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2012 ToT Fall Junior O p5 several field trips for a class of 20 students

Source:

March 22, 2020
combinatorics

Problem Statement

For a class of 2020 students several field trips were arranged. In each trip at least one student participated. Prove that there was a field trip such that each student who participated in it took part in at least 1/201/20-th of all field trips.