On the Scores of Soccer Without Draw
Source: Iranian Combinatorics Olympiad 2020 P1
April 22, 2020
combinatorics
Problem Statement
In a soccer league with teams every two team have played exactly once and no game have lead to a draw. The participating teams are ordered first by their points (3 points for a win, 1 point for a draw, 0 points for a loss) then by their goal difference (goals scored minus goals against) in a normal soccer table. Is it possible for the goal difference in such table to be strictly increasing from the top to the bottom?Proposed by Abolfazl Asadi