Party linguistics - Liceo Scientifico R. Bruni (Padova)

Liceo Scientifico R. Bruni (Padova)
In a certain party there are n people, each of them speaks more than one language, each language is spoken by at least two people, no two people share knowledge of more than one language. It is possible to communicate a message by passing from one person to another, translating when necessary. Every person knows how to translate between the languages he knows, but understands nothing about a language he doesn't know.

(a) Under what conditions is it possible to pass a message among everyone, from one person to another, without the same person having to participate in sharing the message more than once?
(b) Find conditions under which it is possible to guarantee that a message can circulate by exploiting all the linguistic ties existing in the party (and therefore necessarily passing through the same person as many times as the languages he knows)?
(c) If a linguistic genius comes to the party who speaks all the languages spoken in the party, how do the answers to the above questions change?
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