if you then start at the right place.
You may never pass over a "catch"; you must always remove the card and
start afresh.

275.--THE SIXTEEN SHEEP.

[Illustration:

+========================+
|| | | | ||
|| 0 | 0 | 0 | 0 ||
+-----+-----+-----+------+
|| | | | ||
|| 0 | 0 | 0 | 0 ||
+========================+
|| || | || ||
|| 0 || 0 | 0 || 0 ||
+-----+=====+=====+------+
|| | || | ||
|| 0 | 0 || 0 | 0 ||
+========================+

]

Here is a new puzzle with matches and counters or coins. In the
illustration the matches represent hurdles and the counters sheep. The
sixteen hurdles on the outside, and the sheep, must be regarded as
immovable; the puzzle has to do entirely with the nine hurdles on the
inside. It will be seen that at present these nine hurdles enclose four
groups of 8, 3, 3, and 2 sheep. The farmer requires to readjust some of
the hurdles so as to enclose 6, 6, and 4 sheep. Can you do it by only
replacing two hurdles? When you have succeeded, then try to do it by
replacing three hurdles; then four, five, six, and seven in succession.
Of course, the hurdles must be legitimately laid on the dotted lines,
and no such tricks are allowed as leaving unconnected ends of hurdles,
or two hurdles placed side by side, or merely making hurdles change
places. In fact, the conditions are so simple that any farm labourer
will understand it directly.

276.--THE EIGHT VILLAS.

In one of the outlying suburbs of London a man had a square plot of
ground on which he decided to build eight villas, as shown in the
illustration, with a common recreation ground in the middle. After the
houses were completed, and all or some of them let, he discovered that
the number of occupants in the three houses forming a side of the square
was in every case nine. He did not state how the occupants were
distributed, but I have shown by the numbers on the sides of the houses
one way in which it might have happened. The puzzle is to discover the
total number of ways in which all or any of the houses might be
occupied, so that there should be nine persons on each side. In order
that there may be no misunderstanding, I will explain that although B is
what we call a reflection of A, these would count as two different
arrangements, while C, if it is turned round, will give four
arrangements; and