Problem #PRU-65676

Problem

In the Land of Linguists live $m$ people, who have opportunity to speak $n$ languages. Each person knows exactly three languages, and the sets of known languages may be different for different people. It is known that $k$ is the maximum number of people, any two of whom can talk without interpreters. It turned out that $11n\le k\le m/2$. Prove that then there are at least $mn$ pairs of people in the country who will not be able to talk without interpreters.