I have frequently had occasion to show that the published answers to a
great many of the oldest and most widely known puzzles are either quite
incorrect or capable of improvement. I propose to consider the old poser
of the table-top and stools that most of my readers have probably seen
in some form or another in books compiled for the recreation of
childhood.
The story is told that an economical and ingenious schoolmaster once
wished to convert a circular table-top, for which he had no use, into
seats for two oval stools, each with a hand-hole in the centre. He
instructed the carpenter to make the cuts as in the illustration and
then join the eight pieces together in the manner shown. So impressed
was he with the ingenuity of his performance that he set the puzzle to
his geometry class as a little study in dissection. But the remainder of
the story has never been published, because, so it is said, it was a
characteristic of the principals of academies that they would never
admit that they could err. I get my information from a descendant of the
original boy who had most reason to be interested in the matter.
The clever youth suggested modestly to the master that the hand-holes
were too big, and that a small boy might perhaps fall through them. He
therefore proposed another way of making the cuts that would get over
this objection. For his impertinence he received such severe
chastisement that he became convinced that the larger the hand-hole in
the stools the more comfortable might they be.
[Illustration]
Now what was the method the boy proposed?
Can you show how the circular table-top may be cut into eight pieces
that will fit together and form two oval seats for stools (each of
exactly the same size and shape) and each having similar hand-holes of
smaller dimensions than in the case shown above? Of course, all the wood
must be used.