Visual Rubik's Cube Solver

In 1992, German mathematician Herbert Kociemba developed a breakthrough technique to navigate the 43 quintillion states of the Rubik's cube without searching the entire group tree.

Phase 1 reduces the arbitrary scrambled cube from the full group G0 = <U, D, L, R, F, B> to a much smaller subgroup G1 = <U, D, L2, R2, F2, B2>. In this subgroup, all 12 edge orientations and 8 corner orientations are fully solved, and all 4 middle-layer edges reside strictly in the equator slice.

Phase 2 then solves the cube to its pristine identity state using exclusively turns from G1. Because G1 contains only 19.5 billion states (compared to 43 quintillion), the search algorithm converges almost instantaneously.

For 36 years after the Rubik's Cube was patented in 1974, mathematicians debated 'God's Number'—the maximum number of moves required to solve the most difficult scrambled state in the Half Turn Metric (HTM).

In July 2010, an international research team composed of Tomas Rokicki, Herbert Kociemba, Morley Davidson, and John Dethridge proved with the aid of Google supercomputing that God's Number is exactly 20.

To solve your physical cube, click on any color in the virtual palette, then click on the corresponding cube facelet in the 3D viewport. Follow these simple steps for 100% accuracy:

If the solver alerts you that the cube state is unsolvable, your physical cube has entered an illegal state (e.g., an accidental corner twist or incorrect reassembly). A random reassembly has only 1 in 12 chance of being solvable.