Henry Ernest Dudeney/Puzzles and Curious Problems/51 - Sharing the Apples/Solution
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Puzzles and Curious Problems by Henry Ernest Dudeney: $51$
- Sharing the Apples
- Eight children had a basket containing $32$ apples.
- They divided them amongst themselves as follows:
- Anne got one apple,
- Mary two,
- Jane three,
- and Kate four.
- Ned Smith took as many as his sister,
- Tom Brown twice as many as his sister,
- Bill Jones three times as many as his sister,
- and Jack Robinson four times as many as his sister.
- What are the full names of the girls?
Solution
- Ned Smith and his sister Jane took $3$ and $3$ respectively.
- Tom and Kate Brown took $8$ and $4$ respectively.
- Bill and Anne Jones took $3$ and $1$ respectively.
- Jack and Mary Robinson took $8$ and $2$ respectively.
Proof
This is exactly the same problem as $38$ - The Picnic from the same collection.
$\blacksquare$
Sources
- 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Solutions: $51$. -- Sharing the Apples
- 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $185$. Sharing the Apples