Puzzle 136 - Knaves and knights

By now you might have heard many, many, many puzzles of some people always telling truth, and others always telling lies. But in real life, we all neither knights, nor knaves. Anyway this puzzle is slightly different - there are couples and these couples both lie or both tell truth or one lies and other one tells truth. (We all like to believe ourselves to be the last one - wink wink)

Dags, Eggs and Fens are being interrogated as one of them is a spy. One of the couples always tells truth. In another couple, both husband and wife always lie. And in the third couple, one of the spouses always lies and the other one always tells truth.

Here are the statements by the three couples when interrogated.

• Mr. Dag: I am not the spy
• Mrs. Dag: Mr. Egg is the spy.

• Mr. Egg: Mr. Dag is truthful.
• Mrs. Egg: Mr. Fen is the spy.

• Mr. Fen: I am not the spy.
• Mrs. Fen: Mr. Dag is the spy.  

 Which person is a spy?

(This puzzle is taken from the book "The Godelian puzzle book" by Raymond Smullyan) 

  

Answer : 

1. If Mr. Dag is the spy, then both Mr. and Mrs. Dags are liars. And also Mr. Egg and Mrs. Egg are liars. Which is not possible. So Mr. Dag is not a spy.
2. If Mr. Egg is a spy, then Mr. Egg is truthful and Mrs. Egg is a liar (as she says Fen is the spy). Also Fens are mixed couple because Mr. Fen is telling truth and Mrs. Fen is lying. As this is not possible, Mr. Egg is not a spy.
3. So the only one remaining - Mr. Fen is the spy.