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Divide the Will

Math brain teasers require computations to solve.


Puzzle ID:#897
Fun:*** (2.41)
Difficulty:*** (2.13)
Submitted By:Michelle***




An old woman died leaving an estate of $1,000,000. Her estate was divided up among her surviving relatives. Her relatives: Jennie, Bobbie, Ellie, Ginnie, Candie, Dannie, Frannie, Annie, Hollie and Kathie were each given an amount of money. The eccentric woman's will stated that each of her relatives was to be given an amount based on the alphabetic order of their first name. The heirs were listed in the order of their names and thus the order of their gift. Annie received the most and Kathie received the least amount. The difference in the amounts given to each person was to be constant. (i.e. The difference between the amount given to the first and second person on the list was the same as the difference in the amount given to the next-to-last and the last person on the list.)

If Ellie received 108,000, how much did each other person receive?

Open Calculator


Annie - 172,000
Bobbie - 156,000
Candie - 140,000
Dannie - 124,000
Ellie - 108,000
Frannie - 92,000
Ginnie - 76,000
Hollie - 60,000
Jennie - 44,000
Kathie - 28,000


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Nov 01, 2001

What happen to the letter I?
This is pretty basic first year algebra.
Aug 23, 2002

or alternativly: they all got exactly the same as the last person on the list got the will overturned as anyone who would divide up their money this way has to be two sandwiches short of a picnic!! only joking. enjoyed seeing a basic problem for a change
Jul 15, 2004

What algebra? -----

This is, at most, elementary 3rd grade arithmetic (and alphabetic ordering): the average amount is $100'000. Ellie is 5th, so the 6th one will be below average by $8000. Thus the difference between what one person and the next gets is $16'000. Then keep adding and subtracting that. -----

Very boring for those of us who are past 3rd grade.
Jan 20, 2009

Giving the 5th term made the easy problem trivial.

The fundamental equation, which can be rearranged to solve for any of the desired values, is:

Min = (Total - Increment x (N^2 - N) / 2) / N

Where Min is the smallest partition; Total is the total amount in all partitions; Increment is the difference between partitions; and N is the number of partitions.

Min = (1000000 - 16000 x (10^2 - 10) / 2) / 10
Min = (1000000 - 16000 x 45) / 10
Min = (1000000 - 720000) / 10
Min = 28000

Mar 31, 2009

I prefer the elegant (but I agree simple) logic of the canuist. Textbook series problem (You did these in the third grade???)

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