THE SIXTEEN SHEEP.
(
Combination and Group Problems)
[Illustration:
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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.
Answer:
The six diagrams on next page show solutions for the cases where we
replace 2, 3, 4, 5, 6, and 7 hurdles. The dark lines indicate the
hurdles that have been replaced. There are, of course, other ways of
making the removals.
