Case 098
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.
Sam
“Rowan and Hayden are both innocent.”
Avery
“Either Sam or Alex is guilty.”
Rowan
“Either Hayden or Alex is guilty.”
Hayden
“Avery and Rowan are both innocent.”
Alex
“Either Rowan or Hayden is guilty.”
Who is guilty?
Solution: Alex
If Alex is guilty, Alex's statement is false and every other statement is true. Testing the other suspects creates at least one contradiction.