Part 19 (1/2)
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.”