3. At a round table, several liars and knights were sitting. The first one said: "Not counting me, there is one more liar than knights here.". The second one said: "Not counting me, there are two more liars than knights here.", and so on up to the last one. How many people could be sitting at the table?
Answer: 2 or 3.

Let there be $n$ people in total. They cannot all be liars, otherwise the $(n-1)$-th person would have told the truth. All statements contradict each other, so there is exactly 1 knight. He sits in the $(n-1)$-th place. For a liar, the statement "Not counting me, there are $(n-3)$ more liars than knights." would be true. To prevent this statement from being true, it must be that $n-3 < 1$, that is, $n < 4$.

(A. Shapovalov)

## Second Round