Henry Ernest Dudeney/Puzzles and Curious Problems/149 - Sheep Stealing

Puzzles and Curious Problems by Henry Ernest Dudeney: $149$

Sheep Stealing

Some sheep stealers made a raid and carried off one-third of the flock of sheep, and one-third of a sheep.

Another party stole one-fourth of what remained, and one-fourth of a sheep.

Then a third party of raiders carried off one-fifth of the remainder and three-fifths of a sheep,

leaving $409$ behind.

What was the number of sheep in the flock?

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Various Arithmetical and Algebraical Problems: $149$. -- Sheep Stealing
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Miscellaneous Puzzles: $221$. Sheep Stealing