The Census Taker
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  1. #1
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    Question The Census Taker

    Here is a math puzzle which was on a local radio show again recently. The person who posts the correct answer will be 'required' to explain the answer. (No, I can't enforce that---but I can add necessary responses )

    A census taker approaches a man on his porch and begins asking questions, one of which is: "How many children do you have, and what are their ages?"

    The man replies: "I have three and the sum of their ages equals my house number".

    The official thinks a bit and says he needs more information, to which the man replies: "The product of their ages is 36".

    The official pauses and then indicates he still needs more facts, to which the homeowner says: My oldest child plays the piano.

    What are the children's ages?


    .

  2. #2
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    Re: The Census Taker

    it could be
    6, 6 and 1
    6, 3 and 2, or
    12, 3 and 1, or
    9, 4, and 1, or
    9, 2, and 2
    18, 2, and 1
    36, 1, and 1

    there isn't enough information to give the correct answer. any of the above the oldest can play the piano, the product of each example is 36, and the instances where the ages are the same could be twins or one of them adopted. the critical information needs the house number. having it you can solve the problem.

  3. #3
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    Re: The Census Taker

    I would not have posted this if there were not one discrete, determinable solution.

  4. #4
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    Re: The Census Taker

    Quote Originally Posted by Scott Young View Post
    it could be
    6, 6 and 1
    6, 3 and 2, or
    12, 3 and 1, or
    9, 4, and 1, or
    9, 2, and 2
    18, 2, and 1
    36, 1, and 1

    there isn't enough information to give the correct answer. any of the above the oldest can play the piano, the product of each example is 36, and the instances where the ages are the same could be twins or one of them adopted. the critical information needs the house number. having it you can solve the problem.
    Last edited by Broccoli1; 06-08-2009 at 05:52 PM.

  5. #5
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    Re: The Census Taker

    this problem has a catch and it plays upon the term "oldest" thus eliminating the possibility of 6,6, and 1. but it doesn't do away with the other possibilities. let's omit the 36,1, and 1 and the 18, 2 and 2 for sake of arguing the oldest constitutes an adult, but the field of possibilities isn't clear enough to champion one answer over any of the others. we are left with 6,3 and 2 or 12, 3, and 1 or 9, 4, and 1, or 9, 2, and 2.

  6. #6
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    Re: The Census Taker

    [Scott Young;288201]this problem has a catch and it plays upon the term "oldest" thus eliminating the possibility of 6,6, and 1.
    not necessarily 2 could be < a year apart -- one's birthday could have been yesterday and the other's tomorrow. . .

    It would seem as if the census taker would have had the house number, they usually work from a printed list that would likely have it or it should be on the house or mailbox
    Last edited by fredf; 06-08-2009 at 07:14 PM.
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  7. #7
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    Re: The Census Taker

    If you read the wording carefully and consider that it means something when he says he needs more information, then it does make sense. It isn't a play on words or some semantic trick, either; it is just a logical puzzle.

  8. #8
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    Re: The Census Taker

    I have a feeling that the answer is an equation, which the census taker must apply to the known house number.

    Good Luck

  9. #9
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    Re: The Census Taker

    Hmmm house number = 13. two combinations add up to 13: 6,6,1 and 9,2,2 either a 6 yo or a 9yo could play the pianno, but oldest implies only one so my answer is 9, 2, and 2
    -- fred

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  10. #10
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    Re: The Census Taker

    Quote Originally Posted by denrep View Post
    I have a feeling that the answer is an equation, which the census taker must apply to the known house number.
    All whole numbers.
    Youngest
    Middle
    Oldest
    HN house number
    Oldest = or greater than minimum piano playing age.
    M less than O
    Y less than O



    Y + M + O= HN
    Y x M x O= 36

    Now, how can you apply 36 to HN, to solve Y M O???

    Good Luck
    Last edited by denrep; 06-08-2009 at 08:05 PM.

  11. #11
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    Re: The Census Taker

    Quote Originally Posted by fredf View Post
    Hmmm house number = 13. two combinations add up to 13: 6,6,1 and 9,2,2 either a 6 yo or a 9yo could play the pianno, but oldest implies only one so my answer is 9, 2, and 2
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  12. #12
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    Re: The Census Taker

    Fredf has it.

    The possible combinations and their sums are:

    • ....Ages .... sum
    • 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


    If you read the wording carefully and consider that it means something when he says he needs more information, then it does make sense. It isn't a play on words or some semantic trick, either; it is just a logical puzzle.
    The census taker is at the front of the house and can see the number but still needs more information because two combinations have the same sum. Only the second set has an older child so that (2, 2, 9 ) is the correct answer
    Last edited by Oldiron2; 06-08-2009 at 08:05 PM.

  13. #13
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    Re: The Census Taker

    oldiron that one is pretty good.

  14. #14
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    Re: The Census Taker

    I liked it because it made me think; it's like the real problems which we all deal with from time to time where we need to evaluate all the factors and think about things which could have happened, even if they're not common.

    BTW, what would you say if a real Census taker asked how many toilets or welders you had; Ask if he meant Welders, Weldors, or Chinese Imports?

    Sorry; I couldn't resist!

  15. #15
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    Re: The Census Taker

    Ans, the oldest is 36 yrs and plays the piano and the others are new born.
    Last edited by transit; 06-09-2009 at 12:27 AM.

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