Problem 3. On an island, there live knights and liars. Knights always tell the truth, while liars always lie. One day, 6 inhabitants of the island gathered together and each said: "Among the other five, there are exactly four liars!". How many knights could there be among them?
Answer: 0 or 2.

Solution. Let's consider two cases: either there is a knight among the attendees, or there is not. If there is at least one knight, then he told the truth, and there are four liars among the attendees. In this case, the second knight also told the truth, while the liars lied, so this case is possible.

If there are no knights, then all present are liars, and they all lied, so this case is also possible.

## Criteria

1 pt. Only the correct answer (both numbers) without justification.

1 6. One of the answers is given, and it is explained why it fits.

2 pts. Both answers are given, and it is explained why they fit.

4 6. The correct answer is given, and it is proven that no other answers fit.