A speculative country builder has a circular
field, on which he has erected four cottages, as shown in the
The field is surrounded by a brick wall, and the owner undertook to put
up three other brick walls, so that the neighbours should not be
overlooked by each other, but the four tenants insist that there shall
be no favouritism, and that each shall have exactly the same length of
wall space for his wall fruit trees. The puzzle is to show
How may be built three walls so that each
tenant shall have the same area of ground, and precisely the same
length of wall?
Of course, each garden must be entirely enclosed
by its walls, and it must be possible to prove that each garden has
exactly the same length of wall.