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

by : $137$

 * A New Match Puzzle
 * 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?


 * Dudeney-Modern-Puzzles-137.png


 * 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?