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Math Help - greek maths puzzle

  1. #1
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    greek maths puzzle

    I found this maths riddle in an article and i can't work it out!!

    somethings telling me this is easier than im making it and it should be quite simple??

    His boyhood lasted 1/6 of his life, he maried after 1/7 more, his beard grew after 1/12 more and his son was born 5 years later, the son lived to half the fathers age and the father died 4 years after the son.

    how long did the father live??



    Any help would be great

    cheers

    Alex
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  2. #2
    Eater of Worlds
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    The son lived to 1/2 his fathers age: S=\frac{1}{2}F

    The fathers life proceeded as follows:

    F=\frac{F}{6}+\frac{F}{12}+\frac{F}{7}+5+S+4

    Sub the first equation into the second and solve for F, the father's age.
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by alexc63 View Post
    I found this maths riddle in an article and i can't work it out!!

    somethings telling me this is easier than im making it and it should be quite simple??

    His boyhood lasted 1/6 of his life, he maried after 1/7 more, his beard grew after 1/12 more and his son was born 5 years later, the son lived to half the fathers age and the father died 4 years after the son.

    how long did the father live??



    Any help would be great

    cheers

    Alex
    Diophantus

    CB
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  4. #4
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    cheers guys

    appreciated
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  5. #5
    Senior Member pacman's Avatar
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    " . . . . have you figured out Diophantus's son's age yet? No? Well - the problem says that the son lived to half his father's life. From the other half, if you take away 1/6th + 1/12th + 1/7th then you are left with with 5+4 = nine years. So 3/28th of his age was 9, so Diophantus turns out to have lived till 84, and his son till 42." -

    Storytelling Science: Aryabhata and Diophantus' son

    "This gives rise to a linear equation in Diophantus’ age x (much simpler than anything Diophantus has done) with x = 84 as the solution." -

    http://www.fen.bilkent.edu.tr/~franz/M300/diopro.pdf




    ok, this site is even better: http://mathworld.wolfram.com/DiophantussRiddle.html

    k
    Last edited by pacman; October 3rd 2009 at 01:58 AM.
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