By Raymond M. Smullyan
Various puzzles facing note play and good judgment, arithmetic and philosophy, that includes Alice and the creatures of Wonderland.
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Additional resources for Alice in Puzzle-Land. A Carrollian tale for children under eighty
Well," said the Duchess, "Three believes that One is mad. Four believes that Three and Two are not both mad. Five believes that One and Four are either both mad or both sane. Six believes that One and Two are both sane. Seven believes that Five is mad. As for the Knave of Hearts, he believes that Six and Seven are not both mad. " Is the Knave of Hearts mad or sane? " asked Alice. "Why, the Cook—she thinks that I am mad. " Alice did not see why this was so funny. "Anyway, my dear," continued the Duchess, "I must now be off to the croquet game.
24 Who Is Mad? "Well," replied the Duchess, "the Hatter once expressed the belief that the March Hare does not believe that all three of them are sane. " What can you deduce about these three? AND THESE THREE? "Then there's the Gryphon, the Mock Turtle, and the Lobster," the Duchess began. "I didn't know there was a real lobster around here," replied Alice. " "Oh, yes, there is a real lobster, and he is as big as the Mock Turtle," replied the Duchess. "Anyway, the Lobster once expressed the belief that the Gryphon believes that exactly one of the three is sane.
Alice was a little startled by this interruption of her thoughts. " said the Gryphon. "Here—let me try you on another. " asked Alice. " quickly replied the Gryphon, who was not at all eager to speak about that subject! " "Then I don't think I know it," replied Alice. " Alice inquired. "The Dormouse was fast asleep the whole time, so he don't figure in this puzzle. Anyway, the two were having raspberry tarts with their tea. " *This puzzle is a variant of a famous old puzzle of the American Sam Lloyd.