MathDB

5

Part of 2019 SAFEST Olympiad

Problems(1)

25 imo IMO participants at a party, same language to at least 10 others

Source: The 1st SAFEST Olympiad 2019 p5

9/9/2019
There are 2525 IMO participants attending a party. Every two of them speak to each other in some language, and they use only one language even if they both know some other language as well. Among every three participants there is a person who uses the same language to speak to the other two (in that group of three). Prove that there is an IMO participant who speaks the same language to at least 1010 other participants
combinatorics