1. On the Island of Knights and Liars, there live knights who always tell the truth and liars who always lie. One day, five residents of this island were asked in turn how many knights were among them.

- One, - answered the first.
- Two, - answered the second.
- Three, - answered the third.
- Don't believe them, they are all liars, - said the fourth.
- You are the liar! - said the fifth to the fourth.

How many knights were there in reality?

Answer: 2.
Solution. Among the first three, there is no more than one knight, since they all give different answers. If we consider the 4th and 5th, one of them is a knight and the other is a liar. Therefore, there is one or two knights in total. In any case, one of the first three told the truth. This means there are two knights: the second and the fifth.