Henry Ernest Dudeney/Modern Puzzles/82 - Army Figures

Modern Puzzles by Henry Ernest Dudeney: $82$

Army Figures

A certain division in an army was composed of a little over twenty thousand men, made up of five brigades.

It was know that one third of the first brigade,

two-sevenths of the second brigade,

seven-twelfths of the third,

nine-thirteenths of the fourth,

and fifteen-twenty-seconds of the fifth brigades happened in every case to be the same number of men.

Can you discover how many men there were in every brigade?

Sources

• 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Arithmetical and Algebraical Problems: Various Arithmetical and Algebraical Problems: $82$. -- Army Figures
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Miscellaneous Puzzles: $165$. Army Figures