8.1. At the Olympiad, students from gymnasiums, lyceums, and regular schools met. Some of them stood in a circle. Gymnasium students always lie to regular school students, lyceum students lie to gymnasium students, and regular school students lie to lyceum students. In all other cases, the students tell the truth. Each one said to their right neighbor: “I am a gymnasium student.” How many students from regular schools were in this circle?
Answer: There were no ordinary school students in the circle.

Solution: Let's assume there was an ordinary school student in the circle. Consider his left neighbor. This neighbor could not be another ordinary school student or a lyceum student, because they would tell the truth. But he also cannot be a gymnasium student, because then he would have lied, and he said the truth. Therefore, the neighbor of the ordinary school student cannot be anyone. Consequently, ordinary school students did not join the circle. Criteria: only the answer - 0 points, answer with verification - 1 point. For the claim that to the right of a gymnasium student there must be a gymnasium student or a lyceum student (in reality, it can be either a lyceum student or a gymnasium student) - deduct 3 points.