MathDB

8

Part of 2017 Moldova Team Selection Test

Problems(1)

There are at least 120 students [2017 Moldova TST, D2, P4]

Source: 2017 Moldova TST, Day 2, Problem 4

3/19/2017
At a summer school there are 77 courses. Each participant was a student in at least one course, and each course was taken by exactly 4040 students. It is known that for each 22 courses there were at most 99 students who took them both. Prove that at least 120120 students participated at this summer school.
combinatorics