2018 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 6


A round robin chess tournament took place between $16$ players. In such a tournament, each player plays each of the other players exactly once. A win results in a score of $1$ for the player, a loss results in a score of $-1$ for the player and a tie results in a score of $0$. If at least $75$ percent of the games result in a tie, show that at least two of the players have the same score at the end of the tournament.


See also

2018 UNM-PNM Contest II (ProblemsAnswer KeyResources)
Preceded by
Problem 5
Followed by
Problem 7
1 2 3 4 5 6 7 8 9 10
All UNM-PNM Problems and Solutions