2. Each of the 10 people is either a knight, who always tells the truth, or a liar, who always lies. Each of them thought of some natural number. Then the first said: “My number is greater than 1”, the second said: “My number is greater than 2”, ..., the tenth said: “My number is greater than 10”. After that, they, in a different order, said (each one phrase): “My number is less than 1”, “My number is less than 2”, ..., “My number is less than 10”. What is the maximum number of knights that could have been among these 10 people? (O. Podlipsky)
Answer: 8. Solution: Those who in the first series of answers said that their numbers are greater than 9 and 10 are definitely liars, because these answers are incompatible with any of the answers in the second series. Therefore, there are no more than eight knights. An example when there are exactly 8 knights: the first eight in the first series of answers thought of the numbers $2, \ldots, 9$ respectively, and they give the answers "My number is less than 3", ..., "My number is less than 10" in the second series of answers. Each of the two liars thought of the number 5, and they give the last two answers of the first series and the first two answers of the second series.