Problem 966

Solution. Let $A$ be one of these students. Among the remaining 5 students, there are three who know $A$, or there are three who do not know $A$. Let's consider the case when we have three acquaintances of $A$. If among these students there are two who know each other, then together with $A$ we have three students who all know each other. Otherwise, we have three students such that each does not know either of the other two students. The case when we have three students who are not acquaintances of $A$ is considered analogously. We leave the details to the reader as an exercise.