1.1. On the Island of Knights and Liars, knights always tell the truth, while liars always lie. One day, a traveler interviewed seven residents of the island.

- I am a knight, - said the first.
- Yes, he is a knight, - said the second.
- Among the first two, there are no less than 50% liars, - said the third.
- Among the first three, there are no less than 65% liars, - said the fourth.
- Among the first four, there are no less than 50% knights, - said the fifth.
- Among the first five, there are no less than 40% liars, - said the sixth.
- Among the first six, there are no less than 65% knights, - said the seventh.

Determine how many knights are among them in reality.
Answer: 5.

Solution: Suppose the first inhabitant is a knight. Then the second is also a knight, while the third and fourth are liars. If, on the other hand, the first is a liar, then the second is also a liar, while the third and fourth are knights. In either case, among the first four, there are exactly two knights and two liars. Therefore, the statements of the fifth, sixth, and seventh inhabitants are true, i.e., they are knights.