo L ( (R E2 D2 R') U' (R D2 E2 R') U ) L'
Even More Basic Building Blocks:
Swap three corners (work on Pyraminx swap edge or Megaminx swap corner):
Demo R' D' R
Demo (R' D' R) U' (R' D R) U Cycles 3 corners
Demo (R' D' R) U (R' D R) U' Cycles 3 corners
Demo (R' D' R) U2 (R' D R) U2 Cycles 3 corners
Swap edges:
Demo M D' M'
Demo (M D' M') U (M D M') U'
Demo (M D' M') U' (M D M') U
Demo M'
Demo (M') U2 (M) U2 Swaps 3 edges on the M slice
Demo M2
Demo (M2) U2 (M2) U2 Swaps 4 edges on the M slice
Demo M E' M'
Demo (M E' M') U (M E M') U'
try to find more ...
A General System for Cycling Three Corners on U and D (work on Pyraminx swap three edges or Megaminx swap three corner):
You have six basic building blocks for the first part (R' D R, R' D' R, R' D2 R, F D F', F D' F', F D2 F'). You can combine these with different turns (D, D', D2 as adjustments within the block) to control the orientation of the cycled pieces.
Demo R' D' R
Demo (R' D' R) U' (R' D R) U Cycles 3 corners
Demo (R' D' R) U (R' D R) U' Cycles 3 corners
Demo (R' D' R) U2 (R' D R) U2 Cycles 3 corners
Swap edges:
Demo M D' M'
Demo (M D' M') U (M D M') U'
Demo (M D' M') U' (M D M') U
Move a side from F to U:
Demo (M') U2 (M) U2 Swaps 3 edges on the M slice
Move a side from D to U:
Demo (M2) U2 (M2) U2 Swaps 4 edges on the M slice
Rotate a center (for 4x4+ cubes, moving a center from R to U):
Demo (M E' M') U (M E M') U'
try to find more ...
A General System for Cycling Three Corners on U and D (work on Pyraminx swap three edges or Megaminx swap three corner):
Target: Move corner 1 -> 2 -> 3 -> 1 (where 1 and 2 are on the U face, and 3 is on the D face).
Step 1.1: Move corner 1 from the U face to the D face (using F, F', R, R', L, L', B, or B').
Step 1.2: Move corner 3 to the position where corner 1 now is (using D, D', or D2).
Step 1.3: Reverse Step 1.1.
Step 2: Move corner 2 to the position where corner 3(originally corner 1) used to be (using U, U', or U2).
Step 3: Reverse Step 1.
Step 4: Reverse Step 2.
Demo (R' D R) U (R' D' R) U'
You have six basic building blocks for the first part (R' D R, R' D' R, R' D2 R, F D F', F D' F', F D2 F'). You can combine these with different turns (D, D', D2 as adjustments within the block) to control the orientation of the cycled pieces.
(L/L'/B/B' are same)
 | Demo | R' D R |
 | Demo | R' D' R |
 | Demo | R' D2 R |
 | Demo | F D F' |
 | Demo | F D' F' |
 | Demo | F D2 F' |
the orientation may be wrong, try add adjustment (D / D' / D2)
D (R' D R)
D' (R' D R)
D2 (R' D R)
D (R' D' R)
D' (R' D' R)
D2 (R' D' R)
...
try adjustment (R' D2 R D'/ R' D R / F' R')
R' D' R vs F D F' vs R' D2 R D' (F D2 F') / R' D R (F D2 F') / F' R' (L D' L') D>
swap three corners with different orientation
 |
Demo (R' D' R) U' (R' D R) U |
 |
Demo L' ( (R' D' R) U2 (R' D R) U2 ) L |
 |
Demo L2 B' ( (R' D' R) U2 (R' D R) U2 ) B L2 |
 |
Demo D' ( (R' D R) U' (R' D' R) U ) D
Demo (F D F') U' (F D' F') U |
 |
Demo L' D' ( (R' D R) U2 (R' D' R) U2 ) D L
Demo L' ( (F D F') U2 (F D' F') U2 ) L |
 |
Demo L2 B' D' ( (R' D R) U2 (R' D' R) U2 ) D B L2
Demo L2 B' ( (F D F') U2 (F D' F') U2 ) B L2 |
 |
Demo D2 B D ( (R' D2 R) U' (R' D2 R) U ) D' B' D2
Demo z' y F D2 ( (R' D' R) U2 (R' D R) U2 ) D2 F' y' z Demo D L2 ( (B' L' B) R2 (B' L B) R2 ) L2 D' |
 |
Demo D2 B L' D ( (R' D2 R) U2 (R' D2 R) U2 ) D' L B' D2
Demo D2 L' D ( (R' D' R) U2 (R' D R) U2 ) D' L D2 Demo z' y ( D2 F (R' D R) U2 (R' D' R) U2 ) F' D2 y' z Demo L2 D ( (B' L B) R2 (B' L' B) R2 ) D' L2 |
 |
Demo D2 B D' L2 B' D2 ( (R' D2 R) U2 (R' D2 R) U2 ) D2 B L2 D B' D2
Demo L D' L ( (R' D2 R) U2 (R' D2 R) U2 ) L' D L' Demo z' y F ( (R' D2 R) U2 (R' D2 R) U2 ) F' y' z Demo D ( (B' L2 B) R2 (B' L2 B) R2 ) D' |
swap three centers:
Demo M E' M' E
Rotate the corners & flip edge on side U:
Demo move the black X to left white X & right white X
#1
Demo U' R U R'
Demo (U' R U R') y' x' - rotate the while cube
Demo (U' R U R' y' x') x 3 - rotate 3 corners & flip 2 edges
Demo (U' R U R' y' x') x 6 - rotate 3 corners
#2
Demo (U' R U R') (R' F R F') (F' U F U')
Demo ( (U' R U R') (R' F R F') (F' U F U') ) x 2
#3
Demo U' Lw Bw U'
Demo (U' Lw Bw U') x 3
Demo (U' Lw Bw U') x 6
4+ cube edge flip:
#1
Demo U' R U R'
Demo (U' R U R') y' x' - rotate the while cube
Demo (U' R U R' y' x') x 3 - rotate 3 corners & flip 2 edges
Demo (U' R U R' y' x') x 6 - rotate 3 corners
#2
Demo (U' R U R') (R' F R F') (F' U F U')
Demo ( (U' R U R') (R' F R F') (F' U F U') ) x 2
#3
Demo U' Lw Bw U'
Demo (U' Lw Bw U') x 3
Demo (U' Lw Bw U') x 6
4+ cube edge flip:
The "Single Edge Flip" is an Illusion
When you see a single edge flipped on a 4x4, it looks like a special case. But it is just an illusion in the middle of the solve.
two edge swap:
Concept:
Don't treat it as a "special case" that needs a magic formula. Treat it as a "temporary separation" .
The goal is to break the edge apart, fix the direction of one piece, and put it back together. This turns the problem back into a normal 3-cycle.
step1: break the edge and re-connect
U2 2R U2 2R2 // first half edge
D' ( (2L D' 2L') U2 (2L D 2L') U2 ) D // 3-cycle second half edge
D' 2R' ( (2R' D 2R) U2 (2R' D' 2R) U2 ) 2R D // 3-cycle remain edge
all edge are correct now
step 2: swap centers
x2
U ( (2B' e 2B) U2 (2B' e' 2B) U2 ) U' // 3-cycle swap center
x
U ( (2B' e 2B) U2 (2B' e' 2B) U2 ) U' // 3-cycle swap center
x
U' ( (2B' e 2B) U2 (2B' e' 2B) U2 ) U // 3-cycle swap center
another version of step 2:
B2 2L U'
(2B' e 2B) U2 (2B' e' 2B) U2 // 3-cycle swap center
U 2L' B2
2r U
(2B' e 2B) U2 (2B' e' 2B) U2 // 3-cycle swap center
U' 2r'
Version 2:
only "2L" to break edge & center => 5 edge need to swap & 4x2 center to swap
Analogy (2x2x2):
It's like the 2x2 PLL. Sometimes you see only two corners need to swap. You do one simple 90° turn (U or U'), and now you have three corners to cycle. This is easy to solve. The 4x4 "single edge flip" is the same idea. You do one simple inner move to turn the "impossible" problem into a "normal" one.
Summary:
No special formula needed. Just break it, flip the piece, and put it back. The rest is just a normal solve.
Single Edge Flip formula NOT easy to remember:
2R' U2 2L F2 2L' F2 2R2 U2 2R U2 2R' U2 F2 2R2 F2
2R2 B2 U2 2L U2 2R' U2 2R U2 F2 2R F2 2L' B2 2R2
* http://www.davidguo.idv.tw/Cube/revenge.html
* http://www.davidguo.idv.tw/cube/Crazy44.htm
(r-1 UU) x 5
R-1 UU l-1 UU r-1two edge swap:
Demo
Demo
Demo scramble
Demo Cross,F2L(3),Top(2x2),Top(2x3+last 2 edge),Last 3 corners
Demo F2L,Cross,Top
Demo Corners First
How to solve the Rubik's Cube?
https://ruwix.com/the-rubiks-cube/how-to-solve-the-rubiks-cube-beginners-method/
https://rubiks-cube-solver.com/
https://rubiks-cube-solver.com/solution.php?cube=0111114131222222222313333333414444444555555555666666666
https://rubiks-cube-solver.com/solution.php?cube=0151111131222222222313333333444444444515555555666666666
http://affairs.ymhs.tyc.edu.tw/reheart/RC/th/math-method.htm
https://www.speedsolving.com/wiki/index.php/Corners_First
https://www.speedsolving.com/wiki/index.php/Edges_First
https://www.speedsolving.com/wiki/index.php/Columns_first
https://www.speedsolving.com/wiki/index.php/Roux_Method
https://www.speedsolving.com/wiki/index.php/Sexy_Method
https://www.ryanheise.com/cube/heise_method.html
https://www.ryanheise.com/cube/commutators.html
https://www.ryanheise.com/cube/last_three_corners.html
https://www.ryanheise.com/cube/corner_3_cycles.html
http://www.speedcubing.com/
http://www.rubik.com.cn/fridrich.htm
http://cube.rider.biz/
https://www.grubiks.com/puzzles/rubiks-revenge-4x4x4/
Google Rubik's Cube - L M R X - U E D Y - F S B Z
https://www.google.com/logos/2014/rubiks/iframe/index.html
2R 2L D 2L' 2R' L2 R2 // move half edge on beside for swap
(2L' 2R' D2 2R 2L )
U
(2L' 2R' D2 2R 2L )
U' // 2x2-cycle edge
R2 L2 2R 2L D' 2L' 2R' // reverse to move edge back
Demo
2R2 U2 2R2 U2
2U2 2R2 2U2
Demo scramble
Demo Cross,F2L(3),Top(2x2),Top(2x3+last 2 edge),Last 3 corners
Demo F2L,Cross,Top
Demo Corners First
How to solve the Rubik's Cube?
https://ruwix.com/the-rubiks-cube/how-to-solve-the-rubiks-cube-beginners-method/
https://rubiks-cube-solver.com/
https://rubiks-cube-solver.com/solution.php?cube=0111114131222222222313333333414444444555555555666666666
https://rubiks-cube-solver.com/solution.php?cube=0151111131222222222313333333444444444515555555666666666
http://affairs.ymhs.tyc.edu.tw/reheart/RC/th/math-method.htm
https://www.speedsolving.com/wiki/index.php/Corners_First
https://www.speedsolving.com/wiki/index.php/Edges_First
https://www.speedsolving.com/wiki/index.php/Columns_first
https://www.speedsolving.com/wiki/index.php/Roux_Method
https://www.speedsolving.com/wiki/index.php/Sexy_Method
https://www.ryanheise.com/cube/heise_method.html
https://www.ryanheise.com/cube/commutators.html
https://www.ryanheise.com/cube/last_three_corners.html
https://www.ryanheise.com/cube/corner_3_cycles.html
http://www.speedcubing.com/
http://www.rubik.com.cn/fridrich.htm
http://cube.rider.biz/
https://www.grubiks.com/puzzles/rubiks-revenge-4x4x4/
Google Rubik's Cube - L M R X - U E D Y - F S B Z
https://www.google.com/logos/2014/rubiks/iframe/index.html
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