Monday, May 11, 2009

A mathematical who-done-it?

Sue tells me her oldest has discovered the joy of logic problems. Here's a fun one from the exercises in Enderton's A Mathematical Introduction to Logic:
There are three suspects for a murder: Adams, Brown, and Clark. Adams says "I didn't do it. The victim was an old acquaintance of Brown's. But Clark hated him." Brown states "I didn't do it. I didn't even know the guy. Besides I was out of town all that week." Clark says "I didn't do it. I saw both Adams and Brown downtown with the victim that day; one of them must have done it." Assume that the two innocent men are telling the truth, but that the guilty man might not be. Who did it?
pic by martinmaters


Rachel said...

It's Brown. If the two innocent people are telling the truth, then either Adams or Brown is lying because their statements are contradictory about whether Brown knew the victim or not. So, Clark must be telling the truth. Clark's true statement then contradicts Brown's claim to have been out of town. Book 'em, Dano.

HM said...

Case closed!