MathDB

In Greifswald there are three schools called

A,B

and

C

, each of which is attended by at least one student. Among any three students, one from

A

, one from

B

and one from

C

, there are two knowing each other and two not knowing each other. Prove that at least one of the following holds:
[*]Some student from

A

knows all students from

B

. [*]Some student from

B

knows all students from

C

. [*] Some student from

C

knows all students from

A

Problem Statement