MathDB

3

Part of 2020 Vietnam Team Selection Test

Problems(1)

A football game

Source: 2020 Vietnam TST P3

6/29/2020
Suppose nn is a positive integer, 4n4n teams participate in a football tournament. In each round of the game, we will divide the 4n4n teams into 2n2n pairs, and each pairs play the game at the same time. After the tournament, it is known that every two teams have played at most one game. Find the smallest positive integer aa, so that we can arrange a schedule satisfying the above conditions, and if we take one more round, there is always a pair of teams who have played in the game.
VietnamTSTcombinatorics