Raymond M. Smullyan - The Riddle of Scheherazade: And Other Amazing Puzzles, Ancient and Modern

THIS IS A BORZOI BOOK
PUBLISHED BY ALFRED A. KNOPF, INC.

Copyright 1997 by Raymond Smullyan

All rights reserved under International and Pan-American Copyright Conventions. Published in the United States by Alfred A. Knopf, Inc., New York, and simultaneously in Canada by Random House of Canada Limited, Toronto. Distributed by Random House, Inc., New York.

http://www.randomhouse.com/

Portions of this work were originally published in Discover magazine.

Library of Congress Cataloging-in-Publication Data
Smullyan, Raymond M.
The riddle of Scheherazade, and other amazing puzzles, ancient and modern / by Raymond Smullyan.1st ed.
p. cm.
eISBN: 978-0-307-81983-3
1. Mathematical recreations. 2. Logic puzzles. I. Title.
QA95.S4997 1997
793.74dc21 9651505 CIP

v3.1

Book One of this volume begins where Edgar Allan Poe left off in his remarkable story The Thousand-and-Second Tale of Scheherazade. In this tale, Poe paints a very different picture of the ultimate fate of Scheherazade than that given in the Arabian Nights! But I have gone him one better and leave you here a puzzle-tale that I believe will intrigue and amuse you, and which ends in a way that naturally leads to a new field called Coercive Logic, which is the start of Book Two. This is followed by some new logic puzzles, logic tricks and games, Gdelian puzzles, and ends with some very baffling paradoxes!

Again my thanks to my editor, Ann Close, and the production editor, Melvin Rosenthal, for their expert help.

Elka Park, New York
September 1996

It will be remembered that in the usual version of the Arabian Nights, a certain monarch, having reason to believe in the infidelity of his queen, not only had her put to death but vowed by his beard and the Prophet to espouse each night the most beautiful maiden in his dominions, and the next morning to deliver her to the executioner. This unexampled inhumanity went on for some time and spread a panic of consternation throughout the city. Instead of the praises and blessings the people had once lavished upon their monarch, they now poured curses on his head. However, the grand viziers elder daughter, Scheherazade, cleverly mastered the situation by marrying the king (against the urgent advice of her father) and arranging that her sister Dinerzade sleep with her in the nuptial chamber. Shortly before daybreak, she began telling her sister a wondrous tale, which the king overheard. When the hour of execution came, the monarch was so curious to hear how the tale ended that he granted her a twenty-four-hour stay of execution. The next night she finished the story, but began another one, which she was unable to finish in time (sic!), and so the king granted her another days stay of execution. This went on for a thousand and one nights, at the end of which the king either forgot his vow or got himself absolved of it, and hence not only spared Scheherazade but ceased carrying out his ferocious edict.

All this, according to the Arabian Nights. Now, Edgar Allan Poe has informed us in his remarkable story The Thousand-and-Second Tale of Scheherazade that the ending as reported in the Arabian Nights is simply not correct! In his own words:

Having had occasion, lately, in the course of some Oriental investigations, to consult the Tellmenow Isitsornot, a work whichis scarcely known at all, even in Europe, and which has never been quoted to my knowledge, by any American. I was not a little astonished to discover that the literary world has hitherto been strangely in error respecting the fate of the viziers daughter, Scheherazade, as that the denouement there given, if not altogether inaccurate, as far as it goes, is at least to blame in not having gone much further. For full information on this interesting topic, I must refer the inquisitive reader to the Isitsornot itself; but, in the meantime, I shall be pardoned for giving a summary of what I there discovered.

Poe then goes on to tell us what happened on the thousand-and-second night: My dear sister, said Scheherazade, now that this odious tax is so happily repealed, I feel that I have been guilty of withholding from you and the kingthe full conclusion of the history of Sinbad the sailor. She then went on to describe one miracle after anotheror rather what seemed in those days to be miracles, but which in our time are simply common scientific truthsfor example, things (light) that travel at the speed of 186,000 miles a second. The king got more and more irritatedly skeptical as Scheherazade went on, until he finally said: Stop! I cant stand that and I wont. You have already given me a dreadful headache with your lies. The day, too, I perceive is beginning to breakUpon the whole, you might as well get up and be throttled. And so poor Scheherazade was executed.

All this according to the Isitsornot. But unknown to its author, whoever that may be, as well as to Edgar Allan Poe, this fascinating book, like the Arabian Nights, is also in error concerning the fate of Scheherazade! It was my good fortune to be allowed to read another oriental book of such a secret nature that I had to swear I would never reveal its title. I can tell you, though, its subtitle, which is A Critique of the Isitsornot. My source is by far the most reliable of all, and goes on to explain that almost everything in the aforementioned volume is correct, but the last sentence is sadly in error. And now, I am happy to be able to report to you the real truth of the entire situation. This truth is more amazing than anything told in either the Arabian Nights or the Isitsornot, and reveals Scheherazade as a female of such fantastic logical ingenuity that she might well be the envy of the greatest logicians of our time! What really happened will now be related:

True, the king did say (in Arabic), Upon the whole, you might as well get up and be throttled. But Scheherazade replied, Whatever pleases Your Majesty pleases me, but I am really sad for your sake, not mine.

Why for my sake? asked the king.

Because of the puzzles I had planned to entertain you with, replied Scheherazade.

Puzzles? said the king. I love puzzles! Will you tell me some tonight if I stay your execution?

I will tell you some every night as long as it pleases Your Majesty to let me live, replied Scheherazade.

And so, on the thousand-and-third night, the puzzles began, and went on for many nights, at the conclusion of which comes the most amazing part of the entire story! The puzzles themselves range from very simple and tricky to subtle and complex, culminating in the grand question of Scheherazade, which may well be the most clever logic puzzle of all time!

I will now set forth the events exactly as recorded in my secret source. Many of the puzzles (though not the best ones) have come down through history and are rather well known. But I will include them allpartly for the sake of those readers who may not be familiar with them, but mainly out of fidelity to my secret source, which is certainly a document of historical importance in its own right and should be treated with respect.