MathDB

4

Part of 2002 Junior Balkan Team Selection Tests - Moldova

Problems(1)

9 chess players

Source: 2002 Moldova JBMO TST p4

2/25/2021
99 chess players participate in a chess tournament. According to the regulation, each participant plays a single game with each of the others. At a certain moment of the competition it was found that exactly two participants played the same number of party. To prove that in this case, not a single chess player played any the game, or just one chess player played with everyone else.
combinatorics