Girl Talk
A census-taker calls at a house. He asks the woman living there the ages of her three daughters.
The woman says,"If you multiply their ages the total is 72;if you add together their ages the total is same as the number on my front door,which you can see."
The census-taker says, "That is not enough information for me to calculate their ages."
The woman says, "Well,my eldest daughter has a cat with a wooden leg."
The census-taker replies, "Ah! Now I know their ages."
Find the sum of squares of the ages of the girls
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1 solution
First, we start off by listing all the factors of 7 2 , then add them up because all of them are possible to be the girls' age
It might be long, so I want you to write it down yourself
The census-taker may think that he can already solve it because he knows the woman's door number, BUT , there are two sums that are equal to the door number, 2 , 6 , 6 and 3 , 3 , 8 thus he can't know their ages
Then, the woman told him that he has an eldest daughter, only 3 , 8 , 8 has an eldest daughter because the other one only has a youngest daughter