2. Three brothers returned from fishing. Mother asked each of them how many fish they caught together. Vasya said: "More than ten", Petya: "More than eight", Kolya: "More than fifteen". How many fish could have been caught (list all possibilities), if it is known that two brothers told the truth, while the third one lied?
Answer: 16, 17 or 18. Solution. If the brothers caught more than 18 fish, then all of them told the truth. If the brothers caught no more than 15 fish, then Petya and Kolya lied. In both cases, we get a contradiction with the problem's condition. If, however, the brothers caught more than 15 but no more than 18 fish, Vasya and Petya told the truth, while Kolya lied, which corresponds to the problem's condition.