Case 155
The Stolen Watch
A valuable watch disappeared during a private gathering.
Rule: exactly one suspect is guilty. The guilty suspect lies. Every innocent suspect tells the truth.
Parker
“Neither Casey nor Logan is guilty.”
Avery
“Parker is innocent.”
Casey
“Neither Avery nor Logan is guilty.”
Hayden
“Either Parker or Logan is guilty.”
Logan
“Parker and Casey are both innocent.”
Who is guilty?
Solution: Hayden
If Hayden is guilty, Hayden's statement is false and every other statement is true. Testing the other suspects creates at least one contradiction.