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In each of three schools with $300$ students, every student from every school knows $301$ students from the remaining two schools. Prove that there are three students, each from the separate school, that know each other.

Is this problem a variation on Theorem on friends and strangers?

How can we approach these types of problem where we have bigger numbers (we can't actually draw a graph with $300$ vertices)?

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    I think this is application of Dirichlet principle, since 301>300 – 2017-01-23
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    Also, if A knows B who knows C, does this mean that A and C know each other? – 2017-01-23
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    Here is the answer to the general case (where each school has $n$ students and every student knows $n+1$ students from other schools): http://math.stackexchange.com/a/1264278/242413 – 2017-01-24

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