Henry Ernest Dudeney/Puzzles and Curious Problems/134 - The Bag of Nuts

Puzzles and Curious Problems by Henry Ernest Dudeney: $134$

The Bag of Nuts

There are $100$ nuts distributed between $5$ bags.

In the first and second there are altogether $52$ nuts;

in the second and third there are $43$;

in the third and fourth there are $34$;

in the fourth and fifth, $30$.

How many nuts are there in each bag?

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Various Arithmetical and Algebraical Problems: $134$. -- The Bag of Nuts
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Miscellaneous Puzzles: $207$. The Bag of Nuts