7.4. On a certain island, there are 2022 people, each of whom is either a knight, who always tells the truth, or a liar, who always lies. One day, all the inhabitants of this island stood in a circle, and each was asked in turn, "Is the person to your left a liar?" The total number of "Yes" answers was 2, and the number of "No" answers was 2020. After that, everyone was asked, "Is the person to your right, skipping one person, a liar?" Again, there were 2 "Yes" answers and 2020 "No" answers. How many "Yes" answers will be received if everyone is asked, "Is the person standing opposite you in the circle a liar?" (Find all possible answers and prove that there are no others.)
Solution. We will denote knights and liars as K and L, respectively. Note that in pairs of adjacent KK or LL, the person on the right cannot say that the person on the left is a liar. Therefore, the positive answer to the first question could only come from pairs KL and LK. This means that since there were two "Yes" answers, the entire circle consists of one group of consecutive liars and one group of consecutive knights (and the "Yes" answers came from the two boundaries of these groups).

Now consider the second question. We already know that there is at least one knight and one liar. Suppose there are at least two knights and two liars. Then "Yes" would be answered by the two rightmost knights and the two rightmost liars. This means there would already be four answers, which contradicts the condition. Therefore, either the knights or the liars consist of only one person.

For the third question, "Yes" will be answered only by a knight and a liar standing opposite each other. But from the previous paragraph, we already know that there is only one such pair, so there will be two "Yes" answers again.

Criteria. Only the answer - 0 points.

The answer with an example of a specific arrangement - 1 point.

Proof of the first paragraph - 3 points.

Proof of the second paragraph - another 3 points.