Tennis players in a tournament
Source: Argentina TST 2011, Problem 5
August 31, 2014
combinatorics proposedcombinatoricsgraph theory
Problem Statement
At least players take part in a tennis tournament. Each participant plays exactly one match against each other participant. After the tournament has ended, we find out that each player has won at least one match. (There are no ties in tennis).
Show that in the tournament, there was at least one trio of players such that beat , beat , and beat .