There are 30 students arranged in a circle, with their eyes closed. The instructor places a hat on each student's head. 20 of the hats are black, 10 are white. The students then open their eyes. They can see each other student's hat, but not their own hat.
The instructor says "At least one of you is wearing a black hat."
He then gives the following instruction:
"Any student who has determined that his or her hat is black, please sit down."
Of course, no one sits down, because nobody can see his or her own hat. (There are no mirrors in the room, and the students are not allowed to discuss what they see.)
A minute later, the instructor repeats the previous instruction:
"Any student who has determined that his or her hat is black, please sit down."
No-one moves.
The instructor repeats this same instruction every minute for the next thirty minutes.
QUESTION 1: what happens, and when?
QUESTION 2: State exactly what new piece of information the instructor provided when he said "At least one student's hat is black." After all, this fact was already known by every student.