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

Puzzles and Curious Problems by Henry Ernest Dudeney: $256$

Catching the Prisoners

Make a rough diagram on a sheet of paper, and use counters to indicate the two warders (marked as $W$) and the two prisoners (marked as $P$).

At the beginning the counters must be placed in the squares shown.

The first player moves each of the warders to an adjacent cell, in any direction.

Then the second player moves each prisoner to an adjoining cell;

and so on until each warder captures his prisoner.

If one warder makes a capture, both he and his captive are out of the game, and the other player continues alone.

You may come to the conclusion that it is a hopeless chase, but it can really be done if you use a little cunning.

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.

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

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

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Solutions: $256$. -- Catching the Prisoners
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $380$. Catching the Prisoners