Toughest Age Question

Discussion in 'Undergraduate Math' started by divya bisht, Nov 7, 2011.

  1. divya bisht

    divya bisht Guest

    Toughest Age Question
    ( Source :

    Two old friends, Jack and Bill, meet after a long time.
    Three kids
    Jack: Hey, how are you man?
    Bill: Not bad, got married and I have three kids now.
    Jack: That’s awesome. How old are they?
    Bill: The product of their ages is 72 and the sum of their ages is the
    same as your birth date.
    Jack: Cool… But I still don’t know.
    Bill: My eldest kid just started taking piano lessons.
    Jack: Oh now I get it.

    How old are Bill’s kids?

    Update Answers at :
    divya bisht, Nov 7, 2011
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  2. divya bisht

    Barb Knox Guest

    This is a thoroughly wretched problem. A date is *not* an integer. It
    is a triple of integers (yyyy,mm,dd) or a pair of integers (yyyy,ddd).

    I infer you mean for the "birth date" to not include the year, and for
    dd/mm to be considered as a decimal integer by removing the slash, but
    that still leaves fatal ambiguities:

    * Is the 8th of January 8/01 or 8/1 ?
    * What about the parts of the world where dates are conventionally
    mm/dd ? Then that date would be 108 or 18.

    | BBB b \ Barbara at LivingHistory stop co stop uk
    | B B aa rrr b |
    | BBB a a r bbb | Quidquid latine dictum sit,
    | B B a a r b b | altum videtur.
    | BBB aa a r bbb |
    Barb Knox, Nov 8, 2011
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  3. divya bisht

    Country Boy

    Dec 15, 2021
    Likes Received:
    How Jack's birth date is written or even what it is irrelevant! A crucial point here is that we typically state peoples ages as integers- "7 years old", not "7 years and 3 months" or "7.25 years". 72= 8(9)= 2(2)(2)(3)(3). How many ways can we separate those into 3 different ages? I see only 2 different ways:
    [2(2)], [2(3)], [3] or 3, 4, and 6.
    [2(3)], [2(3)], [2] or 2, 6, and 6.

    The point of "My eldest kid just started taking piano lessons." is that there IS an "eldest kid" which tells us that the three children's ages are 3, 4, and 6, not "2, 6, 6".
    Country Boy, Dec 26, 2021
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