Alice, Bob, and Cathy are on trial. Exactly one of them is guilty. They each make a statement:
- Alice says, "Bob is innocent!"
- Bob says, "Cathy is innocent!"
- Cathy says one of the three is guilty (maybe herself), but we don't hear who.
The judge knows who is guilty, and heard Cathy's statement. She says, "I could tell you what Cathy said and how many true statements were made, but you still wouldn't know who is guilty."
The judge adds, "I will tell you that the guilty party told the truth. Now if I told you how many true statements were made, you would know who is guilty."
Who is guilty?