9.2. On an island, 20 people live, some of whom are knights who always tell the truth, and the rest are liars who always lie. Each islander knows for sure who among the others is a knight and who is a liar. When asked by a visitor how many knights live on the island, the first islander answered: "None," the second: "No more than one," the third: "No more than two," the fourth: "No more than three," and so on, the twentieth stated: "No more than nineteen." So how many knights live on the island?
Answer: 10.

Solution: If the first islander were a knight, he would have lied in his answer, which cannot be the case. Therefore, the first is a liar, and there are no more than 19 knights on the island. This means the twentieth islander told the truth, so he is a knight, and there is at least one knight on the island. Then, if the second islander were a knight, there would already be two knights including the twentieth, and he would have lied, so the second is a liar, and there are no more than 18 knights. Therefore, the nineteenth told the truth and is a knight. Continuing this way, it is easy to see that the first to tenth islanders are all liars, and the eleventh to twentieth are all knights.

Grading Criteria: Established that the first is a liar: 1 point. Established that the first is a liar and the second is a knight: 2 points. Given the correct answer and constructed an example with verification: 3 points. Any incorrect answer: 0 points.