Brazil FC and Graphs
Source: Brazil National Olympiad Junior 2021 #6
February 14, 2022
combinatorics
Problem Statement
In a football championship with teams, each team play with another exactly once. The score of the match(es) is three points to the winner, one point to both players if the match end in draw(tie) and zero point to the loser. The final of the tournament will be played by the two highest score teams. Brazil Football Club won the first match, and it has the advantage if in the final score it draws with any other team. Determine the least score such that Brazil Football Club has a chance to play the final match.