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By Sam Loyd

After gathering 770 chestnuts, the three little girls divided them up so that their amounts were in the same proportion as their ages. As often as Mary took four chestnuts, Nellie took three, and for every six that Mary received, Susie took seven.

How many chestnuts did each girl get?

Solution:

We learn from the manner in which the nuts were divided that the girls' ages are in the proportions 9:12:14. Therefore the 770 chestnuts were divided so that the youngest girl got 198, the next oldest got 264, and the oldest got 308.

As for the ages of the girls, they cannot be determined exactly. All we know is that their ages are in the proportions 9:12:14. Judging by the picture (unreproducible on E2), a good guess would be 4½, 6 and 7 years.

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