MathDB

4

Part of 2000 Singapore MO Open

Problems(1)

one can find 27 people in party who have all shaken hands with each other

Source: Singapore Open Math Olympiad 2000 2nd Round p4 SMO

4/2/2020
In a party of 10001000 people, the number of people who have shaken hands with at most 962962 people is less than or equal to 3737. Show that one can find 2727 people in the party who have all shaken hands with each other.
combinatorics