Three islanders and three accusations

Question

On an island, every resident is either a knight (who always tells the truth) or a knave (who always lies). You meet three residents and each says exactly one thing:

Ada: "Bruno is a knave."
Bruno: "Ada and Carl are different types" (one a knight, one a knave).
Carl: "Ada is a knight."

Which of the three are knights, and which are knaves?

Accepted Answer

Let's test Carl's claim as the anchor, since it links directly to Ada. Carl says "Ada is a knight." Whatever Carl is, his statement and Ada's status are tied: if Carl tells the truth then Ada is a knight, and if Carl lies then Ada is a knave. Either way, Carl and Ada are the same type (both knights or both knaves). Now look at Bruno, who claims "Ada and Carl are different types." We just showed Ada and Carl are the same type, so Bruno's claim is false. A false statement can only come from a knave, so Bruno is a knave. Turn to Ada, who says "Bruno is a knave." That is exactly what we just prov…

Three islanders and three accusations

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