A
young fellow named Dawkins, just home from Australia, was introduced to
the club by one of the members, in order that he might relate an
extraordinary stroke of luck that he had experienced "down under," as
the
circumstances involved the solution of a poser that could not fail to
interest all lovers of puzzle problems.
After the club dinner, Dawkins
was asked to tell his story, which he did, to the following
effect:
"I have told you,
gentlemen, that I was very much
down on my
luck.
I had
gone out to Australia to try to retrieve my fortunes, but had met with
no
success, and the future was looking very dark.
I was, in fact,
beginning
to feel desperate.
One hot summer day I happened to be seated in a
Melbourne wineshop, when two fellows entered, and engaged in
conversation. They thought I was asleep, but I assure you I was very
wide
awake.
"'If only I could
find the right field,' said one
man, 'the
treasure
would be mine; and as the original owner left no heir, I have as much
right to it as anybody else.'
"'How would you
proceed?' asked the other.
"'Well, it is like
this: The document that fell
into my hands
states
clearly that the field is square, and that the treasure is buried in it
at a point exactly two furlongs from one corner, three furlongs from
the
next corner, and four furlongs from the next corner to that.
You see,
the
worst of it is that nearly all the fields in the
district
are square;
and I doubt whether there are two of exactly the same size.
If only I
knew the size of the field I could soon discover it, and, by taking
these
simple measurements, quickly secure the treasure.'
"'But you would not
know which corner to start
from, nor which
direction
to go to the next corner.'
"'My dear chap,
that only means eight spots at the
most to dig
over; and
as the paper says that the treasure is three feet deep, you bet that
wouldn't take me long.'
"Now,
gentlemen,"
continued Dawkins, "I happen to
be a bit of
a
mathematician; and hearing the conversation, I saw at once that for a
spot to be exactly two, three, and four furlongs from successive
corners
of a square, the square must be of a particular area. You can't get
such
measurements to meet at one point in any square you choose.
They can
only
happen in a field of one
size, and that is just what these men never
suspected. I will leave you the puzzle of working out just what that
area
is.
"Well,
when I
found the size of the field, I was
not long in
discovering
the field itself, for the man had let out the district in the
conversation.
And I did not need to make the eight digs, for, as luck
would have it, the third spot I tried was the right one.
The treasure
was
a substantial sum, for it has brought me home and enabled me to start
in
a business that already shows signs of being a particularly lucrative
one.
I often smile when I think of that poor fellow going about for the
rest of his life saying:
'If only I knew the size of the field!' while
he
has placed the treasure safe in my own possession.
I tried to find the
man, to make him some compensation anonymously, but without
success.
Perhaps he stood in little need of the money, while it has saved me
from
ruin."
Could
the reader
have discovered the required area
of the
field from
those details overheard in the wineshop?
It is an elegant little
puzzle,
and furnishes another example of the practical utility, on unexpected
occasions, of a knowledge of the art of problem-solving.
See
answer
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