Sick Monks Leave the Monastery
Date: 09/21/2002 at 06:07:25 From: Stergios Subject: A recreational problem with monks Hello, A friend of mine has told me a problem that seems to be unsolvable. In a monastery, the monks meet only once a day. They do not talk or sing to each other to communicate. One day the chief monk tells them that there are sick monks among them who must leave the monastery during the meeting. Each of the sick monks has a red cross on his forehead. After three days, all the sick monks have left. How many sick monks were there in the monastery? Thank you.
Date: 09/21/2002 at 15:08:22 From: Doctor Shawn Subject: Re: A recreational problem with monks Stergios, It's the Monastary of Perfect Logicians! The way to solve this problem is through induction. The problem should probably specify that the sick monks should leave immediately AFTER the meeting, and not interact with each other in between. Suppose there is one sick monk (he has a cross on his forehead). The chief monk makes the announcement that there are sick monks in the monastery. The sick monk can look around, realize that there are no other monks with a cross, and sadly get up and leave after the meeting. This will happen on the first day. Now, suppose there are TWO sick monks. When the announcement is made, each sick monk can see the other sick monk, and so each will expect the other to leave after the meeting is over. The next day, each will be very surprised to find the other sick monk still there. The sick monks will realize that each of them was waiting for someone else to leave - and since no one else is sick, it must be them. So after the second meeting, both monks will sadly walk away. Can you take it from here? - Doctor Shawn, The Math Forum http://mathforum.org/dr.math/
Date: 09/21/2002 at 20:19:45 From: Stergios Subject: Thank you (A recreational problem with monks) Thank you very much. I think that I really understand the way you work. It's very exciting.
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