What “20 moves” actually means
A Rubik’s Cube has about 43 quintillion reachable arrangements: positions that can be produced by turning the cube, rather than arbitrary sticker patterns. The result says that every one of those positions can be solved in 20 moves or fewer. It does not mean every scramble needs 20 moves; many take far less.
The count uses the face-turn metric: turning one face by a quarter-turn or a half-turn counts as one move. Under a convention that counts a half-turn as two quarter-turns, the number would be different. The result is about the shortest possible solution in that counting system—not about how many moves a person would usually make.
How computers checked a space too large to inspect directly
The challenge was to prove a maximum, not merely to find short solutions for a large sample. Researchers used computer searches that organized cube positions into manageable groups and used symmetry: rotating or reflecting a position can reveal cases that are equivalent for the search. They also used precomputed information to rule out branches that could not lead to a solution within the move limit.
This made it possible to cover the full set of legal positions without listing and solving them one by one. The search established the upper bound: no position requires more than 20 face turns. To show that 20 is not just a loose ceiling, it also established that at least one position cannot be solved in fewer.
A worst case, not a solving recipe
The proof does not give a practical method for a person to solve any scramble in 20 moves. It answers a different question: how bad can the hardest possible position be if every move is chosen optimally? The surprising implication is that the cube’s enormous number of arrangements hides a remarkably small worst-case distance—though finding that shortest route is another problem entirely.
