In Tripleland, natives always go in trios: a knight, a knave, and a liar.

Once I met such a trio, and I asked one of the natives a simple question ("simple" meaning, "of six words or less"); he answered, and I knew what type he was. Then, I asked another of the natives a different simple question; he answered, and I knew what type he was, and therefore, the type of the third one too.

"Logical" thinking: This cannot be. The natives could be in six possible orders. Two yes-no questions allow four combinations. Thus, you cannot pick one out of six with only two questions; you need one more!

How could this be? What's wrong with the reasoning above?

Call the three natives A, B, and C. You asked A, "Are you a liar?" He said, "Yes." Neither a knight nor a liar can say this, so A is a knave. Then, you asked B, "Do you exist?" If B said, "Yes," then he is a knight, so C is a liar. If B said, "No," then he is a liar, so C is a knight. The reason you only needed two questions is because you got lucky with A's answer. If A said, "No," then you would need more questions.

Posted by Math Man on 2012-10-20 16:35:00