MathDB

5

Part of 2017 Caucasus Mathematical Olympiad

Problems(2)

II Caucasus Mathematical Olympiad, 9.5

Source: II Caucasus Mathematical Olympiad

3/20/2018
In a football tournament 2020 teams participated, each pair of teams played exactly one game. For the win the team is awarded 33 points, for the draw -- 11 point, for the lose no points awarded. The total number of points of all teams in the tournament is 554554. Prove that there exist 77 teams each having at least one draw.
combinatorics
copy of existing problem

Source: II Caucasus Mathematical Olympiad

3/20/2018
In a football tournament 2020 teams participated, each pair of teams played exactly one game. For the win the team is awarded 33 points, for the draw -- 11 point, for the lose no points awarded. The total number of points of all teams in the tournament is 554554. Prove that there exist 77 teams each having at least one draw.
combinatorics