7.2. At a round table, 7 aborigines are sitting: knights, liars, and bores (there is at least one representative of each tribe at the table). A knight always tells the truth, a liar always lies. A bore lies if at least one knight is sitting next to them, and in other cases, they can say anything.

How many knights could be at the table if, in response to the question "Who are your neighbors?" each answered "Both of my neighbors are bores"? Provide all possible options and explain why there are no others.
Answer: 1 or 2.

Solution: Two knights cannot sit next to each other, so there are no more than three knights.

If there are 3 knights at the table, then there must be at least 4 bores, but in this case, there are no liars at the table. This is a contradiction.

Next, we will provide examples of seating arrangements with 1 and 2 knights at the table:
![](https://cdn.mathpix.com/cropped/2024_05_06_6da6c43758d247368fa8g-1.jpg?height=392&width=1420&top_left_y=2334&top_left_x=318)

## Criteria:

7 points - correct answer and a fully justified solution;

4 points - only one correct answer with justification;

answer only - 0 points.