Henry Ernest Dudeney/Modern Puzzles/137 - Hurdles and Sheep

Modern Puzzles by Henry Ernest Dudeney: $137$

Hurdles and Sheep

This is a little puzzle that you can try with matches.

A farmer says that four of his hurdles will form a square enclosure just sufficient for one sheep.

That being so, what is the smallest number of hurdles that he will require for enclosing ten sheep?

Everything depends upon the shape of your enclosure.

The only other way of placing four matches (or hurdles) in $A$ is to form a diamond-shaped figure,

and the more attenuated this diamond becomes the smaller will be its area, until the sides meet,

when there will be no area enclosed at all.

If you place six matches, as in $B$, you will have room for $2$ sheep.

But if you place them as in $C$, you will have room for one sheep, as seven-tenths of a sheep will only exist as mutton.

And if you place them as $D$, you can still only accommodate two sheep, which is the maximum for six hurdles.

Now, how many hurdles do you require for ten sheep?

Sources

• 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Geometrical Problems: Various Geometrical Puzzles: $137$. -- Hurdles and Sheep
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Match Puzzles: $495$. Hurdles and Sheep