The problem of the Buried Treasure was of quite a different character. 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.'
[Illustration]
"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.