[Illustration]
One object that I had in view when presenting this little puzzle was to
point out the uncertainty of the meaning conveyed by the word "oval."
Though originally derived from the Latin word _ovum_, an egg, yet what
we understand as the egg-shape (with one end smaller than the other) is
only one of many forms of the oval; while some eggs are spherical in
shape, and a sphere or circle is most certainly not an oval. If we speak
of an ellipse--a conical ellipse--we are on safer ground, but here we
must be careful of error. I recollect a Liverpool town councillor, many
years ago, whose ignorance of the poultry-yard led him to substitute the
word "hen" for "fowl," remarking, "We must remember, gentlemen, that
although every cock is a hen, every hen is not a cock!" Similarly, we
must always note that although every ellipse is an oval, every oval is
not an ellipse. It is correct to say that an oval is an oblong
curvilinear figure, having two unequal diameters, and bounded by a curve
line returning into itself; and this includes the ellipse, but all other
figures which in any way approach towards the form of an oval without
necessarily having the properties above described are included in the
term "oval." Thus the following solution that I give to our puzzle
involves the pointed "oval," known among architects as the "vesica
piscis."
[Illustration: THE TWO STOOLS.]
The dotted lines in the table are given for greater clearness, the cuts
being made along the other lines. It will be seen that the eight pieces
form two stools of exactly the same size and shape with similar
hand-holes. These holes are a trifle longer than those in the
schoolmaster's stools, but they are much narrower and of considerably
smaller area. Of course 5 and 6 can be cut out in one piece--also 7 and
8--making only _six pieces_ in all. But I wished to keep the same number
as in the original story.
When I first gave the above puzzle in a London newspaper, in
competition, no correct solution was received, but an ingenious and
neatly executed attempt by a man lying in a London infirmary was
accompanied by the following note: "Having no compasses here, I was
compelled to improvise a pair with the aid of a small penknife, a bit of
firewood from a bundle, a piece of tin from a toy engine, a tin tack,
and two portions of a hairpin, for points. They are a fairly serviceable
pair of compasses, and I shall keep them as a memento of your puzzle."