Question: One day I saw an extremely beautiful lady on this island which consisted of only knights (that always are truthful) and knaves (that always lie) and was immediately smitten with her. I longed to know whether or not she was married, but I did not have the courage to ask her. The next day I came across her brother Alfred and he made such an indirect statement from which I could immediately deduce that the girl is not married. What could be the statement?
I have modified this puzzle which was initially of a different form in the book The Godelian puzzle book: Puzzles, Paradoxes and Proofs in the chapter Some Curious Adventures (Problem 7). Its solution is a bit different than this version of question.
Here is my solution:
Alfred must have said, "If she is married, I am a knave. "Suppose the girl is married. Then, if Alfred is a knight, the statement made by Alfred indicates that he is a knave(contradiction). But if he is a knave, then he must be false which will indicate that if the girl is married, then he is a knight. But that means Alfred is a knight because the girl is married. Thus, the girl should be unmarried and you can hit on her!
You can suggest your own solutions.