The Canterbury Puzzles, and Other Curious Problems

Part 1

Transcriber's note:

In mathematical expressions the carat character (^) indicates that the following term is an exponent.

THE CANTERBURY PUZZLES

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PRESS OPINIONS ON "THE CANTERBURY PUZZLES."

"It is a book of remarkable ingenuity and interest."--Educational Times.

"The most ingenious brain in England ... a fascinating new book."--Evening News.

"A capital book of posers."--Daily News.

"The Puzzles ... reach the limit of ingenuity and intricacy; and it is well for the sanity of his readers that the author gives a list of solutions at the end of the book."--Observer.

"A book that will provide much entertainment for Christmas gatherings ... ingenious puzzles and problems invented by 'Sphinx,' the Puzzle King."--The Captain.

"Mr. Dudeney, whose reputation is world-wide as the puzzle and problem maker of the age ... sure to find a wide circulation ... as attractive in appearance as its contents are fascinating."--English Mechanic and World of Science.

"An exceedingly ingenious constructor and solver of fascinating puzzles, mathematical and otherwise."--School Guardian.

"A book which ought to be highly popular ... it is all mighty ingenious, and very intelligently put before the reader."--Sheffield Telegraph.

"It is matter for delight that Mr. Henry E. Dudeney has collected into a volume those mysterious puzzles of his which have appeared in many journals ... contains quite a number of ingenious new mental problems ... a valuable introduction."--The Lady.

"For the long winter evenings Mr. Dudeney's book of puzzledom is to be recommended. Mr. Dudeney has made a study of every kind of puzzle there is ... he supplies you with every kind of brain-twister."--The Daily Chronicle.

"Took up more of the reviewer's time than he could well afford to give it; he wanted to solve some of the curious problems that it contains, and for ingenious persons who want employment on a wet day, he promises from it abundant scope."--Yorkshire Post.

"A well-known master puzzler ... provides an abundance of seasonable occupation for the ingenious, with an introduction on the general question of puzzles, which is one of the most interesting parts of the book. He is a skilful inventor."--Nottingham Guardian.

"Will enjoy the entertainment provided ... ingenious and witty."--The Guardian.

"Extremely ingenious book, which abounds in problems that will keep the reader busy for hours--until in despair he turns to the answers at the end."--Manchester Guardian.

"The setting of these perplexities is novel ... a dramatic background being thus provided which prevents too great aridity.... The book should be much in request."--The Morning Leader.

THE CANTERBURY PUZZLES

By the same Author "AMUSEMENTS IN MATHEMATICS" 3s. 6d.

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First Edition, 1907

THE CANTERBURY PUZZLES

And Other Curious Problems

HENRY ERNEST DUDENEY

Author of "Amusements in Mathematics," Etc.

Part 2

Second Edition (With Some Fuller Solutions and Additional Notes)

Thomas Nelson and Sons, Ltd. London, Edinburgh, and New York 1919

CONTENTS

PREFACE 9

INTRODUCTION 11

THE CANTERBURY PUZZLES 23

PUZZLING TIMES AT SOLVAMHALL CASTLE 58

THE MERRY MONKS OF RIDDLEWELL 68

THE STRANGE ESCAPE OF THE KING'S JESTER 78

THE SQUIRE'S CHRISTMAS PUZZLE PARTY 86

ADVENTURES OF THE PUZZLE CLUB 94

THE PROFESSOR'S PUZZLES 110

MISCELLANEOUS PUZZLES 118

SOLUTIONS 163

INDEX 251

PREFACE

When preparing this new edition for the press, my first inclination was to withdraw a few puzzles that appeared to be of inferior interest, and to substitute others for them. But, on second thoughts, I decided to let the book stand in its original form and add extended solutions and some short notes to certain problems that have in the past involved me in correspondence with interested readers who desired additional information.

I have also provided--what was clearly needed for reference--an index. The very nature and form of the book prevented any separation of the puzzles into classes, but a certain amount of classification will be found in the index. Thus, for example, if the reader has a predilection for problems with Moving Counters, or for Magic Squares, or for Combination and Group Puzzles, he will find that in the index these are brought together for his convenience.

Though the problems are quite different, with the exception of just one or two little variations or extensions, from those in my book Amusements in Mathematics, each work being complete in itself, I have thought it would help the reader who happens to have both books before him if I made occasional references that would direct him to solutions and analyses in the later book calculated to elucidate matter in these pages. This course has also obviated the necessity of my repeating myself. For the sake of brevity, Amusements in Mathematics is throughout referred to as A. in M.

HENRY E. DUDENEY.

THE AUTHORS' CLUB, July 2, 1919.

INTRODUCTION

Readers of The Mill on the Floss will remember that whenever Mr. Tulliver found himself confronted by any little difficulty he was accustomed to make the trite remark, "It's a puzzling world." There can be no denying the fact that we are surrounded on every hand by posers, some of which the intellect of man has mastered, and many of which may be said to be impossible of solution. Solomon himself, who may be supposed to have been as sharp as most men at solving a puzzle, had to admit "there be three things which are too wonderful for me; yea, four which I know not: the way of an eagle in the air; the way of a serpent upon a rock; the way of a ship in the midst of the sea; and the way of a man with a maid."

Probing into the secrets of Nature is a passion with all men; only we select different lines of research. Men have spent long lives in such attempts as to turn the baser metals into gold, to discover perpetual motion, to find a cure for certain malignant diseases, and to navigate the air.

From morning to night we are being perpetually brought face to face with puzzles. But there are puzzles and puzzles. Those that are usually devised for recreation and pastime may be roughly divided into two classes: Puzzles that are built up on some interesting or informing little principle; and puzzles that conceal no principle whatever--such as a picture cut at random into little bits to be put together again, or the juvenile imbecility known as the "rebus," or "picture puzzle." The former species may be said to be adapted to the amusement of the sane man or woman; the latter can be confidently recommended to the feeble-minded.

The curious propensity for propounding puzzles is not peculiar to any race or to any period of history. It is simply innate in every intelligent man, woman, and child that has ever lived, though it is always showing itself in different forms; whether the individual be a Sphinx of Egypt, a Samson of Hebrew lore, an Indian fakir, a Chinese philosopher, a mahatma of Tibet, or a European mathematician makes little difference.

Theologian, scientist, and artisan are perpetually engaged in attempting to solve puzzles, while every game, sport, and pastime is built up of problems of greater or less difficulty. The spontaneous question asked by the child of his parent, by one cyclist of another while taking a brief rest on a stile, by a cricketer during the luncheon hour, or by a yachtsman lazily scanning the horizon, is frequently a problem of considerable difficulty. In short, we are all propounding puzzles to one another every day of our lives--without always knowing it.

A good puzzle should demand the exercise of our best wit and ingenuity, and although a knowledge of mathematics and a certain familiarity with the methods of logic are often of great service in the solution of these things, yet it sometimes happens that a kind of natural cunning and sagacity is of considerable value. For many of the best problems cannot be solved by any familiar scholastic methods, but must be attacked on entirely original lines. This is why, after a long and wide experience, one finds that particular puzzles will sometimes be solved more readily by persons possessing only naturally alert faculties than by the better educated. The best players of such puzzle games as chess and draughts are not mathematicians, though it is just possible that often they may have undeveloped mathematical minds.

Part 3

It is extraordinary what fascination a good puzzle has for a great many people. We know the thing to be of trivial importance, yet we are impelled to master it; and when we have succeeded there is a pleasure and a sense of satisfaction that are a quite sufficient reward for our trouble, even when there is no prize to be won. What is this mysterious charm that many find irresistible? Why do we like to be puzzled? The curious thing is that directly the enigma is solved the interest generally vanishes. We have done it, and that is enough. But why did we ever attempt to do it?

The answer is simply that it gave us pleasure to seek the solution--that the pleasure was all in the seeking and finding for their own sakes. A good puzzle, like virtue, is its own reward. Man loves to be confronted by a mystery, and he is not entirely happy until he has solved it. We never like to feel our mental inferiority to those around us. The spirit of rivalry is innate in man; it stimulates the smallest child, in play or education, to keep level with his fellows, and in later life it turns men into great discoverers, inventors, orators, heroes, artists, and (if they have more material aims) perhaps millionaires.

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