Henry Ernest Dudeney/Puzzles and Curious Problems/241 - A Hurdles Puzzle/Solution

by : $241$

 * A Hurdles Puzzle

Solution
The answer completely depends on the arrangement of the hurdles to make the pen.

Consider the following diagrams:


 * Dudeney-Puzzles-and-Curious-Problems-241-solution.png

The original answer that is frequently seen is that it can be done with $2$ hurdles.

The arrangement given is that of $A$, a long paddock $1$ hurdle wide and $24$ hurdles long, enclosing an area of $24$ square hurdles.

In $B$, we see we have added $2$ more hurdles to the short sides, making a paddock $2$ hurdles wide and $24$ hurdles long, enclosing an area of $48$ square hurdles.

But consider.

With $50$ hurdles you can make a paddock as in $C$, $156$ square hurdles by making it $12 \times 13$, which is $6 \tfrac 1 2$ times the size of the original $24 \times 1$ paddock.

Or you can make a $6 \times 8$ paddock with $28$ hurdles, as in $D$.

And so on.

also manages to arrange $50$ hurdles in an elongated kite shape with sides $12$, $12$, $13$, $13$ explaining that this is also $48$ square hurdles in area, but his diagram is unconvincing.