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## WILSON'S POSER.

(

Money Puzzles)

"Speaking of perplexities--" said Mr. Wilson, throwing down a magazine

on the table in the commercial room of the Railway Hotel.

"Who was speaking of perplexities?" inquired Mr. Stubbs.

"Well, then, reading about them, if you want to be exact--it just

occurred to me that perhaps you three men may be interested in a little

matter connected with myself."

It was Christmas Eve, and the four commercial travellers were spending

the holiday at Grassminster. Probably each suspected that the others had

no homes, and perhaps each was conscious of the fact that he was in that

predicament himself. In any case they seemed to be perfectly

comfortable, and as they drew round the cheerful fire the conversation

became general.

"What is the difficulty?" asked Mr. Packhurst.

"There's no difficulty in the matter, when you rightly understand it. It

is like this. A man named Parker had a flying-machine that would carry

two. He was a venturesome sort of chap--reckless, I should call him--and

he had some bother in finding a man willing to risk his life in making

an ascent with him. However, an uncle of mine thought he would chance

it, and one fine morning he took his seat in the machine and she started

off well. When they were up about a thousand feet, my nephew

suddenly--"

"Here, stop, Wilson! What was your nephew doing there? You said your

uncle," interrupted Mr. Stubbs.

"Did I? Well, it does not matter. My nephew suddenly turned to Parker

and said that the engine wasn't running well, so Parker called out to my

uncle--"

"Look here," broke in Mr. Waterson, "we are getting mixed. Was it your

uncle or your nephew? Let's have it one way or the other."

"What I said is quite right. Parker called out to my uncle to do

something or other, when my nephew--"

"There you are again, Wilson," cried Mr. Stubbs; "once for all, are we

to understand that both your uncle and your nephew were on the machine?"

"Certainly. I thought I made that clear. Where was I? Well, my nephew

shouted back to Parker--"

"Phew! I'm sorry to interrupt you again, Wilson, but we can't get on

like this. Is it true that the machine would only carry two?"

"Of course. I said at the start that it only carried two."

"Then what in the name of aerostation do you mean by saying that there

were three persons on board?" shouted Mr. Stubbs.

"Who said there were three?"

"You have told us that Parker, your uncle, and your nephew went up on

this blessed flying-machine."

"That's right."

"And the thing would only carry two!"

"Right again."

"Wilson, I have known you for some time as a truthful man and a

temperate man," said Mr. Stubbs, solemnly. "But I am afraid since you

took up that new line of goods you have overworked yourself."

"Half a minute, Stubbs," interposed Mr. Waterson. "I see clearly where

we all slipped a cog. Of course, Wilson, you meant us to understand that

Parker is either your uncle or your nephew. Now we shall be all right if

you will just tell us whether Parker is your uncle or nephew."

"He is no relation to me whatever."

The three men sighed and looked anxiously at one another. Mr. Stubbs got

up from his chair to reach the matches, Mr. Packhurst proceeded to wind

up his watch, and Mr. Waterson took up the poker to attend to the fire.

It was an awkward moment, for at the season of goodwill nobody wished to

tell Mr. Wilson exactly what was in his mind.

"It's curious," said Mr. Wilson, very deliberately, "and it's rather

sad, how thick-headed some people are. You don't seem to grip the facts.

It never seems to have occurred to either of you that my uncle and my

nephew are one and the same man."

"What!" exclaimed all three together.

"Yes; David George Linklater is my uncle, and he is also my nephew.

Consequently, I am both his uncle and nephew. Queer, isn't it? I'll

explain how it comes about."

Mr. Wilson put the case so very simply that the three men saw how it

might happen without any marriage within the prohibited degrees. Perhaps

the reader can work it out for himself.

CLOCK PUZZLES.

"Look at the clock!"

_Ingoldsby Legends_.

In considering a few puzzles concerning clocks and watches, and the

times recorded by their hands under given conditions, it is well that a

particular convention should always be kept in mind. It is frequently

the case that a solution requires the assumption that the hands can

actually record a time involving a minute fraction of a second. Such a

time, of course, cannot be really indicated. Is the puzzle, therefore,

impossible of solution? The conclusion deduced from a logical syllogism

depends for its truth on the two premises assumed, and it is the same in

mathematics. Certain things are antecedently assumed, and the answer

depends entirely on the truth of those assumptions.

"If two horses," says Lagrange, "can pull a load of a certain weight, it

is natural to suppose that four horses could pull a load of double that

weight, six horses a load of three times that weight. Yet, strictly

speaking, such is not the case. For the inference is based on the

assumption that the four horses pull alike in amount and direction,

which in practice can scarcely ever be the case. It so happens that we

are frequently led in our reckonings to results which diverge widely

from reality. But the fault is not the fault of mathematics; for

mathematics always gives back to us exactly what we have put into it.

The ratio was constant according to that supposition. The result is

founded upon that supposition. If the supposition is false the result is

necessarily false."

If one man can reap a field in six days, we say two men will reap it in

three days, and three men will do the work in two days. We here assume,

as in the case of Lagrange's horses, that all the men are exactly

equally capable of work. But we assume even more than this. For when

three men get together they may waste time in gossip or play; or, on the

other hand, a spirit of rivalry may spur them on to greater diligence.

We may assume any conditions we like in a problem, provided they be

clearly expressed and understood, and the answer will be in accordance

with those conditions.

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