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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.

See The Solution Submitted by Old Original Oskar!    
Rating: 4.3333 (3 votes)

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Solution Solution | Comment 2 of 3 |

If Louie had answered “no” to the question “Are you the thief?”, only Jacob could be removed from the suspect list with each Louie and Karl remaining the possible thief, therefore Louie must have answered “yes”, and the judge had decided that Karl is the thief.

Jacob is a healthy knight. Karl is a healthy liar. Louie lied to the judge’s questions, but it is unknown if he is a liar or just a sick knight.

  Posted by Dej Mar on 2007-04-13 15:03:16
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