BALTIC-WAY 2011 Problem 8

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 $A$ .