problem about king and prisoners

I describe this problem as a story....;)

Once a upon a time there was a king and one day he prepared a party for his family . There was exactly thousand of wine bottle for this party. But a rebel puts poison in a wine bottle to assassinate the king and somehow king knew that and he wanted to find that poisoned bottle before the party. There was one day to begin the party. So he ordered his servants to use king's prisoners to find that bottle. It will take couple of hours to die after drinking this poisons.
The challenge is finding the poisoned bottle using minimum number of prisoners.
I heard this probelm from viduneth

problem about monks

This is a famous question that I heard from one of my friends.
problem description
There is a set of monks who is meditating. All of them get together to a certain location daily and meet each other but they are not talking with each other and no any other communication used but thinking power of every monk is at the same level. One day a god came to them and told them a fixed number of people will sick tomorrow. Every monk who is sick has a red spot on their forehead and anyone can see this red spot except himself(if you are infected you can't see your red spot but can see others ones). When monks get together the monks who have been infected will realize they have the illness and will not participate to the meeting the next day onward.  The god know 10 monks will get sick at this time and so us(The problem solvers but monks don't know the count is 10 but monks know that is a fixed number )..;)
The question is that
How many number of days it will take not to come to the meeting for monks who has the illness from the day they became ill?
I heard this problem from darshana