Raymond Smullyan's What is the Name of This Book? contains a puzzle which I'll paraphrase here:
- Of the identical twins Tweedledum and Tweedledee, one of them lies on Mondays, Tuesdays and Wednesdays and tells the truth on the other days of the week; the other lies on Thursdays, Fridays, and Saturdays and tells the truth on the other days of the week.
- One of the twins owns a rattle; the other does not. Alice wants to restore the rattle to its rightful owner.
- Alice comes across one of the twins and asks him: "Who really owns the rattle?"
- He replies: "The true owner of the rattle is telling the truth today." [Edit: this previously incorrectly said "is lying today."]
- Humpty Dumpty claims that the probability this twin owns the rattle is thirteen fourteenths. How did he come up with that number?
My question: is Humpty Dumpty right?