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 d.i.c.kens 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 fict.i.tious 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 pa.s.sage 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 ent.i.tled:

_"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 compet.i.tion 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 trans.m.u.tation [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' const.i.tute 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 ill.u.s.trated 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 amus.e.m.e.nt of some special child friend.

Indeed, the puzzles and riddles and games had acc.u.mulated to such an extent that he was arranging to publish a book of them with ill.u.s.trations 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!"