Question: Question in Graph theory: (a) Suppose that in a group of 17 people, every pair of people is able to converse in either English, Spanish,

Question in Graph theory:

(a) Suppose that in a group of 17 people, every pair of people is able to converse in either English, Spanish, or German. Prove that among these people, there is a group of three people who can converse together simultaneously in one language.

(b) Part (a) shows that $R(3,3,3) \leq 17$. Generalizing this argument, give a bound on $R(3,3,3,3)$.

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