Problem

Source: 2017 Latvia BW TST P8

Tags: combinatorics



$2017$ chess players participated in the chess tournament, each of them played exactly one chess game with each other. Let's call a trio of chess players $A, B, C$ a principled one, if $A$ defeated $B$, $B$ defeated $C$, and $C$ defeated $A$. What is the largest possible number of threes of principled chess players?