during a school year 44 competitions among students were held
Source: 2016 Grand Duchy of Lithuania, Mathematical Contest p2 (Baltic Way TST)
October 3, 2020
combinatorics
Problem Statement
During a school year competitions were held. Exactly students won in each of the competitions. For any two competitions, there exists exactly student who won in both competitions. Is it true that there exists a student who won all of the competitions?