Case 163
The Vanished Key
A locked evidence cabinet was opened without permission.
Rule: exactly one suspect is guilty. The guilty suspect lies. Every innocent suspect tells the truth.
Parker
“Neither Finley nor Harper is guilty.”
Elliot
“Either Parker or Peyton is guilty.”
Finley
“Neither Peyton nor Harper is guilty.”
Peyton
“Either Elliot or Harper is guilty.”
Harper
“Neither Parker nor Finley is guilty.”
Who is guilty?
Solution: Elliot
If Elliot is guilty, Elliot's statement is false and every other statement is true. Testing the other suspects creates at least one contradiction.