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?

A harder (longer) way of looking at it:

If A was the only truthful one: A and D are both innocent, but in that case C would also tell the truth.

If B was the only truthful one: either B or A is guilty, but in any case D would be also telling the truth.

If C was the only truthful one: A is lying, so A or D did it. If A did it, B would be telling the truth, but if D did it, everything works out fine.

If D was the only truthful one: B or C is guilty, so A would be telling the truth too.

If E was the only truthful one: E did it, so A would also be telling the truth.

Posted by e.g. on 2004-04-21 10:10:54