9.2. Six people - liars and knights - sat around a table. Liars always lie, while knights always tell the truth. Each of them was given a coin. Then each of them passed their coin to one of their two neighbors. After that, 3 people said: "I have one coin," while the other 3 said: "I have no coins." What is the maximum number of knights that could have been sitting at the table?
Answer: 4.

Solution: After passing the coins, each person sitting at the table can have 0, 1, or 2 coins. The total number of coins will be 6. Note that if a person lies, they will state a number of coins that differs from the actual number by 1 or 2. Since the total number of coins based on the answers differs from the actual total by $6-3=3$, at least 2 people must have lied. Therefore, there are no more than 4 knights at the table. Suppose the knights sitting at the table pass the coins as follows (arrows indicate the direction of the coin transfer; the number of coins after the transfer is in parentheses): $\leftrightarrow K(1)-L(0) \rightarrow L(1) \rightarrow L(1) \rightarrow L(1) \rightarrow K(2) \leftrightarrow$. In this case, all knights tell the truth, while the liars lie, saying they have 0 coins.

Comment: It is proven that there are no more than 4 knights at the table - 5 points. It is proven that there can be 4 knights at the table - 2 points.