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.