Mr Thompson's Maths Blog

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Friday, June 02, 2006

The "Census Problem"
A logic problem for all to think about over a cool glass of lemonade through the weekend. Prize to best explained post by end of June deadline...

A census taker approaches a house and asks the woman who answers the door,"How many children do you have, and what are their ages?"
Woman: "I have three children, the product of their ages are 36, the sum of their ages are equal to the address of the house next door."
The census taker walks next door, comes back and says, "I need more information."
The woman replies, "I have to go, my oldest child is sleeping upstairs."
Census taker: "Thank you, I now have everything I need."
What are the ages of each of the three children?

2 Comments:

Anonymous Chris Longden said...

This one is definatly harder than the missing square puzzle

Well, this tells me there must be 2 or more different possible sets of factors from the original information he had since he couldnt work it out from that information. After working out all the sets of 3 factors of 36, the only sum of the factors which appeared twice or more is 13. If the childrens age total 13, the sets of factors could either be 9,2,2 of 6,6,1. She says her oldest child is asleep, and since Oldest Child is not plural, it means there is only one oldest child, ruling out the possibility of 6,6,2. My answer is that her children are 9,2 and 2

8:07 pm  
Anonymous Anonymous said...

in the possibility of 6 6 1
one of the six year olds must have popped out first, making it the oldest so that can't be ruled out

1:19 pm  

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