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(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
"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
"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.
"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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