### Brain Teasers

# Divide the Will

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?

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

### Answer

Annie - 172,000Bobbie - 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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## Comments

What happen to the letter I?

This is pretty basic first year algebra.

This is pretty basic first year algebra.

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

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.

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.

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

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

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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