2. In a correspondence mathematics olympiad, out of 500 participants, exactly 30 did not like the problem conditions, exactly 40 did not like the organization of the event, and finally, exactly 50 did not like the method of determining the winners of the olympiad. We will call an olympiad participant "significantly dissatisfied" if they were dissatisfied with at least two out of the three aspects of the olympiad. What is the maximum number of "significantly dissatisfied" participants that could have been at this olympiad?
Solution. In total, there were $120=30+40+50$ "dissatisfactions" expressed, so there cannot be more than 60 "significantly dissatisfied" individuals, because otherwise they would have more than 120 "dissatisfactions" in total, which contradicts the condition. It remains to show that there could have been 60 of them. For example, participants 1 - 40 are dissatisfied with the organization of the event, participants 1 - 10 and $41-60-$ are dissatisfied with the problem conditions, and participants 11 - 60 are dissatisfied with the determination of the winners.

Answer: 60.