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

I guess we should first start analysing from Alice. She was correct. Thus we are left with 2 possiblities.

Take the case where the Rabbit and Duchess were telling the truth.  So straight away, we will take it as Gryphon stole the tarts. Now as we look at what Rabbit said, the Lizard was truthful. From his comments, the cook is definitely telling the truth.. We are not that sure about the Cat and the Caterpillar though. The cook's statement doesn't really help us. because he was trying to imply that a person who had past offenses might be more likely to commit it again. This is not a good statement and we can leave that out. When we look at the second part of the Rabbit's statement, the Knave of hearts must be lying. And that contradicts to the fact that the cook is telling the truth. Thus, the Rabbit and the Duchess must be lying.

Gryphon must have stolen the tarts. Just to do a check, we look at what goes on when both of them were lying. The Gryphon did stole the tarts, as for the Rabbit's statement, The Lizard was lying. Now we are not sure if the cook is lying or not. Also the Knave of Hearts would be telling the truth. And it tallys that when the mad hatter is right, the cook is right too. But their statements doesn't matter.

Posted by Joanna on 2004-04-04 13:39:08