96 Geometrical Problems.^7 .. \
ci···-·~- THE TRIANGULAR
PLANTATION
A man had a plantation of twenty-
one trees set out in the triangular
form shown in our diagram. If he
wished to enclose a triangular piece of
ground with a tree at each of the three
angles, how many different ways of
doing it are there from which he might
select? The dotted lines show three
ways of doing it. How many are there
altogether?'1K1. THE CIRCLE AND DISCSDuring a recent visit to a fair we
saw a man with a table, on the oilcloth
covering of which was painted a large
red circle, and he invited the public to
cover this circle entirely with five tin
discs which he provided, and offered
a substantial prize to anybody who
was successful. The circular discs were
all of the same size, and each, of
course, smaller than the red circle.
The diagram, where three discs are
shown placed, will make everything
clear.
He showed that it was "quite easy
when you know how" by covering up
the circle himself without any ap-
parent difficulty, but many tried over
and over again and failed every time.
I should explain that it was a condi-
tion that when once you had placed
any disc you were not allowed to shift
it, otherwise, by sliding them about
after they had been placed, it might
be tolerably easy to do.
Let us assume that the red circle is
six inches in diameter. What is the
smallest possible diameter (say, to
the nearest half-inch) for the five
discs in order to make a solution
possible?