The Queen of Hearts had just finished making a marvelous batch of tarts, and had gone off to fetch her husband, the King of Hearts. When she came back, the tarts had vanished!

A huge investigation was put forth, and across the land the knights of the king searched high and low for the tarts. Fortunately, they were discovered on a beach, just moments before being devoured by the Gryphon and the Mock Turtle. Both were brought to trial before the King. In the course of the subsequent investigation, it was determined that one of them had stolen the tarts, but not both of them.

At the trial, the following witnesses came forward to make statements:

Duchess: The Gryphon never stole the tarts!
Cook: But he had stolen things in the past.
Cheshire Cat: Well, the Mock Turtle has stolen things in the past.
Catarpillar: The Cheshire Cat has stolen things in the past!
March Hare: The Cook and the Cheshire Cat are both right.
Dormouse: The Cook and the Caterpillar are both right.
Mad Hatter: Either the Cheshire Cat or the Caterpillar is right, and maybe both.
Bill the Lizard: Either the March Hare or the Dormouse is right, and maybe both.
Knave of Hearts: The Cook and the Mad Hatter are both right.
The White Rabbit: Bill the Lizard is right, and the Knave of Hearts is wrong!

There was dead silence as everyone tried to puzzle through all of the statements. The Queen, growing frustrated, was just about to order everyone's head cut off, when Alice stood up.

Alice: It just so happens that the White Rabbit and the Duchess are either both telling the truth or both lying.

Now, since we know that Alice never tells a lie, can you work out who stole the tarts?

Adapted from Raymond Smullyan's Alice in Puzzleland

If either the White Rabbit or the Duchess are both telling the truth, then the Mock Turtle stole the tart. However, if both are lying, then the Gryphon stole it.

Let’s assume that both are telling the truth.

For White Rabbit’s statement to be true, both the antecedent (“Bill the Lizard is right”) and the consequent (“the Knave of Hearts is wrong”) must be true. If either one is false, then both the White Rabbit and the Duchess are lying.

So, let’s assume the consequent is right—that is, that the knave of hearts is wrong.

This entails:

Cook is false-->Gryphon stole things in the past.
Mad Hatter is false--> both Cheshire cat and Caterpillar are false.
Cheshire cat is false--> Mock Turtle never stole things in past.
Caterpillar is false--> Cheshire Cat never stole things in past.

Now, let’s assume the antecedent is right—that is, that Bill the Lizard is right.

This entails the truth of either the March Hare or the Dormouse being true.

If March Hare is true--> Cook is true and Cheshire cat is true.
If Dormouse is true--> Cook is true and Caterpillar is true.

HOWEVER, if consequent was true (as assumed earlier), then it was said that the Cook, Caterpillar, and Cheshire Cat are all false. Three contradictions here! Thus, the antecedent is false, which makes White Rabbit’s entire statement false. Thus the White Rabbit and the Duchess are both lying. The Gryphon did it.

Posted by Charlie on 2004-05-10 15:33:25