Answer :
The puzzle was to cut the two shoes (including the
hoof contained within the outlines) into four pieces, two pieces each,
that would fit together and form a perfect circle. It was also
stipulated that all four pieces should be different in shape.
As a
matter of fact, it is a puzzle based on the principle contained in that
curious Chinese
symbol the Monad.
The above diagrams give the correct solution to
the problem. It will be noticed that 1 and 2 are cut into the required
four pieces, all different
in shape, that fit together and form the perfect circle shown in
Diagram 3.
It will further be observed that the two pieces A and B of
one shoe and the two pieces C and D of the other form two exactly
similar halves of the circle—the Yin and the Yan of the great
Monad.
It will be seen that the shape of the horseshoe is more easily
determined from the circle than the dimensions of the circle from the
horseshoe, though the latter presents no difficulty when you know that
the curve of the long side of the shoe is part of the circumference of
your circle.
The difference between B and D is instructive, and the
idea is useful in all such cases where it is a condition that the
pieces must be different in shape. In forming D we simply add on a
symmetrical piece, a curvilinear square, to the piece B.
Therefore, in
giving either B or D a quarter turn before placing in the new position,
a precisely similar effect must be produced.
