Answer :
Though this puzzle presents no great difficulty to
any one possessing a knowledge of algebra, it has perhaps rather
interesting features.
Seeing, as one does in the illustration, just one
corner of the proposed square, one is scarcely prepared for the fact
that the field, in order to comply with the conditions, must contain
exactly 501,760 acres, the fence requiring the same number of rails.
Here is a little rule that will always apply where
the length of the rail is half a pole.
Multiply the number of rails in
a hurdle by four, and the result is the exact number of miles in the
side of a square field containing the same number of acres as there are
rails in the complete fence.
Thus, with a onerail fence the field is
four miles square; a tworail fence gives eight miles square; a
threerail fence, twelve miles square; and so on, until we find that a
sevenrail fence multiplied by four gives a field of twentyeight miles
square.
In the case of our present problem, if the field be made
smaller, then the number of rails will exceed the number of acres;
while if the field be made larger, the number of rails will be less
than the acres of the field.
