Question 150

# 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 is 36, the sum of their ages is 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?

Solution

It is given, product of their ages is 36.
Possible combinations are:
1*1*36 - sum = 38
1*2*18- sum = 21
1*3*12 - sum = 16
1*4*9 - sum = 14
1*6*6 -sum = 13
2*2*9 - sum = 13
2*3*6 - sum = 11
3*3*4 - sum = 10
The census takers comes back and ask for more information implies that the sum is 13. There are two possibilities for only sum 13, as there are two possibilities census taker comes back and asks for other clue.
(1, 6, 6) or (2, 2, 9)
The woman says her oldest child is sleeping upstairs. Therefore, the ages will be (2, 2, 9).

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