Learn how and when to remove this template message Dudeney was born in the village of Mayfield, East Sussex , England, one of six children of Gilbert and Lucy Dudeney. His grandfather, John Dudeney, was well known as a self-taught mathematician and shepherd; his initiative was much admired by his grandson. Dudeney learned to play chess at an early age, and continued to play frequently throughout his life. This led to a marked interest in mathematics and the composition of puzzles. Chess problems in particular fascinated him during his early years.
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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. 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.
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. 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? 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.
In starting on a tour through the wide realm of Puzzledom we do well to remember that we shall meet with points of interest of a very varied character. I shall take advantage of this variety. People often make the mistake of confining themselves to one little corner of the realm, and thereby miss opportunities of new pleasures that lie within their reach around them.
One person will keep to acrostics and other word puzzles, another to mathematical brain-rackers, another to chess problems which are merely puzzles on the chess-board, and have little practical relation to the game of chess , and so on.
And there is really a practical utility in puzzle-solving. Regular exercise is supposed to be as necessary for the brain as for the body, and in both cases it is not so much what we do as the doing of it from which we derive benefit. The daily walk recommended by the doctor for the good of the body, or the daily exercise for the brain, may in itself appear to be so much waste of time; but it is the truest economy in the end.
Albert Smith, in one of his amusing novels, describes a woman who was convinced that she suffered from "cobwigs on the brain. They keep the brain alert, stimulate the imagination, and develop the reasoning faculties. And not only are they useful in this indirect way, but they often directly help us by teaching us some little tricks and "wrinkles" that can be applied in the affairs of life at the most unexpected times and in the most unexpected ways.
There is an interesting passage in praise of puzzles in the quaint letters of Fitzosborne. Here is an extract: "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. It is an art, indeed, that I would recommend to the encouragement of both the Universities, as it affords the easiest and shortest method of conveying some of the most useful principles of logic.
I am not referring to acrostics, anagrams, charades, and that sort of thing, but to puzzles that contain an original idea. Well, you cannot invent a good puzzle to order, any more than you can invent anything else in that manner. Notions for puzzles come at strange times and in strange ways. They are suggested by something we see or hear, and are led up to by other puzzles that come under our notice.
It is useless to say, "I will sit down and invent an original puzzle," because there is no way of creating an idea; you can only make use of it when it comes. You may think this is wrong, because an expert in these things will make scores of puzzles while another person, equally clever, cannot invent one "to save his life," as we say. The explanation is very simple. The expert knows an idea when he sees one, and is able by long experience to judge of its value. Fertility, like facility, comes by practice.
Sometimes a new and most interesting idea is suggested by the [Pg 15] blunder of somebody over another puzzle. A boy was given a puzzle to solve by a friend, but he misunderstood what he had to do, and set about attempting what most likely everybody would have told him was impossible.
But he was a boy with a will, and he stuck at it for six months, off and on, until he actually succeeded. When his friend saw the solution, he said, "This is not the puzzle I intended—you misunderstood me—but you have found out something much greater! Puzzles can be made out of almost anything, in the hands of the ingenious person with an idea. Coins, matches, cards, counters, bits of wire or string, all come in useful. An immense number of puzzles have been made out of the letters of the alphabet, and from those nine little digits and cipher, 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0.
It should always be remembered that a very simple person may propound a problem that can only be solved by clever heads—if at all. A child asked, "Can God do everything? Yet the difficulty lies merely in the absurd, though cunning, form of the question, which really amounts to asking, "Can the Almighty destroy His own omnipotence?
Professor Tyndall used to invite children to ask him puzzling questions, and some of them were very hard nuts to crack. One child asked him why that part of a towel that was dipped in water was of a darker colour than the dry part. How many readers could give the correct reply? Many people are satisfied with the most ridiculous answers to puzzling questions. If you ask, "Why can we see through glass? They often so merge in character that the best we can do is to sort them into a few broad types.
Let us take three or four examples in illustration of what I mean. First there is the ancient Riddle, that draws upon the imagination and play of fancy. It was said that the Sphinx would destroy herself if one of her riddles was ever correctly answered. It was this: "What animal walks on four legs in the morning, two at noon, and three in the evening? When the Sphinx heard this explanation, she dashed her head against a rock and immediately expired.
This shows that puzzle solvers may be really useful on occasion. Then there is the riddle propounded by Samson. It is perhaps the first prize competition in this line on record, the prize being thirty sheets and thirty changes of garments for a correct solution. The riddle was this: "Out of the eater came forth meat, and out of the strong came forth sweetness. For example, we have been asked from our infancy, "When is a door not a door?
It should be, "When it is a negress an egress. In this class we also find palindromes, or words and sentences that read backwards and forwards alike. These range from the puzzle that the algebraist finds to be nothing but a "simple equation," quite easy of direct solution, up to the profoundest problems in the elegant domain of the theory of numbers. Next we have the Geometrical Puzzle, a favourite and very ancient branch of which is the puzzle in dissection, requiring some plane figure to be cut into a certain number of pieces that will fit together and form another figure.
Most of the wire puzzles sold in the streets and toy-shops are concerned with the geometry of position. But these classes do not nearly embrace all kinds of puzzles even when we allow for those that belong at once to several of the classes. There are many ingenious mechanical puzzles that you cannot classify, as they stand quite alone: there are puzzles in logic, in chess, in draughts, in cards, and in dominoes, while every conjuring trick is nothing but a puzzle, the solution to which the performer tries to keep to himself.
There are puzzles that look easy and are easy, puzzles that look easy and are difficult, puzzles that look difficult and are difficult, and puzzles that look difficult and are easy, and in each class we may of course have degrees of easiness and difficulty.
But it does not follow that a puzzle that has conditions that are easily understood by the merest child is in itself easy. Such a puzzle might, however, look simple to the uninformed, and only prove to be a very hard nut to him after he had actually tackled it. For example, if we write down nineteen ones to form the number [Pg 18] 1,,,,,,, and then ask for a number other than 1 or itself that will divide it without remainder, the conditions are perfectly simple, but the task is terribly difficult.
Nobody in the world knows yet whether that number has a divisor or not. If you can find one, you will have succeeded in doing something that nobody else has ever done. The only number composed only of ones that we know with certainty to have no divisor is Such a number is, of course, called a prime number. The maxim that there are always a right way and a wrong way of doing anything applies in a very marked degree to the solving of puzzles.
Here the wrong way consists in making aimless trials without method, hoping to hit on the answer by accident—a process that generally results in our getting hopelessly entangled in the trap that has been artfully laid for us. Occasionally, however, a problem is of such a character that, though it may be solved immediately by trial, it is very difficult to do by a process of pure reason. But in most cases the latter method is the only one that gives any real pleasure.
When we sit down to solve a puzzle, the first thing to do is to make sure, as far as we can, that we understand the conditions. For if we do not understand what it is we have to do, we are not very likely to succeed in doing it. We all know the story of the man who was asked the question, "If a herring and a half cost three-halfpence, how much will a dozen herrings cost?
It sometimes requires more care than the reader might suppose so to word the conditions of a new puzzle that they are at once [Pg 19] clear and exact and not so prolix as to destroy all interest in the thing. I remember once propounding a problem that required something to be done in the "fewest possible straight lines," and a person who was either very clever or very foolish I have never quite determined which claimed to have solved it in only one straight line, because, as she said, "I have taken care to make all the others crooked!
Then if you give a "crossing the river" puzzle, in which people have to be got over in a boat that will only hold a certain number or combination of persons, directly the would-be solver fails to master the difficulty he boldly introduces a rope to pull the boat across. You say that a rope is forbidden; and he then falls back on the use of a current in the stream.
I once thought I had carefully excluded all such tricks in a particular puzzle of this class.
The Canterbury Puzzles
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