Logic Puzzles

3. Age of Children

A census worker asked a mother for the ages (years, not months) of her three children. The mother replied that the product of their ages is 36, and the sum of their ages is the same as the address (house number) to the north. After looking at that adress, the census worker returned and said to the moter:"I need more information." The mother said: " The oldest is sleeping upstairs." What are the agaes of the three children? What is the address (house number) next door to the north?

Submitted by tartle · Added 12 June 2008

Solution:

The ages of the three children are 9, 2, and 2. The product of these ages is 36 (9 * 2 * 2 = 36), and their sum is 13. The address to the north must be 13, as it matches the sum of the ages. The mention of 'the oldest' indicates there is a distinct oldest child, ruling out other combinations like 6, 6, and 1, which would not have a single oldest child.


Comments (8)

tcagrawal 20 June 2008

Age is 9, 2, 2 AND house no is 13

The reason the census taker could not figure out the children's ages is because, even with knowing the number on the house next door, there were still two possibilities.

The only way that the product could be 36 and still leave two possibilities is if the sum equals 13. These possibilities being 9, 2 and 2 and 6, 6 and 1.

When the home owner stated that her "Oldest" child is sleeping she was giving ths census taker the fact that there is an "oldest." The children's ages are therefore 9,2 and 2.

SmilingFaces96 8 July 2008

I agree with the answer, but disagree with the logic of discerning a difference between 9, 2, 2 and 6, 6, 1 by using the term "oldest". Oldest is an adjective and can refer to 1 child or 2 children.

The oldest (child) is sleeping upstairs OR The oldest (children) are sleeping upstairs.

The key to selecting the proper grouping is the verb. "Is" refers to a singular noun whereas "Are" would refere to a plural noun. In speeking, we tend to leave out the nouns when they are understood.

Therefore, since the woman used "is" in her statement, you can infer that there is only one child sleeping upstairs and it is the oldest.

GrassMan 29 November 2009

I wont agree to what SmilingFaces96 has posted. If you read what tartle has posted (The mother said: " The oldest is sleeping upstairs." ) It is very obvious that there is only one child that is sleeping upstairs. So I agree with tcagarwal about his answer. But I fail to understand how did you deduce the no 13 of the next house when nothing relevant is given. Or am i missing something?

applescript 26 December 2009

Alot of possibilities. I thought the same way as tcagrawal.

1,1,36 = 38
1,2,18 = 21
1,3,12 = 16
1,4,9 = 14
1,6,6 =13

2,2,9 =13
2,3,6 = 11

3,3,4 =10

Since 13 appears twice, it is likely that it might be used for this question as a trick. However, the mum says the oldest is sleeping, which is a reference to only one child and therefore there must be only one eldest kid. Hence by that logic, 2 2 9 seems to be the only answer..

birju 22 March 2010

if u see all the combinations u will find sum of ages is diffrent for all cases except 9,2,2 and 1,6,6 both equals 13 . since officer asks for additional info after this it means that he was confused in these 2 cases else he wouldnt had asked

Excursion 31 August 2010

it could still be 6, 6, 1. the "oldest" could be one of them because one of them is the oldest by at least a few minutes

tsumare 4 January 2011

What exactly is the 2010 Census and how does America count the people? Like I look at Census.gov and they list how many people that live in the United States..when will this be put up anytime soon?

dave08 18 January 2014

yeah. that is 13 and ages are 9 2 and 2. when the cencus taker saw the adress to the north, she asked more info to the mother because there are 2 possibilities.

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