Henry Ernest Dudeney/Puzzles and Curious Problems/251 - Nine Men in a Trench/Solution
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Puzzles and Curious Problems by Henry Ernest Dudeney: $251$
- Nine Men in a Trench
- Here are nine men in a trench.
- 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.
Sources
- 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Solutions: $251$. -- Nine Men in a Trench
- 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $376$. Nine Men in a Trench