To me it feels a little bit like Levin's universal search (https://www.quora.com/How-is-it-possible-that-an-existing-algorithm-solve-NP-complete-problems-in-polynomial-time-if-and-only-if-P-NP/answer/Mark-Gritter) in that it keeps ticking things off an infinite list. If the right answer's there, then we'll get to it eventually. The clever bit is ensuring that if the mean value isn't on the list, then we'll make only finitely many mistakes.