Who Stole the Tarts? Part IX

"Here is the baking pan," said the King, "so now you can make me the tarts."

"Without a recipe?" inquired the Queen.

"Use your usual recipe," cried the King impatiently, "last time your tarts were delicious!"

"Can't," said the Queen. "The recipe is in my cookbook, and the cookbook has just been stolen!"

Well, the most likely suspect was the Duchess's Cook, and the cookbook was indeed found in the Duchess's kitchen. The only possible suspects were the Cook, the Duchess, and the Cheshire Cat.

"The Cheshire Cat stole it!" said the Duchess at the trial.

"Oh, yes, I stole it!" said the Cheshire Cat with a grin.

"I didn't steal it!" said the Cook.

As it turned out, the thief had lied and at least one of the others had told the truth.

Who stole the cookbook?

(Source: Alice in Puzzle Land: A Carrollian Tale for Children Under Eighty by Raymond Smullyan)

As in part VII, an initially larger number of possibilities is constrained by the content of the statements to only two possibilities:

• Duchess is truthful; Cheshire Cat is truthful; Cook is lying
• Duchess is lying; Cheshire Cat is lying; Cook is truthful

In the first possible world, the Duchess and Cheshire Cat jointly confirmed that the latter stole the cookbook. But the Cook is lying and therefore also stole the cookbook, resulting in a contradiction. (It seems to be implied here that there was only one thief, which makes sense.) The only other alternative is the latter: the Cook is truthful, and did not steal the cookbook, and both the Duchess and the Cheshire Cat are lying about the guilty party. The only remaining party to take the blame is the Duchess.