7.3. On an island where knights and liars live, several (more than two) people gathered around a round table. It is known that there were both knights and liars at the table, and each said such a phrase: "Only one of my two neighbors is a knight." Who is more at the table: knights or liars, and by how many times? (Knights always tell the truth, liars always lie; and everyone knows who is who).
Answer: There are twice as many knights. Solution. Consider an arbitrary knight (by the condition of the problem, there are knights at the table). From his truthful words, it follows that a knight sits on one side of him, and a liar on the other. Without loss of generality, we can assume that the knight is sitting to his right, and the liar to his left. Then from this knight neighbor to the left sits our first knight, which means a liar sits to his right. If another liar sat to the right of this liar, the statement about only one knight neighbor would have been true, so a knight must sit to the right of the liar. Reasoning similarly, we get the chain "knight-knight-liar-knight-knight-liar..." and so on. Since we could have started the reasoning from any knight, such periodicity should be observed throughout the round table (and reach the first knight from the other side). Thus, the number of people at the table is divisible by three, and there are twice as many knights as liars.