7.2 On the Island of Truth and Lies, there are knights who always tell the truth, and liars who always lie. One day, 15 residents of the island lined up by height (from tallest to shortest, the tallest being the first) for a game. Each had to say one of the following phrases: "There is a liar below me" or "There is a knight above me." In the end, those standing from the fourth to the eighth position said the first phrase, while the rest said the second. How many knights were among these 15 people, given that all residents have different heights?
# Answer: 11

Solution. The formation cannot consist of only liars (in such a case, 4-8 would be telling the truth). Consider the tallest knight, let's call him R. He could only say the first phrase, so the positions 1, 2, and 3 must be occupied by liars, and R stands from 4 to 8. In addition, there is a liar who is shorter than R, let's call him L. This liar cannot say the second phrase, so he must say the first phrase and stand no later than the 8th position but no earlier than the 5th position. Therefore, from the 9th to the 15th position, only knights stand. A liar cannot stand at the 4th position, as L is shorter than him. Therefore, R stands at the 4th position. If there are other liars between R and L, they must also say the first phrase, but L is shorter than them, which is a contradiction.

We conclude that liars stand at positions $1, 2, 3,$ and 8, while the remaining positions are occupied by knights.