The question is asking what is the shortest sequence of moves that will have the cube solved at some point during the sequence. The most obvious such sequence would be one that has every solution to every position followed immediately by its inverse. This would be incredibly long, somewhere in the hundreds of quadrillions of moves. Is it even possible to find a shorter sequence?
2026-03-26 02:47:52.1774493272
What is the Shortest Set of Moves Needed to Solve a Rubik's Cube?
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You are looking for what is sometimes called the "devil's algorithm", which is a Hamiltonian cycle over cube states.
People have wondered about such a thing for some time, and there are explicit constructions; see here for example.