MathDB

10.8

Part of 2009 All-Russian Olympiad Regional Round

Problems(1)

20 people be seated at 4 tables

Source: All-Russian MO 2009 Regional 10. 8

8/27/2024
At a party, a group of 2020 people needs to be seated at 44 tables. The seating arrangement is called successful if any two people at the same table are friends. It turned out that successful seating arrangements exist. In a successful seating arrangement, exactly 55 people sit at each table. What is the greatest possible number of pairs of friends in this companies?
combinatorics