1. Each of the three friends either always tells the truth or always lies. They were asked the question: "Is there at least one liar among the other two?" The first answered: "No," the second answered: "Yes." What did the third answer?
Solution Since the first and second friends gave different answers, one of them is a liar, and the other is a knight. Moreover, the knight could not have answered “No” to the question posed, as in that case, he would have lied (there is definitely a liar among the two remaining). Therefore, the first one is a liar. He lied, which means that among the two remaining, there must be a liar, and it can only be the third friend. Thus, the third one answered “No”.

Answer: “No”.

2 A team consisting of Petya, Vasya, and a one-person scooter is participating in a race. The distance is divided into 42 segments of equal length, each with a checkpoint. Petya runs a segment in 9 minutes, Vasya in 11 minutes, and either of them can ride a segment on the scooter in 3 minutes. They start simultaneously, and the team's time is determined by the time of the last person to finish. They agreed that one will ride the first part of the way on the scooter and walk the rest, while the other will do the opposite (the scooter can be left at any checkpoint). How many segments should Petya ride on the scooter to ensure the team achieves the best possible time?

Solution If Petya rides 18 segments and runs the remaining $42-18=24$, he will spend $18 \cdot 3+24 \cdot 9=270$ minutes. In this case, Vasya, on the contrary, will have to ride 24 segments and run 18, which will take $24 \cdot 3+18 \cdot 11=270$ minutes - the same amount of time. If Petya rides fewer segments, his time (and thus the team's time) will increase. If Petya rides more segments, Vasya's time (and the team's time) will increase.

It is sufficient to denote the number of segments Petya rides as \( x \) and solve the equation

$$
x \cdot 3+(42-x) \cdot 9=(42-x) \cdot 3+11 x
$$

Answer: 18.