2. Each of the three boys either always tells the truth or always lies. They were told six natural numbers. After that, each boy made two statements.

Petya: 1) These are six consecutive natural numbers.

2) The sum of these six numbers is even.

Vasya: 1) These are the numbers 1, 2, 3, 4, 5, 6.

2) Kolya is a liar.

Kolya: 1) All these numbers are different and divisible by 3.

2) Each of these numbers is less than 20.

What numbers were told to the boys?
Answer: $3,6,9,12,15,18$. Solution. Among six consecutive natural numbers, there are exactly three odd numbers. Therefore, their sum is odd. This means that Petya lied either the first time or the second time, and thus he is a liar, that is, he lied both times. But then Vasya is also a liar because in his first statement, he named six consecutive natural numbers. Since Vasya said that Kolya is a liar, Kolya actually tells the truth. There are only 6 natural numbers divisible by 3 and less than 20, which gives us the answer.