Henry Ernest Dudeney/Puzzles and Curious Problems/176 - Counting the Loss

Puzzles and Curious Problems by Henry Ernest Dudeney: $176$

Counting the Loss

An officer explained that the force to which he belonged originally consisted of $1000$ men, but that it lost heavily in an engagement,

and the survivors surrendered and were marched down to a concentration camp.

On the first day's march one-sixth of the survivors escaped;

on the second day one-eighth of the remainder escaped, and one man died;

on the third day's march one-fourth of the remainder escaped.

Arrived in camp, the rest were set to work in four equal gangs.

How many had been killed in the engagement?

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Various Arithmetical and Algebraical Problems: $176$. -- Counting the Loss
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Miscellaneous Puzzles: $240$. Counting the Loss