192.—­THE PUZZLE WALL.

[Illustration]

The answer given in all the old books is that shown in Fig. 1, where the curved wall shuts out the cottages from access to the lake.  But in seeking the direction for the “shortest possible” wall most readers to-day, remembering that the shortest distance between two points is a straight line, will adopt the method shown in Fig. 2.  This is certainly an improvement, yet the correct answer is really that indicated in Fig. 3.  A measurement of the lines will show that there is a considerable saving of length in this wall.

193.—­THE SHEEP-FOLD.

This is the answer that is always given and accepted as correct:  Two more hurdles would be necessary, for the pen was twenty-four by one (as in Fig.  A on next page), and by moving one of the sides and placing an extra hurdle at each end (as in Fig.  B) the area would be doubled.  The diagrams are not to scale.  Now there is no condition in the puzzle that requires the sheep-fold to be of any particular form.  But even if we accept the point that the pen was twenty-four by one, the answer utterly fails, for two extra hurdles are certainly not at all necessary.  For example, I arrange the fifty hurdles as in Fig.  C, and as the area is increased from twenty-four “square hurdles” to 156, there is now accommodation for 650 sheep.  If it be held that the area must be exactly double that of the original pen, then I construct it (as in Fig.  D) with twenty-eight hurdles only, and have twenty-two in hand for other purposes on the farm.  Even if it were insisted that all the original hurdles must be used, then I should construct it as in Fig.  E, where I can get the area as exact as any farmer could possibly require, even if we have to allow for the fact that the sheep might not be able to graze at the extreme ends.  Thus we see that, from any point of view, the accepted answer to this ancient little puzzle breaks down.  And yet attention has never before been drawn to the absurdity.

[Illustration

A                 24
+--------------------------------+
|             24                 |1
+--------------------------------+

B
+--------------------------------+
|             48                 |2
+--------------------------------+
24
C
+--------------------+          D
|                    |     +----------+
|                    |     |          |
|                    |12   |    48    |6
|       156          |     |          |
|                    |     +----------+
|                    |           8
|                    |
|                    |
+--------------------+
13

12         .    E    13
.    ’        ’   .
.   ’                         ’   .
’   .                 .   ’
12     ’   .    ’    13

]

194.—­THE GARDEN WALLS.

The puzzle was to divide the circular field into four equal parts by three walls, each wall being of exactly the same length.  There are two essential difficulties in this problem.  These are:  (1) the thickness of the walls, and (2) the condition that these walls are three in number.  As to the first point, since we are told that the walls are brick walls, we clearly cannot ignore their thickness, while we have to find a solution that will equally work, whether the walls be of a thickness of one, two, three, or more bricks.