Alicia and Bruno are each given a different natural number in secret (1 is the smallest natural number, 2 is the second smallest, and so on). They are then tasked with guessing which of them has the larger number. The following conversation ensues:
Alicia: I don’t know who has the bigger number.
Bruno: I don’t know either.
Alicia: Upon further reflection, I remain ignorant.
Bruno: Alas, I’m still unsure too.
Alicia: Now that you say that, I actually know which of us has the bigger number!
Bruno: Cool! In that case, I know what both of the numbers are.
What numbers were Alicia and Bruno given?
Common knowledge concerns not only what you know, but what you know about what others know about what you know, and so on. It may seem esoteric, but when taken to its logical extreme, common knowledge has bizarre consequences and serves as the basis for many puzzles and even real-world engineering hurdles.
Find the solution at the bottom of this page.