Henry Ernest Dudeney/Puzzles and Curious Problems/131 - Feeding the Monkeys

Puzzles and Curious Problems by Henry Ernest Dudeney: $131$

Feeding the Monkeys

A man went to the zoo with a bag of nuts to feed the monkeys.

He found that if he divided them equally amongst the $11$ monkeys in the first cage he would have $1$ nut over;

if he divided them equally amongst the $13$ monkeys in the second cage there would be $8$ left;

if he divided them amongst the $17$ monkeys in the last cage $3$ nuts would remain.

He also found that if he divided them equally amongst the $41$ monkeys in all $3$ cages,

or amongst the monkeys in any $2$ cages,

there would always be some left over.

What is the smallest number of nuts that the man could have in his bag?

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Various Arithmetical and Algebraical Problems: $131$. -- Feeding the Monkeys
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Miscellaneous Puzzles: $204$. Feeding the Monkeys