Slight correction. Soviet Academy of Sciences is not an educational institution, nor it is limited to those who were born in Moscow.

A lot of university students in Moscow, Kyiv, St. Petersburg or any bigger Soviet city weren't actually born there. If you were from another city the university will give you dorm room if you pass the entry exams.

In case of Pajitnov luck is more about getting a job at Academy of Sciences, but probably it has something to do with his talents.