4. The inhabitants of an island are either scoundrels or knights: knights always tell the truth, scoundrels always lie. One evening at the bar, Alberto says: "Bruno is a knight"; Bruno says: "......all three knights" (at that moment a truck passes and it is not clear whether Bruno said "We are all..." or "We are not all..."); Carlo says: "Bruno said that we are not all three knights". How many of them are knights?
(A) 0
(B) 1
(C) 2
(D) 3
(E) it is not possible to determine.
4. The answer is (A). Based on Alberto's statement, Alberto and Bruno are of the same type. If Carlo is a knight, Bruno says "we are not all three knights," which is true if and only if Bruno is a knave. Therefore, Carlo is necessarily a knave. Since Bruno's statement is of the type "(not) we are all three knights," Bruno said "we are all three knights," which is false, so Bruno is a knave, and consequently, so is Alberto.

Notice that, without knowing the type of statement made by Bruno (for example, he might have said "the baristas are all three knights"), one cannot determine what Bruno is, nor consequently what Alberto is.

## Second Solution

If Carlo is a knave, Bruno said "we are all three knights," which is false, so they are all knaves. If Carlo were a knight, then Bruno would have actually said "we are not all three knights," which can only be true if Alberto is a knave. But then Bruno would also be a knave, and could not have made a true statement. Therefore, the only possibility is that they are all knaves.