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?

Simply from the conditions on the problem, we can conclude that Cindy's statement is tautological. If the antecedent of the main connective (the conditional statement) is false, the statement is true as a whole. And if the antecedent is true, we know that Cindy did it and thus Derek could not have done it, so the statement remains true. Thus the others must all be liars.

If we consider the statement of Derek, we know that, since it is false, its negation must be true. That is, we know for certain that Derek did do it and Bob didn't do it and Cindy didn't do it.

We note that the other statements also become false in this situation.

So, Derek is the villain responsible for the despicable murder.

Posted by Timothy on 2004-04-23 22:51:18