Which Alice?

196 Pages·2007·1.42 MB·English

PENGUIN BOOKS
ALICE IN PUZZLE-LAND
Born in New York City, Raymond Smullyan received his M.S.
from the University of Chicago and his Ph.D. from Princeton
University. He has taught at Dartmouth and Princeton and is
currently on the faculty of Lehman College in New York. In
addition to being a professor of mathematical logic, he has per-
formed as a professional magician. His other books are Theory
of Formal Systems, First-Order Logic, The Tao Is Silent, What
Is the Name of This Book?, This Book Needs No Title, The
Chess Mysteries of Sherlock Holmes, The Chess Mysteries of the
Arabian Knights, and The Lady or the Tiger?. Mr. Smullyan
has also contributed to collective works on mathematics and has
written for Scientific American and other magazines.

ALICE IN
PUZZLE-LAND

A Carrollian Tale for Children Under Eighty

RAYMOND SMULLYAN

With an introduction by Martin Gardner

ILLUSTRATED BY GREER FITTING

PENGUIN BOOKS
Penguin Books Ltd, Harmondsworth,
Middlesex, England
Penguin Books, 40 West 23rd Street.
New York, New York 10010, U.S.A.
Penguin Books Australia Ltd, Ringwood,
Victoria, Australia
Penguin Books Canada Limited, 2801 John Street.
Markham, Ontario, Canada L3R 1B4
Penguin Books (N.Z.) Ltd, 182-190 Wairau Road,
Auckland 10, New Zealand

First published in the United States of America by
William Morrow and Company. Inc., 1982 Published
in Penguin Books 1984

Copyright © Raymond M. Smullyan, 1982 All
rights reserved Reprinted 1984

LIBRARY OF CONGRESS CATALOGING IN PUBLICATION DATA
Smullyan, Raymond M.
Alice in puzzle-land.
Originally published: New York: Morrow. 1982.
Summary: A range of puzzles dealing with word play
and logic, mathematics and philosophy, featuring Alice
and the creatures of Wonderland.
1. Puzzles. [1. Puzzles] I. Carroll. Lewis, 1832-1898.
Alice's adventures in Wonderland. II. Title.
GV1493.S624 1984 793.73 83-25141 ISBN 0 14
00.7056 7

Printed in the United States of America by
R. R. Donnelley & Sons Company, Harrisonburg, Virginia
Set in Baskerville

Except in the United States of America, this book is
sold subject to the condition that it shall not, by way
of trade or otherwise, be lent, re-sold, hired out, or
otherwise circulated without the publisher's prior
consent in any form of binding or cover other than
that in which it is published and without a similar
condition including this condition being imposed on
the subsequent purchaser
Preface

This book, like Alice's Adventures in Wonderland and Through
the Looking-Glass, is truly for readers of all ages. By this I do not
mean that all of it is for every age, but for every age, some of it is for
that age. For example, the extremely elementary puzzles of Chapter
Four are particularly for the very young reader who has not yet
learned algebra (and, as the Gryphon wisely says, "You don't needs
no algebra!"). At the opposite extreme are the prize puzzles of
Chapters Five and Nine; these will intrigue the expert as much as
the beginner. Chapter Ten has a special and unusual status.
This year (1982) marks the one-hundred-fiftieth anniversary of
the birth of Lewis Carroll, to whom this book is dedicated. I believe
Carroll would have particularly enjoyed the Humpty chapter, which
deals with paradoxes (one of Carroll's favorite themes), but in the
inimitable manner of Humpty Dumpty. This chapter was great fun
to write (as were all the other chapters!). Indeed, the whole project
of re-creating the spirit of Carroll's writings has been a delight from
beginning to end.
My heartfelt thanks go to Greer Fitting, for all the lovely
illustrations; to Maria Guarnaschelli, for her excellent editorship;
and to Iver Kern, who carefully went through the entire manuscript
and provided a host of helpful suggestions.

—RAYMOND SMULLYAN

Elka Park, New York
January 1, 1982

v

Contents

PREFACE v
INTRODUCTION viii

Part I—Wonderland Puzzles 1

1. WHICH ALICE? 3
2. WHO STOLE THE TARTS? 7
3. WHO IS MAD? 20
4. THE GRYPHON AND THE MOCK TURTLE 30
5. THE KING'S STORY 52

Part II—Looking-Glass Logic 63

6. THE TWELFTH QUESTION 65
7. TWEEDLEDUM OR TWEEDI.EDEE? 74
8. AND THAT'S THE BEAUTIFUL PART OF IT! 85
9. THE WHITE KNIGHT COULDN'T QUITE REMEMBER 101
10. LOOKING-GLASS LOGIC 114
11. THE RED KING'S THEORY 127
12. WHICH ALICE? 133

SOLUTIONS TO THE PUZZLES 137
Introduction

Raymond Smullyan is a unique set of personalities that
includes a philosopher, logician, mathematician, musician, magi-
cian, humorist, writer, and maker of marvelous puzzles. Because he
is a skillful writer and humorist, he enjoys presenting his puzzles in
narrative forms that often parody great works of popular fiction.
And he does this so well that his puzzle books are, incredibly, a
pleasure to read even if you never try to solve a single puzzle!
Ray's first puzzle book (I call him Ray because we are old friends)
was titled What Is the Name of This Book? It introduced his knights
(who speak only truth), his knaves (who always lie), and such
characters as Inspector Craig, Bellini and Cellini, Count Dracula,
and Lewis Carroll's Alice and the creatures of Wonderland. Of
course readers who actually worked on the puzzles of this book,
whatever its name, found the book doubly rewarding, and at the
end they were given a remarkable bonus—an insight into Kurt
Gödel's famous proof, the greatest of modern mathematical discov-
eries.
Ray's first collection of original chess problems, The Chess Mysteries
of Sherlock Holmes, surrounds each problem with a pastiche about
Holmes and Watson. So faithful are these tales to the spirit of the
canon that Sherlockians who never play a game of chess can enjoy
them for the dialogue alone. A second collection of chess problems,
The Chess Mysteries of the Arabian Knights, embed the problems in
parodies of the tales of Scheherazade.

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