MathDB
Ping pong matches between two teams of 1000

Source: Baltic Way 1998

January 11, 2011
combinatorics proposedcombinatorics

Problem Statement

Consider a ping-pong match between two teams, each consisting of 10001000 players. Each player played against each player of the other team exactly once (there are no draws in ping-pong). Prove that there exist ten players, all from the same team, such that every member of the other team has lost his game against at least one of those ten players.