Question 35
Consider $n$ persons, each of them speaking at most 3 languages. From any 3 persons there are at least two which speak a common language.
i) For $n \le 8$, exhibit an example in which no language is spoken by more than two persons.
ii) For $n \ge 9$, prove that there exists a language which is spoken by at least three persons.
i) For $n \le 8$, exhibit an example in which no language is spoken by more than two persons.
ii) For $n \ge 9$, prove that there exists a language which is spoken by at least three persons.