20 people be seated at 4 tables
Source: All-Russian MO 2009 Regional 10. 8
August 27, 2024
combinatorics
Problem Statement
At a party, a group of people needs to be seated at 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 people sit at each table. What is the greatest possible number of pairs of friends in this companies?