Bootin D. ..

Several guard brigades of the same size slept for the same number of nights. Each guard slept more nights than there are guards in a brigade, but fewer than the number of brigades. How many guards are in a brigade if all the guards together slept for 1001 person-nights?
$1001=7 \cdot 11 \cdot 13$.

## Solution

Let $s$ be the number of guards in a squad, $b$ be the number of squads, and $n$ be the number of nights one guard slept. Then $2 b n=1001$.

But $1001=7 \cdot 11 \cdot 13$, and the numbers $7,11,13$ are prime. Considering that $s<n<b$, we get $s=7$.

Answer

7 guards.

Submit a comment