Henry Ernest Dudeney/Puzzles and Curious Problems/251 - Nine Men in a Trench/Solution

by : $251$

 * Nine Men in a Trench
 * Here are nine men in a trench.


 * Dudeney-Puzzles-and-Curious-Problems-251.png


 * No. $1$ is the sergeant, who wishes to place himself at the other end of the line -- at point $1$ --
 * all the other men returning to their proper places at present.
 * There is no room to pass in the trench, and for a man to climb over another would be a dangerous exposure.
 * But it is not difficult with these three recesses, each of which will hold a man.
 * How is it to be done with the fewest possible moves?
 * A man may go any distance that is possible in a move.

Solution
Move the men in the following order:
 * $2 - 1$, $3 - 2$, $4 - 3$, $5 - 11$, $6 - 4$, $7 - 5$, $8 - 6$,
 * $9 - 7$, $1 - 13$, $9 - 10$, $8 - 9$, $1 - 12$, $7 - 13$, $6 - 8$
 * $5 - 7$, $1 - 11$, $4 - 12$, $3 - 6$, $2 - 5$, $1 - 1$, $2 - 2$
 * $3 - 3$, $4 - 4$, $5 - 5$, $6 - 6$, $7 - 7$, $8 - 8$, $9 - 9$

and the sergeant is in his place in $28$ moves.