Problem
COM-B1-M04-P018 Player with at Least Average Wins
#18
★★★☆☆ Level 3 of 5
In a tournament, each of \(n\) players played each other exactly once, with no draws. Prove that some player won at least \((n-1)/2\) games.
Count total wins.
There are \(n(n-1)/2\) games, each giving exactly one win. The average number of wins per player is \((n(n-1)/2)/n=(n-1)/2\). Hence some player has at least the average.
Average argument in a tournament.