Case 274
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.
Taylor
“Jules is innocent.”
Sam
“Neither Frankie nor Jules is guilty.”
Frankie
“Taylor and Jules are both innocent.”
Jules
“Taylor and Sam are both innocent.”
Parker
“Either Taylor or Frankie is guilty.”
Who is guilty?
Solution: Parker
If Parker is guilty, Parker's statement is false and every other statement is true. Testing the other suspects creates at least one contradiction.