This famous puzzle is here: https://www.popularmechanics.com/science/math/a26564/solution-to-riddle-of-the-week-27/
https://xkcd.com/blue_eyes.html
My question: Given n+1 people with blue eyes, the n+1 person will see that no one leaves/dies at the nth iteration and hence realizes that he has blue eyes. However, it appears to me you also need to prove that nobody will leave/die before the nth iteration. Is there something that I'm missing that means it's not required.
The thing about this problem is that instead of each person having a unique perspective, every single person has the exact same thought process because they are, at least according to the problem, identical. This means that if one person can figure out that they have blue eyes, by definition, so can everyone else. Therefore, for any iteration before the $nth$ one, nobody will leave/die because they do not have enough information yet. Then on the $nth$ iteration, everyone will leave.