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
If we speak of an ellipse—a conical
ellipse—we are on safer ground, but here we must be careful
I recollect a Liverpool town councillor, many
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!"
must always note that although every ellipse is an oval, every oval is
not an ellipse.
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."
following solution that I give to our puzzle involves the pointed
"oval," known among architects as the "vesica piscis."
The dotted lines in the table are given for
greater clearness, the cuts being made along the other lines.
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
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.
a fairly serviceable pair of compasses, and I shall keep them as a
memento of your puzzle."