God's Number: Why Every Rubik's Cube Can Be Solved in 20 Moves

God's Number is 20. Every one of the Rubik's Cube's 43,252,003,274,489,856,000 possible positions — all 43 quintillion of them — can be solved in at most 20 face turns. That was proven in July 2010 by Tomas Rokicki, Herbert Kociemba, Morley Davidson and John Dethridge, with the help of about 35 CPU-years of computing time donated by Google. However hopeless your scramble looks, it is never more than 20 moves from solved.

The name comes from the idea of a "God's algorithm" — a solver with perfect knowledge that always takes the shortest possible route. God's Number is the worst day such a solver could ever have.

What does God's Number actually mean?

God's Number is the length of the optimal solution for the worst possible position — not the average scramble. It is measured in the half-turn metric, where any turn of a face counts as one move: a quarter turn like R, its reverse R', and a half turn like R2 all cost the same.

Most positions never get near the limit. Of the 43 quintillion reachable arrangements, the great majority sit comfortably below the ceiling, with optimal solutions in the high teens. Positions that genuinely need all 20 are extraordinarily rare — but they exist, and proving exactly where the ceiling sat took thirty years.

How was God's Number proven?

The proof was a thirty-year squeeze between two bounds: the most moves any known position needed, and the most moves any position could possibly need. The first serious upper bound came in 1981, when the mathematician Morwen Thistlethwaite devised an algorithm guaranteeing that any cube could be solved in at most 52 moves. Not fast, not pretty — but a hard ceiling, at a time when the cube craze was in full swing (a story we tell in our history of the cube).

The next leap came in the 1990s, when Herbert Kociemba published his two-phase algorithm, which in practice finds solutions of roughly 20 moves for any position you give it — strong evidence that 20 was the magic number, but evidence is not proof.

Proof meant checking, in effect, every position. In 2010, Rokicki, Kociemba, Davidson and Dethridge carved the full space of 43 quintillion positions into a vast collection of smaller subproblems, solved each one with heavily optimised search code, and burned through the lot using around 35 CPU-years of computing that Google donated to the project. The answer: no position anywhere in the space needs more than 20 moves. The ceiling and the floor met, and God's Number was settled at exactly 20.

The superflip: the position that needs all 20

The superflip is the most famous hard position on the cube: every piece sits in its correct place, but all twelve edges are flipped in place. At a glance it looks tantalisingly close to solved — the corners and centres already sit perfectly, and each edge is just one flip from home — yet in 1995 Michael Reid proved that no solution shorter than 20 moves exists for it. That pinned the lower bound at 20: hard proof that God's Number could be no smaller, which the 2010 result eventually matched from above.

There is a pleasing irony in it: one of the very hardest positions on the cube is not a chaotic mess but a perfectly symmetrical pattern. The cube saves some of its worst for its tidiest.

Why don't humans solve in 20 moves?

Human methods trade optimality for patterns a brain can actually recognise. An optimal 20-move solution has no visible logic — no cross, no layers, no landmarks — which is why nobody solves that way by hand. The beginner layer-by-layer method takes around 100–200 moves; full CFOP, the choice of most world-class speedcubers, averages about 55–60.

And that is fine. Speedcubers win by turning faster and recognising cases sooner, not by approaching God's Number. A 55-move solution executed in seconds beats a 20-move solution you could never find. Efficiency and solvability are different games — humans play one, computers play the other.

Try a 20-ish move solution on your own cube

You can watch a near-optimal solution happen on your own scramble. Moobix's quick mode runs Kociemba's two-phase algorithm right in your browser and typically returns solutions of 20–22 moves — paint in your cube at the free solver and compare its answer with the 100-plus moves a human method would take. If you'd rather build the human skill, the interactive lessons and the scramble challenge are the places to start.

Either way, the next time a scrambled cube looks impossible, remember the maths: whatever state it is in, solved is at most twenty turns away.