Henry Ernest Dudeney/Puzzles and Curious Problems/256 - Catching the Prisoners/Solution

by : $256$

 * Catching the Prisoners

Solution
The trick is that it is impossible for the warder to catch the nearer prisoner.

He has to aim for the one on the opposite side of the prison.

Let the squares be labelled $1$ to $40$, reading across then down.

Let the prisoners and warders be labelled $P_1$, $P_2$, $W_1$ and $W_2$ as shown.


 * Dudeney-Puzzles-and-Curious-Problems-256-solution.png

Then we present a specimen game, where the warders' moves are above the line, the prisoners's below.


 * $\dfrac {19-20 \ 22-14} {17-18 \ 24-23}, \dfrac {20-21 \ 14-13} {18-26 \ 23-31}, \dfrac {21-22 \ 13-12} {26-27 \ 31-32}, \dfrac {22-23 \ 12-20} {27-26 \ 32-40}, \dfrac {23-31 \ 20-19} {40-32 \ 26-34}, \dfrac {31-32 \text { Capture} \ 19-27} {\qquad \qquad \qquad \ 34-33}, \dfrac {27-26} {33-25}, 26-25 \text { Capture}$