Case 162
The Swapped Envelope
A sealed envelope was replaced with an empty one.
Rule: exactly one suspect is guilty. The guilty suspect lies. Every innocent suspect tells the truth.
Peyton
“Quinn is innocent.”
Rowan
“Peyton and Quinn are both innocent.”
Casey
“Peyton and Rowan are both innocent.”
Quinn
“Either Rowan or Noah is guilty.”
Noah
“Either Casey or Quinn is guilty.”
Who is guilty?
Solution: Noah
If Noah is guilty, Noah's statement is false and every other statement is true. Testing the other suspects creates at least one contradiction.