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
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.
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
Of course, all the
wood must be used.