In general I find commentary here too negative on AI, but I'm a bit squeamish about maximalist claims re: AI mathematical reasoning vs. human population based off this, even setting aside lottery-ticket-hypothesis-like concerns.

It's a common logic puzzle, Google can't turn up an exact match to the wording you have, but ex. here: https://www.futilitycloset.com/2018/03/03/three-hat-problem/