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Strange Symmetric Sickness (Posted on 2007-04-13) Difficulty: 3 of 5
A strange epidemic affected about half the population of a Liars and Knights island. The sickness was strange: sick liars behaved as knights and always told the truth, while sick knights behaved as liars and lied all the time.

During that time, there was a theft, and a judge confronted the three suspects: Jacob, Karl, and Louie. It was a sure thing that one of them was guilty, and also that the two innocent ones knew perfectly well who was the guilty one.

The judge asked Jacob: "What do you know about the theft?". Jacob answered "The thief is a liar". The judge then asked him "Is he healthy or sick?", and Jacob answered "He is healthy".

The judge then asked Karl: "What do you know about Jacob?", and Karl answered "He is a liar". The judge asked "Healthy or sick?", and Karl added "Jacob is sick".

The judge thought for a while, and then asked Louie "Are you the thief?". Louie answered (yes or no), and the judge decided the case.

Who was the thief?

I got this problem from a book by Raymond Smullyan.

  Submitted by Old Original Oskar!    
Rating: 4.3333 (3 votes)
Solution: (Hide)
Karl's answers are both true or both false, but in any case, Jacob is truthful: he is a sick liar or a healthy knight.

From Jacob's answers, the thief is a healthy liar, and thus a liar: Jacob cannot be the liar.

If Louie had answered "No", he could be lying (and be guilty) or telling the truth (and Karl would be guilty).

Since the judge worked out who was guilty, Louie must have answered "Yes", and thus cannot be the thief, who would have lied: Karl was the thief.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
answerK Sengupta2007-05-09 12:39:28
SolutionSolutionDej Mar2007-04-13 15:03:16
Hints/TipsInitial Ramblngs (part spoiler)Vernon Lewis2007-04-13 14:56:47
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