Your task is to correctly deduce the secret numbers.
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.Consider the infamous Two Generals’ Problem. Two generals belong to the same army, but their troops have been split up and enemy territory separates them.
General A writes a message saying, “Let’s both attack at noon tomorrow. Please confirm that you received this message so I know the plan is on.”General B receives this and replies, “Message received. We’ll attack at noon tomorrow. Please confirm that you received this so I know the plan is on.” B needs confirmation from A, because if B’s message never delivers, then A won’t know that B agreed to the plan and won’t attack. So if B doesn’t get a confirmation back, he can’t be sure that the plan is on. You probably see where this is headed.General A: “Yes, I got your message saying that you’re down to attack at noon. So we’re on. Please confirm that you’ve received this.”
B needed this confirmation and wouldn’t attack without it. So of course A needs to know that B got the confirmation he needed so that A isn’t alone at noon tomorrow. This reasoning carries on forever, with each general requiring confirmation from the other in order to be completely assured that they agree.This isn’t just logical sleight of hand.
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