Table of Contents
3×3 Rubik's Cube formula
All States, Transformations and Solving Steps for the Top Face of a 3×3 Rubik’s Cube
2×2 Rubik's Cube formula
4×4 Rubik's Cube formula
5×5 Rubik's Cube formula
Rubik's Cube formula

  • Below are all possible states of the top face of a 3×3 Rubik’s Cube:
  • The transformations and solving methods for all states are listed below:
Formula 1：R U R' U R U2 R'
Formula 2：R U2 R' U' R U' R'
State Result after Formula 1 Result after Formula 2 Solving Operation
Target State Ⅱ-1 Ⅰ-1 —
Ⅰ-1 Target State Ⅲ-1 Formula 1
Ⅰ-2 Ⅵ-1 Ⅳ-4 U’ + Formula 1
Ⅰ-3 Ⅶ-1 Ⅱ-3 U2 + Formula 1
Ⅰ-4 Ⅴ-1 Ⅳ-1 U + Formula 1
Ⅱ-1 Ⅲ-2 Target State Formula 2
Ⅱ-2 Ⅳ-4 Ⅴ-4 U’ + Formula 2
Ⅱ-3 Ⅰ-3 Ⅶ-1 U2 + Formula 2
Ⅱ-4 Ⅳ-1 Ⅵ-2 U + Formula 2
Ⅲ-1 Ⅰ-1 Ⅶ-3 Formula 1 + Formula 1
Ⅲ-2 Ⅶ-3 Ⅱ-1 Formula 2 + Formula 2
Ⅳ-1 Ⅰ-4 Ⅱ-4 Formula 1 + U + Formula 1
Ⅳ-2 Ⅵ-4 Ⅴ-3 U’ + Formula 1 + U + Formula 1
Ⅳ-3 Ⅴ-2 Ⅵ-3 U + Formula 1 + U’ + Formula 1
Ⅳ-4 Ⅰ-2 Ⅱ-2 Formula 1 + U’ + Formula 1
Ⅴ-1 Ⅶ-2 Ⅰ-4 Formula 2 + U + Formula 1
Ⅴ-2 Ⅴ-3 Ⅳ-3 U’ + Formula 2 + U + Formula 1
Ⅴ-3 Ⅳ-2 Ⅴ-2 U + Formula 1 + U’ + Formula 2
Ⅴ-4 Ⅱ-2 Ⅶ-4 Formula 1 + U’ + Formula 2
Ⅵ-1 Ⅶ-4 Ⅰ-2 Formula 2 + U’ + Formula 1
Ⅵ-2 Ⅱ-4 Ⅶ-2 Formula 1 + U + Formula 2
Ⅵ-3 Ⅳ-3 Ⅵ-4 U’ + Formula 1 + U + Formula 2
Ⅵ-4 Ⅵ-3 Ⅳ-2 U + Formula 2 + U’ + Formula 1
Ⅶ-1 Ⅱ-3 Ⅰ-3 Formula 1 + U2 + Formula 2
Ⅶ-2 Ⅵ-2 Ⅴ-1 U’ + Formula 1 + U2 + Formula 2
Ⅶ-3 Ⅲ-1 Ⅲ-2 U2 + Formula 1 + U2 + Formula 2
Ⅶ-4 Ⅴ-4 Ⅵ-1 U + Formula 1 + U2 + Formula 2