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# Where there's a will, there's a ... puzzle

## Question

A dying man, knowing his wife was pregnant, left a will that divided his estate between his child and his wife, giving 1/3 to the wife if she gave birth to a son, and 2/3 to the wife if she birthed a daughter. As it turned out, she birthed fraternal twins: a son and a daughter. You are executor of the will. Wishing to adhere as closely as possible to the man's wishes, how will you divide the estate among the three heirs?

If you desire more guidance than what has been provided, the situation is clear: there is no more guidance than what has been provided. You are the law.

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Consider splitting estate as follows

E=estate, W=wife,S=son, D=daughter
1/2E=(1/2*1/3W)+(1/2*2/3S)+ 0D and
1/2E-(1/2*2/3W)+0S+(1/2*1/3D)
-----------------------------------------
E= 1/2W+1/3S +1/6D
Edited by jhawk

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According to the OP wife gets 1/2 of what the son gets. and daughter gets half of what the wife gets.So the property will be divided in the ratio 2:4:1; i.e. if the property is 'a', wife will get 2a/7, son will get 4a/7, and daughter will get a/7.

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One way to look at it is -

wife gets twice to that of girl and half of that of son
so if the man had X amount of property, then daughter gets X/7, Wife gets 2*X/7 and son gets 4*X/7

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Mom should get 30%

Son should get 60%

Daughter should get 10%

1. son should get twice the inheirtance as mom

so 2x -> x where x is mom's money

2. Daughter should get 1/3 of the money that mom gets

so 1/3 x --> where x is mom's money

well 2x + x + 1/3 x add up to all the money so

2x + x + 1/3 x = 100%

where x = 30

so 2x = 60

and 1/3 x =10

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Mom should get 30%

Son should get 60%

Daughter should get 10%

1. son should get twice the inheirtance as mom

so 2x -> x where x is mom's money

2. Daughter should get 1/3 of the money that mom gets

so 1/3 x --> where x is mom's money

well 2x + x + 1/3 x add up to all the money so

2x + x + 1/3 x = 100%

where x = 30

so 2x = 60

and 1/3 x =10

If i am not missing something, then daughter should get half of mom and not 1/3rd.

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Oops.

Mom should get 30%

Son should get 60%

Daughter should get 10%

1. son should get twice the inheirtance as mom

so 2x -> x where x is mom's money

2. Daughter should get 1/3 of the money that mom gets

so 1/3 x --> where x is mom's money

well 2x + x + 1/3 x add up to all the money so

2x + x + 1/3 x = 100%

where x = 30

so 2x = 60

and 1/3 x =10

If i am not missing something, then daughter should get half of mom and not 1/3rd.

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Since the wife gave birth to both a daughter and a son, she should get 1/3 of the estate for giving birth to a son and the other 2/3 for giving birth to a daughter. So I would give the wife the whole estate.

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1. Daughter (1/7) gets half of mother's (2/7) share, and son (4/7) gets twice mother's share.
Most popular solution.
2. Mother (5/15) always gets at least one-third of estate. Son (8/15) gets four times daughter's (2/15) share
3. If first twin born is son (6/9), give him his two-thirds. Mother (2/9) twice daughter's (1/9) share.
4. If first twin born is daughter (3/9), give her her one-third. Son (4/9) twice mother's (2/9) share.

Are there others?

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1. Daughter (1/7) gets half of mother's (2/7) share, and son (4/7) gets twice mother's share.

Most popular solution.

2. Mother (5/15) always gets at least one-third of estate. Son (8/15) gets four times daughter's (2/15) share
3. If first twin born is son (6/9), give him his two-thirds. Mother (2/9) twice daughter's (1/9) share.
4. If first twin born is daughter (3/9), give her her one-third. Son (4/9) twice mother's (2/9) share.

Are there others?

ya.

wife gets nothing, son gets nil, daughter gets zilch and dark magician gets all of it

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How about two more, which are rather mother-centric:

The wife splits the middle since she gave birth to one of each gender - she gets half. If there were only one offspring then a son would have gotten twice as much as a daughter, so we give 2/6 to the son and 1/6 to the daughter

The mother gets 1/3 because she gave birth to a daughter, AND she gets 2/3 because she gave birth to a son. So the mother gets it all.

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I think the puzzle has become something of a Rorschach test.

Interesting.

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Since the will mentions nothing about giving any inheritance to the children, the widow must get the whole thing: 1/3 for giving birth to the son and 2/3 -- for the daughter. That leaves nothing for the executor, which is unfair.

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I think it unfair also, that the puzzle poser is left without benefit. Sigh.

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