Problem

Source: 2018 China Southeast MO Grade 10 P7

Tags: combinatorics, graph theory



There are $24$ participants attended a meeting. Each two of them shook hands once or not. A total of $216$ handshakes occured in the meeting. For any two participants who have shaken hands, at most $10$ among the rest $22$ participants have shaken hands with exactly one of these two persons. Define a friend circle to be a group of $3$ participants in which each person has shaken hands with the other two. Find the minimum possible value of friend circles.