193.—­THE SHEEPFOLD.

It is a curious fact that the answers always given to some of the best-known puzzles that appear in every little book of fireside recreations that has been published for the last fifty or a hundred years are either quite unsatisfactory or clearly wrong.  Yet nobody ever seems to detect their faults.  Here is an example:—­A farmer had a pen made of fifty hurdles, capable of holding a hundred sheep only.  Supposing he wanted to make it sufficiently large to hold double that number, how many additional hurdles must he have?

194.—­THE GARDEN WALLS.

[Illustration]

A speculative country builder has a circular field, on which he has erected four cottages, as shown in the illustration.  The field is surrounded by a brick wall, and the owner undertook to put up three other brick walls, so that the neighbours should not be overlooked by each other, but the four tenants insist that there shall be no favouritism, and that each shall have exactly the same length of wall space for his wall fruit trees.  The puzzle is to show how the three walls may be built so that each tenant shall have the same area of ground, and precisely the same length of wall.

Of course, each garden must be entirely enclosed by its walls, and it must be possible to prove that each garden has exactly the same length of wall.  If the puzzle is properly solved no figures are necessary.

195.—­LADY BELINDA’S GARDEN.

Lady Belinda is an enthusiastic gardener.  In the illustration she is depicted in the act of worrying out a pleasant little problem which I will relate.  One of her gardens is oblong in shape, enclosed by a high holly hedge, and she is turning it into a rosary for the cultivation of some of her choicest roses.  She wants to devote exactly half of the area of the garden to the flowers, in one large bed, and the other half to be a path going all round it of equal breadth throughout.  Such a garden is shown in the diagram at the foot of the picture.  How is she to mark out the garden under these simple conditions?  She has only a tape, the length of the garden, to do it with, and, as the holly hedge is so thick and dense, she must make all her measurements inside.  Lady Belinda did not know the exact dimensions of the garden, and, as it was not necessary for her to know, I also give no dimensions.  It is quite a simple task no matter what the size or proportions of the garden may be.  Yet how many lady gardeners would know just how to proceed?  The tape may be quite plain—­that is, it need not be a graduated measure.

[Illustration]

196.—­THE TETHERED GOAT.

[Illustration]

Here is a little problem that everybody should know how to solve.  The goat is placed in a half-acre meadow, that is in shape an equilateral triangle.  It is tethered to a post at one corner of the field.  What should be the length of the tether (to the nearest inch) in order that the goat shall be able to eat just half the grass in the field?  It is assumed that the goat can feed to the end of the tether.