Rubik's Cube: How Commutators Work!

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[A, B] means A B A' B' (commutator)
[A: B] means A B A' (conjugate) where A is 1 or more setup moves.

► Pure Commutator Method 1:
[interchange move, solve odd piece]

► Pure Commutator Method 2:
[solve odd piece, reverse interchange move]

► Conjugate:
Setup, Commutator, Undo Setup

A "pure" commutator does not need setup moves, and has a 3 move way to solve the odd piece.
Note: sometimes you have to pick between method 1 or 2 to get a pure commutator.

► Pure 3 Corner Exercises (scrambles):
1. D' B' L' B' L F' L' B L F B D
2. R F' L F L' B' L F' L' B F R'
3. R' U' R U L' U' R' U R L
4. B R B R' F2 R B' R' F2 B'
5. F' B D' F U2 F' D F U2 B'

Solutions:
1. [L, D R' D'] or [U' R' U, L'] (method 1 or 2)
2. [D2, L U L'] or [F' U2 F, D2] (method 1 or 2)
3. [L', F R F'] or [F' D' F, U] (different interchanges)
4. [F2, U' B U] (method 1 only)
5. [F R2 F', L'] (method 2 only)

► Pure 3 Edge Exercises (scrambles):
1. L2 U' L2 U L2 R2 D' L2 D R2
2. F' R U' R U D' F2 U' D R U R' F
3. B2 R B R' L U' R' U R L' B (from video)
4. R' U' R' U' R U R U R U'
5. R F' R' F' R F R F R F' R2

Solutions:
1. [M2, F' U F] or [D' L2 D, M2] (method 1 or 2)
2. [E', R U' R'] or [B U2 B', E] (method 1 or 2)
3. [U, F' E F] or [R' E2 R, U'] (method 1 or 2)
4. [U, B' E B] or [L' E2 L, U'] (method 1 or 2)
5. [L S2 L', F'] (method 2 only)

► Conjugate 3 Corner Exercises (scrambles):
1. U2 L U2 D B U B' D' B U' B' U2 L' U2 (from video)
2. U' B' U2 B' D' B U2 B' D B2 U

Possible Solutions:
1a. [U: [F2, U B2 U']] = U (F2 U B2 U' F2 U B2 U') U' = 9 moves
1b. [U: [R' B' R, F2]] = 10 moves
2a. [L2: [U', R D2 R']] = 10 moves
2b. [R2: [D', R U2 R']] = 9 moves

► Conjugate 3 Edge Exercises (scrambles):
1. F' R' U2 F B' R2 B F' R F
2. R U F U F B' R2 F' B U F' U' R'

Possible Solutions:
1a. [R2: [F, D' S' D]] = R2 (D' S' D F D' S D F') R2
1b. [F: [E2, B L B']] = F (E2 B L B' E2 B L' B') F'
2a. [R2: [E, R U2 R']] = R2 (E R U2 R' E' R U2 R') R2
2b. [R: [S2, U' F U]] = R (S2 U' F U S2 U' F' U) R'



Beginner:
2x2 Tutorial ►    • Learn How to Solve a 2x2 Rubik's Cube (Beg...  
3x3 Tutorial ►    • Learn How to Solve a Rubik's Cube in 10 Mi...  
4x4 Tutorial ►    • Learn How to Solve a 4x4 in 10 Minutes (Fu...  
5x5 Tutorial ►    • Learn How to Solve a 5x5 in 8 Minutes (Beg...  

Special Tutorials:
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5x5+ ►    • How to Get Fast at 5x5+ (Big Cubes)  

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