7.3. At a large round table, 100 people are sitting. Each of them is either a knight, a liar, or a fool. Knights always tell the truth, liars always lie. A fool tells the truth if a liar is sitting to their left; lies if a knight is sitting to their left; and can say anything if a fool is sitting to their left. Each person at the table said, “A liar is sitting to my right.” How many liars can be at the table? (Find all possible answers and prove that there are no others)
Answer: 0 or 50 liars.

Solution: If there is a liar at the table, then to the right of the liar is either a fool or a knight. In this situation, both of them tell the truth, so the next one after them is again a liar. We get that liars and non-liars alternate, i.e., there are exactly half liars.

If there are no liars at the table, then there are no knights either (because to the right of a knight there must be a liar), and at the table are only fools, and this variant is also possible.

Criteria: Only the answer - 0 points.

Only the answer 50 with an example that this is possible - 1 point.

Only the answer 0 with an example that this is possible - 1 point (adds to the previous one).

Only the case where there are liars is considered - 5 points.

Only the case where there are no liars is considered - 2 points.

In the complete solution, it is stated that there can be 0 liars, but it is not shown that such an example is indeed possible - minus 1 point.