no of matches in a draw / total no of matches, 4n students tournament
Source: Thailand Mathematical Olympiad 2012 p8
August 17, 2020
combinatorics
Problem Statement
first grade students at Songkhla Primary School, including boys and girls, participate in a taekwondo tournament where every pair of students compete against each other exactly once. The tournament is scored as follows:
In a match between two boys or between two girls, a win is worth points, a draw point, and a loss points.
In a math between a boy and a girl, if the boy wins, he receives points, else he receives points. If the girl wins, she receives points, if she draws, she receives points, and if she loses, she receives points.
After the tournament, the total score of each student is calculated. Let be the number of matches ending in a draw, and let be the total number of matches. Suppose that the maximum total score is . Find .