Blue-eyes logic puzzle

[aldiboronti]

Just as a follow-up, there’s a very good inductive proof of the solution on this page.

And on his solution page xkcd poses a few questions “that may force you to further explore the structure of the puzzle:”

1. What is the quantified piece of information that the Guru provides that each person did not already have?

2. Each person knows, from the beginning, that there are no less than 99 blue-eyed people on the island. How, then, is considering the 1 and 2-person cases relevant, if they can all rule them out immediately as possibilities?

3. Why do they have to wait 99 nights if, on the first 98 or so of these nights, they’re simply verifying something that they already know?

He doesn’t provide any answers and even though I’ve just about wrapped my head around the solution now I couldn’t satisfactorily answer any of them!