100 prisoners problem
I'm confused..."Before the first prisoner enters the room, the prisoners may discuss strategy—but may not communicate once the first prisoner enters to look in the drawers."And, in the example given, "That prisoners 5 to 8 will also find their numbers can also be derived from the information gained by the first three prisoners."There's never any explanation of what happens when a prisoner opens a drawer and finds it empty. In the first example given, what happens when prisoner 5 goes in and there's nothing in drawer 5? The algorithm doesn't seem to account for this.It seems like there's some sort of assumption that the later prisoners are gathering information from the earlier prisoners, but the problem set-up seems to preclude this? They're going into a room so they can't watch each other, the drawers are closed afterwards so they can't derive information from which drawers are open/closed, and they're not allowed to communicate.Am I not following something?