Esther is engaged. Her fiancé is either Arthur, Barton, Claude, or Dexter.

1. Each of the four men and Esther is a knight or a liar.
2. Arthur says: "Exactly one of us four men is a knight."
3. Barton says: "Exactly one of us four men is a liar."
4. Claude says: "Arthur or Barton is Esther’s fiancé."
5. Esther says: "My fiancé and I are either both knights, or both of us are liars."

Who is Esther's fiancé?

(In reply to 2 POSSIBLE ANSWERS -spoiler by Ady TZIDON)

Your choice 1: Esther tells the truth. Not so does her fiance, . THERE are 2 liars:  Art & Bar, Claude and DEXTER tell the truth. One of them is her fiance.

reply:
First you say Esther's fiance lies, but then you say her fiance is either Claude or Dexter and they are telling the truth. Claude can't be telling the truth if neither Arthur nor Barton is the fiance. If, however, you mean "one of them" to refer to Arthur or Barton, then, in the case of Arthur, if Esther were a liar she'd be telling the truth about being the same as her fiance Arthur, which can't be, and if she were a knight, she'd be lying about being the same as him, also impossible. If on the other hand it were Barton the same logic would follow as he's also a liar in your scenario.

Your choice 2. Only Arthur tells the truTh. All the other lie , including Esther - his fiancee.

reply:
This claims Arthur to be the fiance. That would mean Claude was telling the truth, contrary to the statement that only Arthur tells the truth.

Posted by Charlie on 2013-03-25 11:45:30