Also by RaymondM Smullyan THEORY OF FORMAL SYSTEMS FIRST ORDER LOGIC THE TAO IS SILENT �&1�mTIl@ITilcQl JF!{lo�mTIlTIll n n�<IDm1 I The Riddle of Dracula and Other Logical Puzzles PRENTICE-HALL, INC., Englewood Cliffs, New Jersey WhatIs the Name of This Book?-The Riddle of Dracula and Other Logical Puzzles, by Raymond M. Smullyan Copyright © 1978 by Raymond M. Smullyan All rights reserved. No part of this book may be reproduced in any form or by any means, except for the inclusion of brief quotationsin a review, without permission in writing from the publisher. Printedin the United States of America Prentice-HallInternational In c., London Prentice-Hall of Australia, Pty. Ltd., Sydney Prentice-Hall of Canada, Ltd., Toronto Prentice-Hall of India Private Ltd., New Delhi Prentice-Hall of Japan, Inc., Tokyo Prentice-Hall of Southeast Asia Pte. Ltd., Singapore Whitehall Books Limited, Wellington, New Zealand 10 9 8 7 6 5 4 3 2 1 Library of Congress Cataloging in Publication Data Smullyan, Raymond M. What is the name of this book? 1. Puzzles. I. Title GV1493.S63 793.7'3 77-18692 ISBN 0-13-955088-7 Dedicated to Linda Wetzel and Joseph Bevando, whose wise counsels have been invaluable. Contents Part One ilLOGICAL RECREATIONS 1. Fooled? 3 2. Puzzles and Monkey Tricks 7 Solutions 14 3. Knights and Knaves 20 Solutions 26 4. Alice in the Forest of Forgetfulness 36 Solutions 46 Part Two. PORTIA'S CASKETS AND OTHER MYSTERIES 5. The Mystery of Portia's Caskets 55 Solutions 62 6. From the Files of Inspector Craig 67 Solutions 74 7. How to Avoid Werewolves-And Other Practical Bits of Advice 82 Solutions 90 8. Logic Puzzles 99 Solutions 110 9. Bellini or Cellini? 118 Solutions 124 Part Three � WEIRD TALES 10. The Island of Baal 135 Solutions 142 11. The Island of Zombies 149 Solutions 153 12. Is Dracula Still Alive? 158 Solutions 169 Part Four. LOGIC. IS A MANY=S:PLENDORED THING 13. Logic and Life 183 14. How to Prove Anything 200 15. From Paradox to Truth 213 Solutions 220 16. Godel's Discovery 225 My Thanks to _______________ First I wish to thank my friends Robert and Ilse Cowen and their ten-year-old-daughter, Lenore, who went through this manuscript together and provided many helpful sugges­ tions. (Lenore, incidentally, suspected all along the true answer to the key question of Chapter 4: Does Tweedledoo really exist, or is he merely a fabrication of Humpty Dumpty?) I am grateful to Greer and Melvin Fitting (authors of the charming and useful book In Praiseof Simple Things) for their kindly interest in my work and for having called it to the attention of Oscar Collier of Prentice-Hall. I also think Melvin should be thanked for actually appearing in this book (thereby refuting my proof that he couldn't appear!). It was a pleasure working with Oscar Collier and others at Prentice-Hall. Mrs. Ilene McGrath who first copy-edited the text made many suggestions which I have gratefully adopted. I thank Dorothy Lachmann for her expert handling of production details. I wish to again mention my two dedicatees, Joseph Bevando and Linda Wetzel, who have been heart and soul with this book from its very inception. My dear wife, Blanche, has helped me with many a query. It is my hope that this book will enable her to decide whether she is married to a knight or a knave. • I 110 Fooled? 1. Was I Fooled? ____________ My introduction to logic was at the age of six. It happened this way: On April 1, 1925, I was sick in bed with grippe, or flu, or something. In the morning my brother Emile (ten years my senior) came into my bedroom and said: "Well, Raymond, today is April Fool's Day, and I will fool you as you have never been fooled before!" I waited all day long for him to fool me, but he didn't. Late that night, my mother asked me, "Why don't you go to sleep?" I replied, "I'm waiting for Emile to fool me." My mother turned to Emile and said, "Emile, will you please fool the child!" Emile then turned to me, and the following dialogue ensued: Emile I So, you expected me to fool you, didn't you? Raymond I Yes. Emile I But I didn't, did I? Raymond I No. Emile I But you expected me to, didn't you? Raymond I Yes. Emile I So I fooled you, didn't II Well, I recall lying in bed long after the lights were turned out wondering whether or not I had really been fooled. On the one hand, if I wasn't fooled, then I did not get what I FOOLED 3 expected, hence I was fooled. (This was Emile's argument.) But witheq ual reason it can be said that ifI was fooled, then I did get what I expected, so then, in what sense was I fooled. So, was I fooled or wasn't I? I shall not answer this puzzle now; we shall return to it in one form or another several times in the course of this book. It embodies a subtle principle which shall be one of our major themes. 2. Was I Lying? _____________ A related incident occurred many years later whe:h I was a graduate student at the University of Chicago. I was a pro­ fessional magician at the time, but my magic business was slow for a brief period and I had to supplement my income somehow. I decided to try getting a job as a salesman. I applied to a vacuum cleaner company and had to take an aptitude test. One of the questions was, "Do you object to telling a little lie every now and again?" Now, at the time I definitely did object-I particularly object to salesmen lying and misrepresenting their products. But I thought to myself that if I truthfully voiced my objection, then I wouldn't get the job. Hence I lied and said "No." Riding back home after the interview, I had the fol­ lowing thoughts. I asked myself whether I objected to the lie I had given to the sales company. My answer was "No." Well, now, since I didn't object to that particular lie, then it follows that I don't object to all lies, hence my "No" answer on the test was not a lie, but the truth! To this day it is not quite clear to me whether I was lying or not. I guess logic might require me to say that I was telling the truth, since the assumption that I was lying leads to a contradiction. So, logic requires me to believe I was telling the truth. But at the time, I sure fe lt as though I was lying! Speaking of lying, I must tell you the incident of Bertrand 4 LOGICAL RECREATIONS Russell and the philosopher G. E. Moore. Russell desa cribed Moore'as one of the most truthful people he had ever met. He once asked Moore, "Have you ever lied?" Moore replied, "Yes." In describingthis incident, Russellwro te: "I think this is the only lie Moore ever told!" Thein cident of my experience with the sales company raises the question of whether it is possible for a person to lie without knowing it. I would answer "No." To me, lying means making a statement, not which is false, but which one believes to be false. Indeed if a person makes a statement which happens to be true, but which he believes to be false, then I would say he is telling a lie. I read of the following incident in a textbook on abnormal psychology. The doctors in a mental institution were thinking of releasing a certain schizophrenic patient. They decided to give him a lie-detector test. One of the questions they asked him was, "Are you Napoleon?" He replied, "No." The machine showed he was lying. I also read somewhere the following incident showing how animals can sometimes dissimulate. An experiment was conducted with a chimpanzee in a room in which a banana was suspended by a string from the center of the ceiling. The banana was too high to reach. The room was empty except for the chimp, the experimenter, the banana and string, and several wooden boxes of various sizes. The purpose of the' experiment was to determine whether the chimp was clever enough to make a scaffolding of the boxes, climb up, and reach the banana. What really happened was this: The experimenter stood in the corner of the room to watch the proceedings, The chimp came over to the corner and anxiously tugged the experimenter by the sleeve indi­ cating that he wanted him to move. Slowly the experimenter followed the chimp. When they came to about the center of the room, the chimp suddenly jumped on his shoulders and got the banana. FOOLED 5 3 .. The Joke Was on Me A fellow graduate student of mine at the University of Chicago had two brothers, aged six and eight. I was a frequent visitor to their house and often did tricks for the children. One day 1 came and said, "1 have a trick in whichI could turn you both into lions." To my surprise, one of them said, "Okay, turn us into lions." 1 replied, "Well, uh, really, uh, I shouldn't do that, because there is no way 1 could tum you back again." The little one said, "I don't care; 1 want you to tum us into lions anyway." 1 replied, "No, really, there's no way 1 can tum you back." The older one shouted, "I want you to turnus into lions!" The little one then asked, "How do you tum us into lions?" I replied, "By saying the magic words." One of them asked, "What are the magic words?" 1 replied, "If I told you the magic words, I would be saying them, and so you would tum into lions." They thought about this for a while, and then one of them asked, " Aren't there any magic words which would bring us back?" 1 replied: "Yes, there are, but the trouble is this.