Question 142
In a class of at least four people the following holds: if four of them sit down at a round table, there is always someone who knows both of their neighbours or knows neither of their neighbours. Prove that it is possible to divide the people into two groups (one of which may be empty) such that in one group everyone knows each other and in the other group nobody knows each other.
(If person $A$ knows person $B$, then $B$ also knows $A$.)
(If person $A$ knows person $B$, then $B$ also knows $A$.)