Trilingual-speaker broadcast channel. A speaker of Dutch, Spanish, and French wishes to communicate simultaneously to three people: D, S, and F. D knows only Dutch but can distinguish when a Spanish word is being spoken as distinguished from a French word; similarly for the other two, who know only Spanish and French, respectively, but can distinguish when a foreign word is spoken and which language is being spoken. Suppose that each language, Dutch, Spanish, and French, has M words: M words of Dutch, M words of French, and M words of Spanish.

(a) can speak to D?

(b) If he speaks to D at the maximum rate, what is the maximum rate at which he can speak simultaneously to S?

(c) If he is speaking to D and S at the joint rate in part (b), can he also speak to F at some positive rate? If so, what is it? If not, why not?