A cop arrested four suspects for the bank robbery. When he interviewed them, each made two statements. From his infrared lie-detector he knew that each man made one "true" and one "false" statement. As a result, he soon found out the culprit.

Given the following statements, can you determine who the culprit was?

‘A’ said: “I did not do it. B did.”

‘B’ said: “A did not do it. C did.”

‘C’ said: “B did not do it. I did.”

‘D’ said: “C did not do it. A did.”

(In reply to solution by Cory Taylor)

That is certainly one algorithm for solving these kinds of puzzles.

I prefer to eliminate as many "clearly" wrong choices as possible before resorting to it though.

In this case, since each person's "X didn't do it" statement would also be true if his "Y did it" statement is true, the "Y did it" statements must be the false ones.

Therefore all the "X didn't do it" statements are true and exonerate the "X's." All the "Y did it" statements are false, and exonerate the "Y's."

D is the only one not exonerated.

Actually, this could have been solved with half the information. The two statements made by any two suspects (except the B/D pairing) would be enough to exonerate the other three.

Posted by TomM on 2003-01-29 04:48:53