Problem:
The inhabitants of an island are either knaves or knights: knights always tell the truth, knaves always lie. One evening at the bar, Alberto says: "Bruno is a knight"; Bruno says: "......all three of us are knights" (at that moment a truck passes by 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?
Pick one
Solution:
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 form "(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.
Note that, without knowing the type of statement made by Bruno (he might, for example, have said "the bartenders are all three knights"), one cannot say what Bruno is, nor consequently what Alberto is.
Solution:
If Carlo is a knave, Bruno said "we are all three knights", which is false, so they are all three knaves. If Carlo were a knight, then Bruno would actually have said "we are not all three knights", which can be true only if Alberto is a knave. But then Bruno would also be a knave, and he could not have made a true statement. Therefore the only possibility is that they are all knaves.