3

Part of 1977 Kurschak Competition

Problems(1)

each student knows a total of n + 1 students at the other two schools

Source: 1977 Hungary - Kürschák Competition p3

Three schools each have

n

students. Each student knows a total of

n + 1

students at the other two schools. Show that there must be three students, one from each school, who know each other.