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
]