The Riddle of Scheherazade: And Other Amazing Puzzles, Ancient and Modern

180 Pages·1997·1.18 MB·English

by  Raymond M. Smullyan

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: 978-0-30781983-3
1. Mathematical recreations. 2. Logic puzzles. I. Title.
QA95.S4997 1997
793.7′4—dc21 96–51505 CIP
v3.1
Contents
Cover
Title Page
Copyright
Preface
BOOK ONE The Grand Question of Scheherazade
I The Source
II In Which Is Related How Scheherazade Entertained the King on the
Thousand-and-Third Night
III Wherein Is Related How Scheherazade Further Entertained the King on the
Thousand-and-Fourth Night
IV The Thousand-and-Fifth Night, in Which Scheherazade Relates Some
Puzzles of Ancient Origin
V The Thousand-and-Sixth Night, in Which Scheherazade Gives the King
Some Problems in Probability
VI The Thousand-and-Seventh Night, in Which Scheherazade Relates Some
Exploits of Some of Ali Baba’s Forty Thieves
VII In Which Scheherazade Relates Some More Puzzles on This Thousand-
and-Eighth Night and Concludes with a Clever Mathematical Observation
VIII In Which Is Related Scheherazade’s Wondrous Account of the
Mazdaysians and Aharmanites
IX The Thousand-and-Tenth Night, in Which Scheherazade Gives a Further
Account of the Mazdaysians and Aharmanites
X In Which Is Related How Scheherazade Entertained the King with Some
Special Items on This Thousand-and-Eleventh Night
XI Scheherazade’s Puzzles and Metapuzzles of the Thousand-and-Twelfth
Night
XII The Thousand-and-Thirteenth Night, in Which Scheherazade Relates the
Story of Al-Khizr
XIII The Grand Question!
BOOK TWO From Scheherazade to Modern Logic
XIV Coercive Logic
XV Right-and Left-Handed Coercion
XVI The Ultimate in Coercive Logic
XVII Variable Liars
XVIII Chinese or Japanese?
XIX Oron and Seth
XX Which Personality?
XXI Oh No!
XXII A Mixed Bag: Some Logic Tricks and Games
XXIII Some Special Problems
XXIV Some Strange Paradoxes!
Solutions to the Scheherazade Puzzles
Other Books by This Author
Preface
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, Gödelian
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

C I
HAPTER
The Source
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 vizier’s 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 day’s 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 Isitsöornot, a work
which—is 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
vizier’s 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
“Isitsöornot” 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 king—the full conclusion of the history of Sinbad the
sailor—.” She then went on to describe one miracle after another—or
rather what seemed in those days to be miracles, but which in our time
are simply common scientific truths—for 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 can’t stand that and I won’t. You have already given me a
dreadful headache with your lies. The day, too, I perceive is beginning to
break—Upon the whole, you might as well get up and be throttled.” And
so poor Scheherazade was executed.
All this according to the Isitsöornot. 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 Isitsöornot.” 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
Isitsöornot, 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 all—partly 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.