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Logical reasoning

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Sharky, a leader of the underworld, was killed by one of his own band of four henchmen. Detective Sharp interviewed the men and determined that all were lying except one. He deduced who killed Sharky on the basis of the following statements:

a. Socko: Lefty killed Sharky.
b. Fats: Muscles didn't kill Sharky
c. Lefty: Muscles was shooting craps with Socko when Sharky was knocked off.
d. Muscles: Lefty didn't kill Sharky.

Who did kill Sharky?

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Suppose Socko is telling the truth. This means that Fats, Lefty and Muscles are lying.
Since Socko is telling the truth, Lefty killed Sharky.
But we assumed that Fats was lying, therefore Muscles killed Sharky.
Hence we get a contradiction. Therefore Socko was not telling the truth and he was lying. Therefore we conclude that Lefty did not kill Sharky.

Now suppose that Fats is telling the truth and Socko, ...

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