July 2018
Problem of the Month

Dividing the Spoils
by Sam Loyd

After gathering 770 chestnuts, the three little girls divided them up so that the 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 to the Problem:

Nellie received 198 chestnuts, Mary got 264 chestnuts, and Susie received 308 chestnuts.

We learn from the manner in which the nuts were divided that the girls' ages were in the ratio 9 : 12 : 14.
Let 9x = number of chestnuts that Nellie got
Let 12x = number of chestnuts that Mary got
Let 14x = number of chestnuts that Susie got

Then 9x + 12x + 14x = 770
So, 35x = 770
x = 22
Note that you cannot determine the exact ages of the three girls.

Correctly solved by:

1. James Alarie	Flint, Michigan
2. Rob Miles	Northbrook, Illinois
3. Ivy Joseph	Pune, Maharashtra, India
4. SreeRoopa Sankararaman	Singapore, Singapore
5. Bob Currie	R E Campbell Company, Houston, Texas
6. Kelly Stubblefield	Mobile, Alabama

Send any comments or questions to: David Pleacher