How many teams played in the tournament?
Source: Mexican Mathematical Olympiad 2004 OMM P4
July 31, 2018
combinatoricsTournament
Problem Statement
At the end of a soccer tournament in which any pair of teams played between them exactly once, and in which there were not draws, it was observed that for any three teams and C, if defeated and defeated , then defeated . Any team calculated the difference (positive) between the number of games that it won and the number of games it lost. The sum of all these differences was . How many teams played in the tournament? Find all possible answers.