Henry Ernest Dudeney/Puzzles and Curious Problems/154 - Marching an Army/Solution

by : $154$

 * Marching an Army
 * A body of soldiers was marching in regular column, with $5$ men more in depth than in front.
 * When the enemy came in sight the front was increased by $845$ men,
 * and the whole was drawn up in $5$ lines.


 * How many men were there in all?

Solution
There were $4550$ men in the army.

Proof
Let $m$ be the total number of men.

Let $n$ be the number of men in front while marching.

We have: