Laws of the cube

Only a 12^th of possible cube states is reachable by twisting the 6 faces (from the solved state). Here's why:

1. Only an even number of cubie swaps is possible (¹/₂ of all states)
2. Only an even number of edges can be flipped (¹/₂ of all states)
3. The total number of corner twists must be divisible by 3 (¹/₃ of all states)

So combined together, these laws mean that:
¹/₂ * ¹/₂ * ¹/₃ = ¹/₁₂ of all states are reachable.

See Also

• Random State Scramble

External Links

• Laws of the Cube (by Ryan Heise)