1. Vasya, Petya, and Kolya study in the same class. Vasya lies in response to any question, Petya alternates between lying and telling the truth, and Kolya lies in response to every third question, and tells the truth in all other cases. One day, each of them was asked six times in a row how many people are in their class. In response, "Twenty-five" was heard five times, "Twenty-six" six times, and "Twenty-seven" seven times. Can we determine from their answers how many people are actually in their class? (Author of the problem - I. Rubanov)
Answer: 27. Solution: Vasya never told the truth, Petya told the truth three times, and Kolya - four times. Thus, the truth was told exactly seven times, which is how we get the answer.