180.—­THE FOUR SONS.

Readers will recognize the diagram as a familiar friend of their youth.  A man possessed a square-shaped estate.  He bequeathed to his widow the quarter of it that is shaded off.  The remainder was to be divided equitably amongst his four sons, so that each should receive land of exactly the same area and exactly similar in shape.  We are shown how this was done.  But the remainder of the story is not so generally known.  In the centre of the estate was a well, indicated by the dark spot, and Benjamin, Charles, and David complained that the division was not “equitable,” since Alfred had access to this well, while they could not reach it without trespassing on somebody else’s land.  The puzzle is to show how the estate is to be apportioned so that each son shall have land of the same shape and area, and each have access to the well without going off his own land.

[Illustration]

181.—­THE THREE RAILWAY STATIONS.

As I sat in a railway carriage I noticed at the other end of the compartment a worthy squire, whom I knew by sight, engaged in conversation with another passenger, who was evidently a friend of his.

“How far have you to drive to your place from the railway station?” asked the stranger.

“Well,” replied the squire, “if I get out at Appleford, it is just the same distance as if I go to Bridgefield, another fifteen miles farther on; and if I changed at Appleford and went thirteen miles from there to Carterton, it would still be the same distance.  You see, I am equidistant from the three stations, so I get a good choice of trains.”

Now I happened to know that Bridgefield is just fourteen miles from Carterton, so I amused myself in working out the exact distance that the squire had to drive home whichever station he got out at.  What was the distance?

182.—­THE GARDEN PUZZLE.

Professor Rackbrain tells me that he was recently smoking a friendly pipe under a tree in the garden of a country acquaintance.  The garden was enclosed by four straight walls, and his friend informed him that he had measured these and found the lengths to be 80, 45, 100, and 63 yards respectively.  “Then,” said the professor, “we can calculate the exact area of the garden.”  “Impossible,” his host replied, “because you can get an infinite number of different shapes with those four sides.”  “But you forget,” Rackbrane said, with a twinkle in his eye, “that you told me once you had planted this tree equidistant from all the four corners of the garden.”  Can you work out the garden’s area?

183.—­DRAWING A SPIRAL.

If you hold the page horizontally and give it a quick rotary motion while looking at the centre of the spiral, it will appear to revolve.  Perhaps a good many readers are acquainted with this little optical illusion.  But the puzzle is to show how I was able to draw this spiral with so much exactitude without using anything but a pair of compasses and the sheet of paper on which the diagram was made.  How would you proceed in such circumstances?