MathDB
Volleyballers throws balls

Source: Saint Petersburg olympiad 2024, 9.4

September 21, 2024
combinatorics

Problem Statement

The coach lined up 200200 volleyball players and gave them mm balls (each volleyball player could get any number of balls). From time to time, one of the volleyball players throws the ball to another (and he catches it). After a while, it turned out that of any two volleyball players, the left one threw the ball to the right exactly twice, and the right one to the left exactly once. For which minimum mm is this possible?