8.2. On a certain island, only knights, who always tell the truth, and liars, who always lie, live. One day, 1001 inhabitants of this island stood in a circle, and each of them said: "All ten people following me in a clockwise direction are liars." How many knights could there be among those standing in the circle?
Answer: 91 knights.

Solution. Note that all people cannot be liars, because then it would mean that each of them is telling the truth. Therefore, among these people, there is at least one knight. Let's number all the people so that the knight is the 1001st in the sequence. Then the 10 people with numbers from 1 to 10 are liars (this follows from the knight's statement). Moreover, the 10 people with numbers 991-1000 are also liars, as they made an incorrect statement (there is a knight among the ten people standing after them). Therefore, since these 10 people stand in a row along our circle after person number 990, he told the truth and, consequently, is also a knight. Repeating the reasoning for him, we get that people with numbers 980-989 are liars, and so on. In the end, we get that the knights are people with numbers $1001, 990, 979, \ldots, 11$, that is, there are a total of $1001 / 11 = 91$ of them.

For completeness of the reasoning, note that we have proven that if the arrangement is possible, it looks exactly like this. It is not difficult to check that there are no contradictions, and the people could indeed stand this way.

Criteria. Only the answer - 0 points.

Only the answer with an example of the arrangement - 2 points.

The case where there are no knights is not considered - do not deduct points.

Not verified that the obtained arrangement fits - do not deduct points.