A terrible crime has been committed and the police round up the usual suspects. During the interrogation of the four men the following accusations and statements are made:

Anderson said "Brimmers did it."
Brimmers said "Dodge did it."
Carter said "I didn't do it."
Dodge said "Brimmers lied when he said I did it."

If only one of the four men was untruthful, which man committed the crime?

I like Syzygy's simplicity better than my approaches, but here they are in case anyone is interested.

Assume Dodge is the only liar. Then that means that Brimmers was not lying when he said Dodge did it. Therefore Dodge did it. But then Anderson’s statement is a lie. Too many liars.

Therefore Dodge was telling the truth, and Brimmers is the only liar. This means that Anderson and Carter are telling the truth. This works with no contradictions.

Therefore Brimmers is the criminal.

You could also approach the problem with the fact that Anderson and Brimmers accuse different men. They can’t both be telling the truth, and since there is only one liar, the liar must be one of them. If Anderson is the liar then Brimmers is telling the truth, and Dodge did do it. But then Dodge’s statement is a lie and we have too many liars. So it must be that Anderson is telling the truth and Brimmers is lying. And again, Anderson’s statement means that Brimmers committed the crime.

Posted by nikki on 2004-11-04 13:18:18