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Math Help - bonus word problem

  1. #1
    Junior Member
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    bonus word problem

    A statistician knocks at a house door. The statistician asks, "how many children do you have?" The man at the door answers, "three". The statistician asks, "what are their ages?" The man answers, "the product of their ages is 36" The statistician, unable to determine their ages, asks for another hint. The man says, "The sum of their ages is the number on the house next door." The Statistician goes next door to determine the number. He returns and asks for another hint. The Man says, " the oldest plays the guitar." The Statistician now knows the ages. what are the ages?

    any help would be appreciated!
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  2. #2
    Senior Member I-Think's Avatar
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    Salutations of the night. Would you believe that just yesterday I was doing this problem. It's called the Census-Taker problem. I ended up looking for the solution on the internet and got extremely irritated when I found out how close I was to the solution. Now I'm hooked on these problems.


    From hint 1 we can see that the age of each child is a factor of 36.
    The crux of the problem is that he could not figure it out from observing the neighboring house number. From this we deduce that there are triplets of the factors of 36 whose sums are equal.
    From observation we see that the only triplets for which this is true are (9,2,2) and (6,6,1).
    Hint 2 states that there is an oldest child, therefore (6,6,1) is not the solution.
    Ages of the children are (9,2,2)
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