MathDB
Table tennis match

Source: Chinese TST 2009 1st quiz P2

March 21, 2009
ceiling functionpigeonhole principleinductiongraph theorycombinatorics proposedcombinatorics

Problem Statement

Let n,k n,k be given positive integers satisfying k\le 2n \minus{} 1. On a table tennis tournament 2n 2n players take part, they play a total of k k rounds match, each round is divided into n n groups, each group two players match. The two players in different rounds can match on many occasions. Find the greatest positive integer m \equal{} f(n,k) such that no matter how the tournament processes, we always find m m players each of pair of which didn't match each other.
Back to ProblemsView on AoPS