A Brief History of Puzzles E-Book

William Hartston

• Herausgeber: Atlantic Books
• Kategorie: Bildung
• Sprache: Englisch

Veröffentlichungsjahr: 2019

Beschreibung

From ancient riddles to modern Sudoku, people have been fascinated by puzzles. Whether they are seen as a glorious waste of time, a harmless way to spend a train journey or a valuable way of exercising the mind, the lure of puzzles has been irresistible. By using over a hundred of examples of the most mindbending, the most challenging, the most satisfying, or simply the most humorous of puzzles throughout the ages, William Hartston traces the development of brainteasers of all varieties and the increasing ingenuity of puzzle setters from ancient civilisations to modern puzzle crazes.

Leseprobe

First published in hardback in Great Britain in 2019

by Atlantic Books, an imprint of Atlantic Books Ltd.

Copyright © William Hartston, 2019

The moral right of William Hartston to be identified as the author of this work has been asserted by him in accordance with the Copyright, Designs and Patents Act of 1988.

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of both the copyright owner and the above publisher of this book.

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A CIP catalogue record for this book is available from the British Library.

Hardback ISBN: 978-1-78649-426-9

E-book ISBN: 978-1-78649-428-3

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Illustrations by Nathan Burton

Printed in Great Britain

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CONTENTS

Acknowledgements

0    Primeval Puzzle Prelude

1    Medieval Maths, Mysteries and Merriment

2    Parisian Perplexities, Problems and Posers

3    The Great Victorian Puzzlers

4    Puzzles Worthy of the Name

5    More Word Puzzles

6    The Logic of Hats

7    The Most Baffling Logic of All

8    Weights, Measures, Speed

9    Psychological Puzzles

10  Miscellaneous and Mysterious

The Prize Puzzle

Solutions

By the same author

How to Cheat at Chess

The Penguin Book of Chess Openings

Soft Pawn

The Ultimate Irrelevant Encyclopedia

The Kings of Chess

Chess – The Making of the Musical

The Drunken Goldfish and Other Irrelevant Scientific Research

How was it for you, Professor?

The Guinness Book of Chess Grandmasters

Teach Yourself Chess

Teach Yourself Better Chess

The Book of Numbers: The Ultimate Compendium of Facts About Figures

Mr Hartston’s Most Excellent Encyclopedia of Useless Information

Forgotten Treasures: A Collection of Well-Loved Poetry (Vols 1, 2 and 3)

The Things That Nobody Knows

Even More Things That Nobody Knows

The Bumper Book of Things That Nobody Knows

Sloths

ACKNOWLEDGEMENTS

From my childhood to my years as a chess player and mathematician and beyond, I have always held a fascination for the challenge of puzzles and I must express great gratitude to the many people who have fuelled this passion. First came writers such as Lewis Carroll, Henry Dudeney and Sam Loyd, whose books and articles awoke my interest in the recreational side of thinking. More recently, I have been inspired, amused and infuriated by modern puzzlers such as Martin Gardner, Raymond Smullyan, Chris Maslanka, David Bodycombe, Alex Bellos and Prof. David Singmaster, all of whom have unwittingly given me ideas for this book. These, incidentally, are among the best names to look out for if you’re looking for the most tantalizing books of puzzles. I am happy to count several of these among my friends and they are the most mentally stimulating company anyone could wish for.

I must also thank all those who have put up with my endless puzzling while I have been collecting puzzles for this book, and my Gogglebox companion Josef Kollar who has been as willing to tantalize me with puzzles as I am with him.

Finally, I should like to thank Cambridge psychology professors Trevor Robbins and Barbara Sahakian for treating me to a splendid breakfast during which they explained how puzzles, quite apart from being fun, may actually be good for you.

PRIMEVAL PUZZLE PRELUDE

‘Evolution has developed the brain’s ability to solve puzzles, and at the same time has produced in our brain a pleasure of solving problems.’

Martin Gardner, recreational mathematics writer, interviewed in the New York Times,19 October 2009

PUZZLE 1

An infuriating fellow took 120 puzzles to try out on some schoolchildren, which, by a remarkable coincidence, is the number of puzzles for you to solve in this book. The first-year children solved some of these, so he gave the second year a larger number of different puzzles, which they also solved. The third year were given even more, as were the fourth year and the fifth year. Each time, the number of puzzles went up by the same amount and at the end he had used up all his puzzles. The total number given to the three highest years was exactly seven times the number given to the first two years. How many puzzles were given to each year?

The answer to Puzzle 1, and the other 119 numbered puzzles in this book, can be found in the Solutions section at the end of this book.

The language used in Puzzle 1 is different and the scenario modernized, but the puzzle is basically problem number 40 in the Rhind Papyrus, a remarkable ancient Egyptian mathematical manuscript that has a good claim on being the oldest puzzle book. Compiled by a scribe called Ahmes or Ahmose around 1550 BC, but known to have borrowed items from works two or three centuries older, it was bought by the Scottish antiquarian Alexander Henry Rhind in Luxor in 1858 and has been kept in the British Museum since 1865.

Containing 91 mathematical problems, divided into arithmetic, geometry and miscellaneous, the papyrus is essentially a mathematics textbook written in a teasing manner to encourage readers to develop the necessary techniques themselves. A modern reader, of course, would find it easy to solve the puzzle given above by using a little algebra, but the ancient Egyptians had to improvise other methods. The first algebra treatise was written around AD 830 by the medieval Persian mathematician, Muhammad ibn Mūsā al-Khwārizmī. He gave his treatise a long name in Arabic, which included the word al-ğabr, meaning ‘the reunion of broken parts’, and puzzlers and mathematicians have called his method ‘algebra’ ever since.

Long before Ahmes set brush to papyrus in Luxor, however, that same city, under its ancient name of Thebes, was the setting for a supposedly much older puzzle of Greek myth. According to the ancients, the city lived in terror of the Sphinx, a ferocious creature with the head of a woman and the body of a lion – in some versions also the wings of an eagle and the tail of a serpent – who had been sent by the gods to punish the Thebans for ancient crimes. The Sphinx was said to kill people who wished to enter Thebes by strangulation (incidentally, the connection between the Sphinx and our similarly named ‘sphincter’ muscles is that both words are derived from a Greek verb meaning to squeeze or strangle) – but, to give her victims a chance, she would first pose them a riddle. If they could not solve it, they were killed.

Nobody ever solved the riddle until Oedipus came along. The riddle the Sphinx asked Oedipus was this: ‘What goes in the morning upon four feet, in the afternoon upon two feet, and in the evening on three feet?’ Oedipus gave the answer ‘Man’, who crawls on all fours in the morning of his life, walks on two legs in the afternoon of his life, and needs a third leg in the form of a walking stick to get around in the evening of his old age. The Sphinx was so annoyed that Oedipus had solved the riddle that she threw herself to her death from a clifftop and Thebes was saved from her terror.

The idea of a hero being prepared to risk his life on his ability to solve riddles has been very powerful throughout history. One modern example comes in J. R. R. Tolkien’s The Hobbit, where Bilbo Baggins and Gollum pose each other riddles. One of Bilbo’s riddles is clearly inspired by the myth of the Sphinx: ‘No-legs lay on one-leg, two-legs sat near on three-legs, four-legs got some.’

The explanation, rather more convoluted than Oedipus’ answer, is that it refers to a fish (no legs) lying on a pedestal table (one leg), at which a man (two legs) is sitting on a three-legged stool and a cat (four legs) gets the scraps.

Another potentially fatal riddle format is seen in the plot of Puccini’s opera Turandot, where the icy princess of the title sets her suitors three riddles in a thoroughly sadistic Who Wants To Marry A Princess? game show format: if they want to wed her, they must answer three riddles; if they get them wrong, their heads are lopped off.

Puccini got the plot from a work by Friedrich Schiller, which was itself an adaptation of a play by the eighteenth-century Italian dramatist and count, Carlo Gozzi. But Gozzi took the story from a work by the twelfth-century Persian poet Nizami Ganjavi, which comprises seven stories, one for each day of the week. Tuesday’s tale was about a cold Russian princess called Turan-Dokht. Puccini’s operatic version moves the story to China, where Prince Calaf falls in love at first sight with the imperious princess Turandot and submits himself to her riddles.

The first riddle is this: ‘In the gloomy night, an iridescent phantom flies. It spreads its wings and rises over infinite, black humanity. Everyone invokes it, everyone implores it! But the phantom disappears at dawn to be reborn in the heart.’

Calaf gives the answer ‘Hope’, which is deemed correct, although I am not convinced it completely satisfies the specifications in Turandot’s riddle.

The second riddle is: ‘It flickers like flame, but is not flame! Sometimes it rages. It is feverish, impetuous, burning, but idleness changes it to languor. If you are lost or defeated, it turns cold. If you dream of winning, it bursts into flame. It has a faint voice, but you listen; it gleams as bright as the sunset!’

Calaf’s answer is ‘Blood’, which sets him up for the final question: ‘Ice that sets you on fire, and through your fire becomes more frosty! Immaculate but dark, if it sets you free, you become a slave! If you become a slave, it makes you king.’

That’s an easy one, and Calaf sees that the answer is Turandot herself.

In ancient times, however, puzzles did not appear only in stories but seem to have been a part of everyday life. Drawings of labyrinths in ancient Greece and Egypt have been dated to before 2000 BC; the ancient Romans had puzzle locks with secret levers; the ancient Chinese from as early as the third century had chains of puzzle rings designed to challenge people to untangle them. The existence of such puzzles in many cultures suggests that people have always liked to tease each other by setting them problems.

The earliest puzzles of all took the form of riddles, mechanical devices and teasing tricks, and their appeal has lasted throughout the ages. The problems that involve pure thinking may have begun with maths lessons in ancient Egypt, but they have undergone a gentle transition to become something less didactic and more fun – and frustrating! And that transition is the subject of our first proper chapter on puzzles.

MEDIEVAL MATHS, MYSTERIES AND MERRIMENT

‘The ingenious study of making and solving puzzles is a science undoubtedly of most necessary acquirement, and deserves to make a part in the meditation of both sexes.’

Sir Thomas Fitzosborne, pseudonym of William Melmoth (1710–1799)

PUZZLES MAY HAVE begun in ancient times with riddles and teasing ways to introduce amusement into maths teaching but it took many more centuries before puzzles for puzzlement’s sake alone became acceptable.

Remarkably, the earliest known collection of something similar to modern recreational puzzles dates back more than 1,200 years. It was probably assembled by Alcuin of York (c.735–804), a highly influential scholar and reformer of the early Christian church who acted as an adviser to the court of Charlemagne.

I say ‘probably’ because there is no definite evidence that the puzzles associated with Alcuin were actually composed or even just collected by him – although the puzzles were discovered at Charlemagne’s court and one of Alcuin’s letters to Charlemagne refers to ‘subtle figures of arithmetic, for pleasure’, which he says are included in the correspondence. Several copies of these Propositiones ad acuendos iuvenes (Propositions to Sharpen the Young) have been found, containing either 53 or 56 problems, presumably depending on which scribe copied the original manuscript. Several of the problems have also been found to date from even earlier times, which supports the view that Alcuin, or whoever assembled the manuscript in the first place, was essentially a collector of puzzles rather than their originator. They may have been intended, in Alcuin’s words, as teaching devices to stimulate young minds, but the tone is impressively playful. Here are three of them, for which the solutions may be found at the end of this book.