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### 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

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.
```
Associated Topics:
High School Logic

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