In writing a story, it's easy to identify problems with the story which you must struggle with for weeks to resolve. But often, you suddenly realize what the entire story is really about, and this makes everything suddenly easy. If by the formulation of the problem we mean that overall understanding, rather than specific obstacles, then yes. For stories.

Hmm. Einstein is perhaps most famous for "discovering" special relativity. But he neither formulated the problem, nor found the solution (I think the Lorentz transformation was already known to be the solution), but reinterpreted the solution as being real. His "greatest error" was introducing the cosmological constant into general relativity--curiously, making a similar error to what everyone else had made when confronted with the constancy of the speed of light, which was refusing to accept that the mathematical result described reality.