Rioplatense 2022 - Level A - Problem 2
Source:
December 6, 2022
combinatorics
Problem Statement
Eight teams play a rugby tournament in which each team plays exactly one match against each of the remaining seven teams. In each match, if it's a tie each team gets point and if it isn't a tie then the winner gets points and the loser gets points. After the tournament it was observed that each of the eight teams had a different number of points and that the number of points of the winner of the tournament was equal to the sum of the number of points of the last four teams.
Give an example of a tournament that satisfies this conditions, indicating the number of points obtained by each team and the result of each match.