Rubik's Cube Solver

How the Rubik's Cube Solver works

The Rubik's cube looks like a toy and behaves like a mathematics problem. It has 43,252,003,274, 489,856,000 reachable positions, about 43 quintillion, yet every one of them can be solved in twenty moves or fewer. A cube solver matters for two groups of people: those with a scrambled cube and no idea where to start, and those learning to solve faster who want to see exactly what an algorithm does. This page serves both, with a 3D cube you can turn, a notation player and a Rubik's cube solver that finds a short solution from any legal state.

A short history in numbers

Ernő Rubik, a Hungarian architecture lecturer, built the first cube in 1974 to teach spatial reasoning, and it went on sale worldwide in 1980. More than 450 million have been sold since. Speed solving took off in the 2000s under the World Cube Association, which now runs thousands of competitions a year; the official single-solve record for the 3×3 fell below 3.2 seconds in 2023. In 2010 a team of researchers, Tomas Rokicki, Herbert Kociemba, Morley Davidson and John Dethridge, used about 35 CPU-years of donated Google computing time to prove that "God's number", the most moves any position needs, is exactly twenty.

Move notation

Each letter turns one face a quarter turn clockwise as you look at that face: U up, D down, R right, L left, F front, B back. An apostrophe means anticlockwise and a 2 means a half turn, so R U R' U' is right up, top left, right down, top right, the "sexy move" that appears in countless algorithms. Slice moves M, E and S turn the middle layers, lowercase letters such as r turn two layers together, and x, y and z rotate the whole cube. Separate moves with spaces. The tool checks the whole sequence before playing it and shows an error instead of playing a partial one.

Entering your own cube

Hold the cube with white on top and green facing you, then read the stickers of each face in rows from top left to bottom right, in the order Up, Right, Front, Down, Left, Back. Write each sticker as the letter of the face whose centre has that colour: U for white, R for red, F for green, D for yellow, L for orange and B for blue. That gives 54 letters, nine per face, with the centres always U R F D L B. The tool checks that every letter appears nine times and that the pieces form a real cube.

How the Rubik's cube solver works

The solution comes from Herbert Kociemba's two-phase algorithm, the method behind most cube solving programs. Phase one brings the cube into a subgroup where every edge is oriented and the four middle-layer edges sit in the middle layer; phase two finishes it using only half turns on four faces plus quarter turns of the top and bottom. The search runs in a background thread with pruning tables built when the page loads, which takes a few seconds the first time. Solutions are typically twenty to twenty-two moves: close to God's number, and far shorter than the hundred-plus moves of a beginner's layer-by-layer method. Finding a guaranteed optimal solution is possible but can take minutes per position, which is why practical solvers settle for near-optimal.

Expert tips and pitfalls

Most "impossible" cubes are typos. A single swapped letter produces a corner with two stickers of the same colour or a count of ten of one letter. Recheck the face you entered last, and make sure you read each face with the cube held in the same orientation.

A reassembled cube may be unsolvable. If a cube was taken apart and put back together, or had stickers peeled and replaced, there is a two-in-three chance it cannot be solved by turning at all. Only one in twelve random reassemblies is solvable. If the letters are right but the tool says the colours do not form a valid cube, look for a twisted corner, flipped edge or swapped pair on the real cube and fix it physically.

Use the solver to learn, not just to finish. Speedcubers learn CFOP (cross, first two layers, orientation, permutation), whose last two steps alone have 57 and 21 algorithms. Paste any algorithm from a tutorial, set Turn speed to Slow and press Play moves to see which pieces move. Type the inverse, reversed and with each move flipped, to undo it.

Keep the orientation fixed. Solutions assume white on top and green in front. Rotate the whole cube mid-solution and every following move is applied to the wrong face.

How to read the result

Press Solve and the solution appears as a move sequence in the notation above, played back turn by turn on the 3D cube so you can follow along with a real one. The solution length tells you how efficient it is; anything around twenty is near the theoretical best. The stats also show the current state as a 54-letter facelet string you can copy and paste back later. Press Reset to return to a solved cube. Download PNG renders the current view at up to 4K; turn the cube to show the faces you want and use Fit view to centre it first.

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