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The Island of Knights and Knaves

This version taken from What Is the Name of This Book, by Raymond Smullyan (Englewood Cliffs, NJ: Prentice-Hall, Inc., 1978.

There is a wide variety of puzzles about an island in which certain inhabitants called knights always tell the truth, and others called knaves always lie. It is assumed that every inhabitant of the island is either a knight or a knave.

Puzzle 1

Three of the inhabitants—A, B and C—were standing together in a garden. A stranger passed by and asked A, "Are you a knight or a knave?" A answered, but rather indistinctly, so the stranger could not make out what he said. The stranger asked B, "What did A say?" B replied, "A said that he is a knave." At this point the third man, C, said, "Don't believe B; he is lying!"

The question is, what are B and C?

Puzzle 2

Suppose you visit the island of knights and knaves. You come across two of the inhabitants lazily lying in the sun. You ask one of them whether the other one is a knight, and you get a (yes-or-no) answer. Then you ask the second one whether the first one is a knight. You get a (yes-or-no) answer.

Are the two answers necessarily the same?


Puzzle 1:  It is impossible for either a knight or knave to say, "I'm a knave," because the knight wouldn't make the false statement that he is a knave, and a knave wouldn’t make the true statement that he is a knave. Therefore, A never did say that he was a knave. So B lied when he said that A said that he was a knave. Hence B is a knave. Since C said that B was lying and B was indeed lying, then C spoke the truth, hence he is a knight. Thus B is a knave and C is a knight. (It is impossible to know what A is.)

Puzzle 2:  Yes they are. If they are both knights, then they will both answer "Yes." If they are both knaves, then again they will both answer "Yes." If one is a knight and the other a knave, then the knight will answer "No," and the knave will also answer "No."

The Emperor's New Clothes
By Hans Christian Andersen

The chamberlains, who were to carry the train, fumbled with their hands on the ground, as if they were lifting up a train. Then they pretended to hold something up in their hands; they dare not let people know that they could not see anything.

And so the Emperor marched in the procession under the beautiful canopy, and all who saw him in the street and out of the windows exclaimed, "How marvelous the Emperor's new suit is! What a long train he has! How well it fits him!" Nobody would let others know that he saw nothing, for then he would have been unfit for his office or too stupid. None of the Emperor's clothes had ever been such a success.

"But he has nothing on at all," said a little child. "Good heavens! Hear what the little innocent says!" said the father, and then each whispered to the other what the child said. "He has nothing on—a little child says he has nothing on at all!" cried all the people at last. And the Emperor too was feeling very worried, for it seemed to him that they were right, but he thought to himself, "All the same, I must keep the procession going now." And he held himself stiffer than ever, and the chamberlains walked on and held up the train which was not there at all.


Another enduring image of honesty—this one from the negative side—derives from a famous scene in Carlo Lorenzini's classic nineteenth-century Italian tale Pinocchio. Walt Disney's animated cartoon version no doubt secured greater currency for the image that it might otherwise have enjoyed; but whatever route, the liar's lengthened nose is now part and parcel of the American cartoonist's instantly recognized repertoire of visual symbols. Carlo Lorenzini—who wrote the tale under the name of his mother’s home town, Collodi—produced this classic not long before his death in 1890.

"And the four pieces—where have you put them?" asked the Fairy.

"I have lost them!" said Pinocchio; but he was telling a lie, for he had them in his pocket.

He had scarcely told the lie when his nose, which was already long, grew at once two fingers longer.

"And where did you lose them?"

"In the wood near here."

At this second lie his nose went on growing.

"If you have lost them in the wood near here," said the Fairy, "we will look for them, and we shall find them: because everything that is lost in that wood is always found."

"Ah! now I remember all about it," replied the puppet, getting quite confused; "I didn't lose the four gold pieces, I swallowed them inadvertently whilst I was drinking your medicine."

At this third lie his nose grew to such an extraordinary length that poor Pinocchio could not move in any direction. If he turned to one side he struck his nose against the bed or the window-panes, if he turned to the other he struck it against the walls or the door, if he raised his head a little he ran the risk of sticking it into one of the Fairy’s eyes.

And the Fairy looked at him and laughed.

"What are you laughing at?" asked the puppet, very much confused, and anxious at finding his nose growing so prodigiously.

"I am laughing at the lie you have told."

"And how can you possibly know that I have told a lie?"

"Lies, my dear boy, are found out immediately, because they are of two sorts. There are lies that have short legs, and lies that have long noses. Your lie, as it happens, is one of those that have a long nose."

Pinocchio, not knowing where to hide himself for shame, tried to run out of the room; but he did not succeed, for his nose had increased so much that it could no longer pass through the door.

The Fairy, as you can imagine, allowed the puppet to cry and to roar for a good half-hour over his nose, which could no longer pass through the door of the room. This she did to give him a lesson, and to correct him of the disgraceful fault of telling lies—the most disgraceful fault that a boy can have. But when she saw him quite disfigured, and his eyes swollen out of his head from weeping, she felt full of compassion for him. She therefore beat her hands together, and at that signal a thousand large birds called woodpeckers flew in at the window. They immediately perched on Pinocchio's nose, and began to peck at it with such zeal that in a few minutes his enormous and ridiculous nose was reduced to its usual dimensions.