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Topic: Family Survey (Read 553 times) |
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wonderful
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Family Survey
« on: Apr 17th, 2008, 1:27pm » |
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In a survey of all married couples living in the same street, we know that every couple has children. All children are single. No two familes have the same number of children. The total number of children is greater than the number of mothers and fathers. The number of fathers plus mothers is greater than the number of sons. The number of sons is greater than the number of daughters. The number of daughters is greater than the number of couples (a mother plus a father geneate one couple). Each daughter has at least one brother and at most one sister. There is one couple that have the number of children greater than the sum of all remaining couple's children.
Question: How many couples are there on the street? How many daughter and how many sons are there in each household?
Have A Great Day!
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| « Last Edit: Apr 17th, 2008, 5:36pm by wonderful » |
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SMQ
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Re: Family Survey
« Reply #1 on: Apr 17th, 2008, 1:43pm » |
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I don't believe the information provided is sufficient to give a unique answer, for instance, both "a single family with three sons and two daughters" and "two families, one with a son and a daughter and one with three sons and two daughters" appear to me to meet all the stated criteria, and I believe the list could be expanded indefinitely, although at some point the number of children becomes impractical...
--SMQ
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wonderful
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Re: Family Survey
« Reply #2 on: Apr 17th, 2008, 4:46pm » |
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Thank you SMQ for pointing that out. Actually, there one more condition that I forgot to include in the original question:
The number of fathers plus mothers is greater than the number of sons.
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Grimbal
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Re: Family Survey
« Reply #3 on: Apr 18th, 2008, 4:20am » |
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What do you mean by "all children are single" ?
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SMQ
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Re: Family Survey
« Reply #4 on: Apr 18th, 2008, 7:52am » |
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Grimbal, I believe it just means that none of the children are themselves parents.
With the addition of that condition, the only solution I find is: three families, one with just a son, one with two daughters and a son, and one with two daughters and three sons. With fewer families it's impossible that the number of parents (twice the number of families) > number of sons > number of daughters > number of families, and with more families it's impossible that the number of parents > the number of sons, since each family can have at most two daughters.
--SMQ
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Grimbal
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Re: Family Survey
« Reply #5 on: Apr 18th, 2008, 8:18am » |
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on Apr 18th, 2008, 7:52am, SMQ wrote:| Grimbal, I believe it just means that none of the children are themselves parents. |
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Thanks, that makes sense. I first thought it means "having no siblings", which doesn't make sense.
And it is too bad. I thought it had to do with some more intricate situation, like neighbor children who married and had children on their own.
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