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6

Part of 2022 Turkey MO (2nd round)

Problems(1)

Several trips in a school with 2022 students

Source: Turkey National Mathematical Olympiad 2022 P6

12/23/2022
In a school with 20222022 students, either a museum trip or a nature trip is organized every day during a holiday. No student participates in the same type of trip twice, and the number of students attending each trip is different. If there are no two students participating in the same two trips together, find the maximum number of trips held.
combinatorics