Henry Ernest Dudeney/Puzzles and Curious Problems/51 - Sharing the Apples

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?

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Age and Kinship Puzzles: $51$. -- Sharing the Apples
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Miscellaneous Puzzles: $185$. Sharing the Apples