92 Geometrical ProblemsBFC, and BGC, are six such triangles. It is not a difficult count if you proceed
with some method, but otherwise you are likely to drop triangles or include
some more than once.- A HURDLES PUZZLE
The answers given in the old books to some of the best-known puzzles are
often clearly wrong. Yet nobody ever seems to detect their faults. Here is
an example. A farmer had a pen made of fifty hurdles, capable of holding a
hundred sheep only. Supposing he wanted to make it sufficiently large to
hold double that number, how many additional hurdles must he have?- THE ROSE GARDEN
"A friend of mine," said Professor
Rackbrane, "has a rectangular gar-
den, and he wants to make exactlyone-half of it into a large bed of roses,
with a gravel path of uniform width
round it. Can you find a general rule
that will apply equally to any rectan-
gular garden, no matter what its pro-
portions? All the measurements must
be made in the garden. A plain rib-
bon, no shorter than the length of the
garden, is all the material required."- CORRECTING A BLUNDER
Mathematics is an exact science,
but first-class mathematicians are apt,
like the rest of humanity, to err badly
on occasions. On refering to Peter
Barlow's valuable work on The Theory
of Numbers, we hit on this problem:
"To find a triangle such that its
three sides, perpendicular, and the
line drawn from one of the angles bi-
secting the base may be all expressed
in rational numbers." He gives as his
answer the triangle 480, 299, 209,
which is wrong and entirely unintel-
ligible.
Readers may like to find a correct
solution when we say that all the five
measurements may be in whole num-
bers, and every one of them less than
a hundred. It is apparently intended
that the triangle must not itself be
right angled.