In the land of Symutra, there was a murder last night. Witnesses saw one person shooting the guy, but no one could see him well enough to identify him. In addition, Alice, Bob, Cindy, Derek, and Evelyn were all seen near the place of the murder shortly after and before the murder. The police brought them in for questioning and they all gave one sentence.

Alice: I didn't do it if and only if Derek didn't do it.

Bob: Alice did do it if I didn't do it.

Cindy: If I did it and Alice didn't do it, Derek didn't do it.

Derek: I didn't do it or Bob did do it, or Cindy did it.

Evelyn: I did it.

It is known for a fact that ONLY one of them did do it. If only one person told the truth, who did it? And who told the truth?

If A told the truth, then A and D would be both guilty (impossible) or both innocent. But if A told the truth, then D lied, which implies that D did it -- so A cannot have told the truth.

If A lied, one of A and D would be innocent, and the other guilty.
If A was the guilty one, B and C would be telling the truth, so A cannot be the guilty one.

Therefore, D did it.

Posted by Oskar on 2004-04-21 08:33:30