CHAPTER XI.

GAMES, RIDDLES, AND PROBLEMS.

 

Lewis Carroll had a mind which never rested in waking hours, and as is the case with all such active thinkers, his hours of sleeping were often broken by long stretches of wakefulness, during which time the thinking machinery set itself in motion and spun out problems and riddles and odd games and puzzles.

“Puzzles and problems of all sorts were a delight to Mr. Dodgson,” writes Miss Beatrice Hatch in the Strand Magazine. “Many a sleepless night was occupied by what he called a ‘pillow problem’; in fact his mathematical mind seemed always at work on something of the kind, and he loved to discuss and argue a point connected with his logic, if he could but find a willing listener. Sometimes, while paying an afternoon call, he would borrow scraps of paper and leave neat little diagrams or word puzzles to be worked out by his friends.”

Logic was a study of which he was very fond. After he gave up in 1881 the lectureship of mathematics which he had held for twenty-five years he determined to make literature a profession; to devote part of his time to more serious study, and a fair portion to the equally fascinating work for children.

“In his estimation,” says Miss Hatch, “logic was a most important study for every one; no pains were spared to make it clear and interesting to those who would consent to learn of him, either in a class that he begged to be allowed to hold in a school or college, or to a single individual girl who showed the smallest inclination to profit by his instructions.”

He took the greatest delight in his subject and wisely argued that all girls should learn, not only to reason, but to reason properly—that is, logically. With this end in view he wrote for their use a little book which he called “The Game of Logic,” and the girls, whose footsteps he had guided in childish days through realms of nonsense, were willing in many instances to journey with him into the byways of learning, feeling sure he would not lead them into depths where they could not follow. The little volume contains four chapters, and the whimsical headings show us at once that Lewis Carroll was the author, and not Charles Lutwidge Dodgson.

Chapter I.........New Lamps for Old.

Chapter II.......Cross Questions.

Chapter III......Crooked Answers.

Chapter IV......Hit or Miss.

To be sure this is not a “play” book, and even as a “game” it is one which requires a great deal of systematic thinking and reasoning. The girl who has reached thinking and reasoning years and does not care to do either, had better not even peep into the book; but if she is built on sturdier lines and wishes to peep, she must do more—she must read it step by step and study the carefully drawn diagrams, if she would follow intelligently the clear, precise arguments. The book is dedicated—

TO MY CHILD-FRIEND.

 

I charm in vain: for never again,

All keenly as my glance I bend,

Will memory, goddess coy,

Embody for my joy

Departed days, nor let me gaze

On thee, my Fairy Friend!

 

Yet could thy face, in mystic grace,

A moment smile on me, ’twould send

Far-darting rays of light

From Heaven athwart the night,

By which to read in very deed

Thy spirit, sweetest Friend!

 

So may the stream of Life’s long dream

Flow gently onward to its end,

With many a floweret gay,

Adown its billowy way:

May no sigh vex nor care perplex

My loving little Friend!

His preface is most enticing. He says: “This Game requires nine Counters—four of one colour and five of another; say four red and five gray. Besides the nine Counters, it also requires one Player at least. I am not aware of any game that can be played with less than this number; while there are several that require more; take Cricket, for instance, which requires twenty-two. How much easier it is, when you want to play a game, to find one Player than twenty-two! At the same time, though one Player is enough, a good deal more amusement may be got by two working at it together, and correcting each other’s mistakes.

“A second advantage possessed by this Game is that, besides being an endless source of amusement (the number of arguments that may be worked by it being infinite), it will give the Players a little instruction as well. But is there any great harm in that, so long as you get plenty of amusement?”

To explain the book thoroughly would take the wit and clever handling of Lewis Carroll himself, but to the beginner of Logic a few of these unfinished syllogisms may prove interesting: a syllogism in logical language consists of what is known as two Premisses and one Conclusion, and is a very simple form of argument when you get used to it.

For instance, supposing someone says: “All my friends have colds”; someone else may add: “No one can sing who has a cold”; then the third person draws the conclusion, which is: “None of my friends can sing,” and the perfect logical argument would read as follows:

1. Premise—“All my friends have colds.”

2. Premise—“No one can sing who has a cold.”

3. Conclusion—“None of my friends can sing.”

That is what is called a perfect syllogism, and in Chapter IV, which he calls Hit or Miss, Lewis Carroll has collected a hundred examples containing the two Premisses which need the Conclusion. Here are some of them. Anyone can draw her own conclusions:

Pain is wearisome;

No pain is eagerly wished for.

In each case the student is required to fill up the third space.

No bald person needs a hairbrush;

No lizards have hair.

 

No unhappy people chuckle;

No happy people groan.

 

All ducks waddle;

Nothing that waddles is graceful.

 

Some oysters are silent;

No silent creatures are amusing.

 

Umbrellas are useful on a journey;

What is useless on a journey should be left behind.

 

No quadrupeds can whistle;

Some cats are quadrupeds.

 

Some bald people wear wigs;

All your children have hair.

The whole book is brimful of humor and simple everyday reasoning that the smallest child could understand.

Another “puzzle” book of even an earlier date is “A Tangled Tale”; this is dedicated—

TO MY PUPIL.

 

Belovéd pupil! Tamed by thee,

Addish, Subtrac-, Multiplica-tion,

Division, Fractions, Rule of Three,

Attest the deft manipulation!

 

Then onward! Let the voice of Fame,

From Age to Age repeat the story,

Till thou hast won thyself a name,

Exceeding even Euclid’s glory!

In the preface he says: “This Tale originally appeared as a serial in The Monthly Packet, beginning in April, 1880. The writer’s intention was to embody in each Knot (like the medicine so deftly but ineffectually concealed in the jam of our childhood) one or more mathematical questions, in Arithmetic, Algebra, or Geometry, as the case might be, for the amusement and possible edification of the fair readers of that Magazine.

“October, 1885. L. C.”

These are regular mathematical problems and “posers,” most of them, and it seems that the readers, being more or less ambitious, set to work in right good earnest to answer them, and sent in the solutions to the author under assumed names, and then he produced the real problem, the real answer, and all the best answers of the contestants. These problems were all called Knots and were told in the form of stories.

Knot I was called Excelsior. It was written as a tale of adventure, and ran as follows:

“The ruddy glow of sunset was already fading into the somber shadows of night, when two travelers might have been observed swiftly—at a pace of six miles in the hour—descending the rugged side of a mountain; the younger bounding from crag to crag with the agility of a fawn, while his companion, whose aged limbs seemed ill at ease in the heavy chain armor habitually worn by tourists in that district, toiled on painfully at his side.”

Lewis Carroll is evidently imitating the style of some celebrated writer—Henry James, most likely, who is rather fond of opening his story with “two travelers,” or perhaps Sir Walter Scott. He goes on:

“As is always the case under such circumstances, the younger knight was the first to break the silence.

“‘A goodly pace, I trow!’ he exclaimed. ‘We sped not thus in the ascent!’

“‘Goodly, indeed!’ the other echoed with a groan. ‘We clomb it but at three miles in the hour.’

“‘And on the dead level our pace is—?’ the younger suggested; for he was weak in statistics, and left all such details to his aged companion.

“‘Four miles in the hour,’ the other wearily replied. ‘Not an ounce more,’ he added, with that love of metaphor so common in old age, ‘and not a farthing less!’

“‘’Twas three hours past high noon when we left our hostelry,’ the young man said, musingly. ‘We shall scarce be back by supper-time. Perchance mine host will roundly deny us all food!’

“‘He will chide our tardy return,’ was the grave reply, ‘and such a rebuke will be meet.’

“‘A brave conceit!’ cried the other, with a merry laugh. ‘And should we bid him bring us yet another course, I trow his answer will be tart!’

“‘We shall but get our deserts,’ sighed the older knight, who had never seen a joke in his life, and was somewhat displeased at his companion’s untimely levity. ‘’Twill be nine of the clock,’ he added in an undertone, ‘by the time we regain our hostelry. Full many a mile have we plodded this day!’

“‘How many? How many?’ cried the eager youth, ever athirst for knowledge.

“The old man was silent.

“‘Tell me,’ he answered after a moment’s thought, ‘what time it was when we stood together on yonder peak. Not exact to the minute!’ he added, hastily, reading a protest in the young man’s face. ‘An’ thy guess be within one poor half hour of the mark, ’tis all I ask of thy mother’s son! Then will I tell thee, true to the last inch, how far we shall have trudged betwixt three and nine of the clock.’

“A groan was the young man’s only reply, while his convulsed features and the deep wrinkles that chased each other across his manly brow revealed the abyss of arithmetical agony into which one chance question had plunged him.”

The problem in plain English is this: “Two travelers spend from three o’clock till nine in walking along a level road, up a hill, and home again, their pace on the level being four miles an hour, up hill three, and down hill six. Find distance walked: also (within half an hour) the time of reaching top of hill.”

Answer. “Twenty-four miles: half-past six.”

The explanation is very clear and very simple, but we will not give it here. This first knot of “A Tangled Tale” offers attractions of its own, for like the dream Alice someone may exclaim, “A Knot! Oh, do let me help to undo it!”

The second problem or “Tale” is called Eligible Apartments, and deals with the adventures of one Balbus and his pupils, and contains two “Knots.” One is: “The Governor of —— wants to give a very small dinner party, and he means to ask his father’s brother-in-law, his brother’s father-in-law, and his brother-in-law’s father, and we’re to guess how many guests there will be.” The answer is one. Perhaps some ambitious person will go over the ground and prove it. The second knot deals with the Eligible Apartments which Balbus and his pupils were hunting. At the end of their walk they found themselves in a square.

“‘It is a Square!’ was Balbus’s first cry of delight as he gazed around him. ‘Beautiful! Beau-ti-ful! And rectangular!’ and as he plunged into Geometry he also plunged into funny conversations with the average English landlady, which we can better follow:

“‘Which there is one room, gentlemen,’ said the smiling landlady, ‘and a sweet room, too. As snug a little back room——’

“‘We will see it,’ said Balbus gloomily as they followed her in. ‘I knew how it would be! One room in each house! No view I suppose.’

“‘Which indeed there is, gentlemen!’ the landlady indignantly protested as she drew up the blind, and indicated the back garden.

“‘Cabbages, I perceive,’ said Balbus. ‘Well, they’re green at any rate.’

“‘Which the greens at the shops,’ their hostess explained, ‘are by no means dependable upon. Here you has them on the premises, and of the best.’

“‘Does the window open?’ was always Balbus’s first question in testing a lodging; and ‘Does the chimney smoke?’ his second. Satisfied on all points, he secured the refusal of the room, and moved on to the next house where they repeated the same performance, adding as an afterthought: ‘Does the cat scratch?’

“The landlady looked around suspiciously as if to make sure the cat was not listening. ‘I will not deceive you, gentlemen,’ she said, ‘it do scratch, but not without you pulls its whiskers. It’ll never do it,’ she repeated slowly, with a visible effort to recall the exact words between herself and the cat, ‘without you pulls its whiskers!’

“‘Much may be excused in a cat so treated,’ said Balbus as they left the house, ... leaving the landlady curtseying on the doorstep and still murmuring to herself her parting words, as if they were a form of blessing, ‘not without you pulls its whiskers!’”

He has given us a real Dickens atmosphere in the dialogue, but the medicinal problem tucked into it all is too much like hard work.

There were ten of these “Knots,” each one harder than its predecessor, and Lewis Carroll found much interest in receiving and criticising the answers, all sent under fictitious names.

This clever mathematician delighted in “puzzlers,” and sometimes he found a kindred soul among the guessers, which always pleased him.

One of his favorite problems was one that as early as the days of the Rectory Umbrella he brought before his limited public. He called it Difficulty No. 1.

“Where in its passage round the earth does the day change its name?”

This question pursued him all through his mathematical career, and the difficulty of answering it has never lessened. Even in “A Tangled Tale” neither Balbus nor his ambitious young pupils could do much with the problem.

Difficulty No. 2 is very humorous, and somewhat of a “catch” question.

“Which is the best—a clock that is right only once a year, or a clock that is right twice every day?”

In March, 1897, Vanity Fair, a current English magazine, had the following article entitled:

“A New Puzzle.”

“The readers of Vanity Fair have, during the last ten years, shown so much interest in Acrostics and Hard Cases, which were at first made the object of sustained competition for prizes in the journal, that it has been sought to invent for them an entirely new kind of Puzzle, such as would interest them equally with those that have already been so successful. The subjoined letter from Mr. Lewis Carroll will explain itself, and will introduce a Puzzle so entirely novel and withal so interesting that the transmutation [changing] of the original into the final word of the Doublets may be expected to become an occupation, to the full as amusing as the guessing of the Double Acrostics has already proved.”

“Dear Vanity,” Lewis Carroll writes:—“Just a year ago last Christmas two young ladies, smarting under that sorest scourge of feminine humanity, the having “nothing to do,” besought me to send them “some riddles.” But riddles I had none at hand and therefore set myself to devise some other form of verbal torture which should serve the same purpose. The result of my meditations was a new kind of Puzzle, new at least to me, which now that it has been fairly tested by a year’s experience, and commended by many friends, I offer to you as a newly gathered nut to be cracked by the omnivorous teeth that have already masticated so many of your Double Acrostics.

“The rules of the Puzzle are simple enough. Two words are proposed, of the same length; and the Puzzle consists in linking these together by interposing other words, each of which shall differ from the next word in one letter only. That is to say, one letter may be changed in one of the given words, then one letter in the word so obtained, and so on, till we arrive at the other given word. The letters must not be interchanged among themselves, but each must keep to its own place. As an example, the word ‘head’ may be changed into ‘tail’ by interposing the words ‘heal, teal, tell, tall.’ I call the two given words ‘a Doublet,’ the interposed words ‘Links,’ and the entire series ‘a Chain,’ of which I here append an example:

Head

heal

teal

tell

tall

Tail

“It is perhaps needless to state that the links should be English words, such as might be used in good society.

“The easiest ‘Doublets’ are those in which the consonants in one word answer to the consonants in the other, and the vowels to vowels; ‘head’ and ‘tail’ constitute a Doublet of this kind. Where this is not the case, as in ‘head’ and ‘hare,’ the first thing to be done is to transform one member of the Doublet into a word whose consonants and vowels shall answer to those in the other member (‘head, herd, here’), after which there is seldom much difficulty in completing the ‘Chain.’...

“Lewis Carroll.”

“Doublets” was brought out in book form in 1880, and proved a very attractive little volume.

“The Game of Logic” and “A Tangled Tale” are also in book form, the latter cleverly illustrated by Arthur B. Frost.

It would take too long to name all the games and puzzles Lewis Carroll invented. Some were carefully thought out, some were produced on the spur of the moment, generally for the amusement of some special child friend. Indeed, the puzzles and riddles and games had accumulated to such an extent that he was arranging to publish a book of them with illustrations by Miss E. Gertrude Thomson, but after his death the plans fell through, and many literary projects were abandoned.

Acrostic writing was one of his favorite pastimes, and he wrote enough of these to have filled a good fat little volume.

His Wonderland Stamp-Case, one of his own ingenious inventions, might come under the head of “Puzzles and Problems,” and, oddly enough, an interesting description of this stamp-case was published only a short time ago in The Nation. The writer describes his own copy which he bought when it was new, some twenty years ago. There is first an envelope of red paper, on which is printed:

The “Wonderland” Postage Stamp-Case,

Invented by Louis Carroll, Oct. 29, 1888.

This case contains 12 separate packets for

Stamps of different values, and 2 Coloured

Pictorial Surprises, taken from “Alice in

Wonderland.” It is accompanied with 8 or

9 Wise Words about Letter-Writing.

1st, post-free, 13d.

On the flap of the envelope is:

Published by Emberlin & Son,

4 Magdalen Street, Oxford.

“The Stamp-Case,” the writer tells us, “consists of a stiff paper folded with the pockets on the inner leaves and a picture on each outer leaf. This Case is inclosed in a sliding cover, and in this way the pictorial surprise becomes possible. A picture of Alice holding the Baby is on the front cover, and when this is drawn off, there is underneath a picture of Alice nursing a pig. On the back cover is the famous Cat, which vanishes to a shadowy grin on the pictures beneath.”

The booklet which accompanied this little stamp-case found its way to many of his girl friends. Now, whether they bought it, or whether, under guise of giving a present, this clever friend of theirs sent them the stamp-case with the “eight or nine words of advice” slyly tucked in, we cannot say, but in the case of Isa Bowman and of Beatrice Hatch the booklet evidently made a deep impression, for both quote from it very freely, and some of the “wise words” are certainly worth heeding, for instance:

Address and stamp the envelope.

“What! Before writing the letter?”

“Most certainly; and I’ll tell you what will happen if you don’t. You will go on writing till the last moment, and just in the middle of the last sentence you will become aware that ‘time’s up!’ Then comes the hurried wind-up—the wildly scrawled signature—the hastily fastened envelope which comes open in the post—the address—a mere hieroglyphic—the horrible discovery that you’ve forgotten to replenish your stamp-case—the frantic appeal to everyone in the house to lend you a stamp—the headlong rush to the Post Office, arriving hot and gasping, just after the box has been closed—and finally, a week afterwards, the return of the letter from the dead letter office, marked, ‘address illegible.’”

Write legibly.

“The average temper of the human race would be perceptibly sweetened if everybody obeyed this rule. A great deal of bad writing in the world comes simply from writing too quickly. Of course you reply, ‘I do it to save time.’ A very good object no doubt; but what right have you to do it at your friend’s expense? Isn’t his time as valuable as yours? Years ago I used to receive letters from a friend—and very interesting letters too—written in one of the most atrocious hands ever invented. It generally took me about a week to read one of his letters! I used to carry it about in my pocket and take it out at leisure times to puzzle over the riddles which composed it—holding it in different positions, till at last the meaning of some hopeless scrawl would flash upon me, when I at once wrote down the English under it; and when several had thus been guessed, the context would help me with the others till at last the whole series of hieroglyphics was deciphered. If all one’s friends wrote like that, life would be entirely spent in reading their letters!”

“My Ninth Rule.—When you get to the end of a note-sheet, and find you have more to say, take another piece of paper—a whole sheet or a scrap, as the case may demand, but whatever you do, don’t cross! Remember the old proverb ‘Cross-writing makes cross-reading.’ ‘The old proverb?’ you say inquiringly. ‘How old?’ Why, not so very ancient, I must confess. In fact—I’m afraid I invented it while writing this paragraph. Still, you know ‘old’ is a comparative term; I think you would be quite justified in addressing a chicken just out of the shell as ‘Old Boy!’ when compared with another chicken that was only half out!”

“Don’t try to have the last word,” he tells us—and again, “Don’t fill more than a page and a half with apologies for not having written sooner.”

On how to end a letter,” he advises the writer to “refer to your correspondent’s last letter, and make your winding up at least as friendly as his; in fact, even if a shade more friendly, it will do no harm.”

“When you take your letters to the post, carry them in your hand. If you put them in your pocket, you will take a long country walk (I speak from experience), passing the post office twice, going and returning, and when you get home you will find them still in your pocket.”

Letter-writing was as much a part of Lewis Carroll as games, and puzzles, and problems, and mathematics, and nonsense, and little girls. Indeed, as we view him through the stretch of years, we find him so many-sided that he himself would have done well to draw a new geometrical figure to represent a nature so full of strange angles and surprising shapes. If one is fond of looking into a kaleidoscope, and watching the ever-changing facets and colours and designs, one would be pretty apt to understand the constant shifting of that active mind, always on the alert for new ideas, but steady and fixed in many good old ones, which had become firm habits.

He was fond of giving his child-friends “nuts to crack,” and nothing pleased him more than to be the center of some group of little girls, firing his conundrums and puzzles into their minds, and watching the bright young faces catching the glow of his thoughts. He knew just how far to go, and when to turn some dawning idea into quaint nonsense, so that the young mind could grasp and hold it. Dear maker of nonsense, dear teacher and friend, dear lover of children, can they ever forget you!