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?

For C's statement to be false, the if part of his statement ("I did it and Alice didn't do it") must be true, and the then part ("Derek didn't do it") must be false, meaning C and D are guilty and A is innocent. Since only one person is guilty, this is impossible; C must be the one telling the truth.

Thus, A is lying, so either A or D must be guilty (if her statement is true, they are both guilty or both innocent).
B is also lying, so B and A must both be innocent for his statement to be false. Thus, D must be guilty.
D's statement must be false as well, so all three parts of his "or" statement need be false. Thus, he (D) is guilty, and B and C are not.
E didn't do it, so her statement is false as well.

So, D did it, and C is telling the truth.

Posted by DJ on 2004-04-21 10:18:59