237. Counting Losses. An English officer recounted that he was part of a detachment that initially numbered 1000 people. During one of the operations, the detachment suffered heavy losses, and those who survived were captured and sent to a prisoner-of-war camp.

On the first day of the journey, \(\frac{1}{6}\) of all the remaining members of the detachment managed to escape, on the second day, \(\frac{1}{8}\) of the remaining and one person died, on the third day, \(\frac{1}{4}\) of all the remaining escaped. The remaining prisoners were divided into 4 equal groups upon arrival at the camp.

How many people died during the operation?
237. During the fighting, 472 people were killed. By making calculations, the reader will find that each of the four camp groups had 72 people.

The general solution can be obtained from the indeterminate equation

\[
\frac{35 x-48}{768}=\text { an Integer, }
\]

where \(x\) is the number of survivors. Solving it in the usual way, we get \(x=528\). Therefore, the number of those killed is 472 \((1000-528)\).