Find their ages
A census-taker knocks on the door of a house and asks the man how old his children are. The exchange is as follows:
Man : I have three children and their ages are all integers. Their product is 225.
Census-taker : That is insufficient information.
Man : The sum of the ages of my three children is equal to my house number.
Census-taker : That is still insufficient.
Man : Sure, my daughter, Yasmine, has two younger brothers.
Census-taker : Aha!!! Now I finally know how old your children are!!
How old is the man's daughter, Yasmine?
The answer is 25.
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1 solution
Express 225 as the product of three integers, we have the following:
{ 2 2 5 , 1 , 1 } , { 7 5 , 3 , 1 } , { 4 5 , 5 , 1 } , { 2 5 , 9 , 1 } , { 2 5 , 3 , 3 } , { 1 5 , 1 5 , 1 } , { 1 5 , 5 , 3 } , { 9 , 5 , 5 }
Their respective sums are 2 2 7 , 7 9 , 5 1 , 3 5 , 3 1 , 3 1 , 2 3 , 1 9 . Considering that the census-taker still does not know how old the three children are even after being told the sum (which happens to be the house number), the sum must not be unique to a particular set of integers. The only such sum is 3 1 . This leaves us with { 2 5 , 3 , 3 } and { 1 5 , 1 5 , 1 } . But considering that the man's daughter, Yasmine, has two younger brothers, we rule out { 1 5 , 1 5 , 1 } as if that is so, Yasmine will have a twin brother and only one younger brother instead. This leaves us with { 2 5 , 3 , 3 } which means she is 2 5 years old. Indeed, this satisfies the given criteria. At 25, she is an elder sister to two 3-year old boys.