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Math Help - problem for those good at math

  1. #1
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    problem for those good at math

    In his will, a nobleman leaves half of his horses to his oldest son, a third to his second son, and a ninth to his youngest son. At his death the nobleman has 17 horses, so none of these bequests results in a whole number of horses for any of the sons. The executor of the will solves this dilemma by adding one of his own heroes to the estate, making a total of 18. Now, according to the provisions of the will, he gives 9 horses to the oldest son, 6 horses to the second son, and 2 to the third son. Thus, each son inherits a little more than he was originally entitled to, and one horse is left over, which the executor takes back again. Everybody is happy, but something seems frond, what is wrong?
    Can you explain clearly, if possible
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  2. #2
    Senior Member ecMathGeek's Avatar
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    Quote Originally Posted by mcdaking84 View Post
    In his will, a nobleman leaves half of his horses to his oldest son, a third to his second son, and a ninth to his youngest son. At his death the nobleman has 17 horses, so none of these bequests results in a whole number of horses for any of the sons. The executor of the will solves this dilemma by adding one of his own heroes to the estate, making a total of 18. Now, according to the provisions of the will, he gives 9 horses to the oldest son, 6 horses to the second son, and 2 to the third son. Thus, each son inherits a little more than he was originally entitled to, and one horse is left over, which the executor takes back again. Everybody is happy, but something seems frond, what is wrong?
    Can you explain clearly, if possible
    1/2 + 1/3 + 1/9 = 9/18 + 6/18 + 2/18 = 17/18

    This does not equal 1 so the way the horses are allocated does not include 100% of the total number of horses. If there are 18 horses then only 17 are inherited. However, if only 17 horses are present then they cannot be properly allocated as the no son can receive 1/2, 1/3, or 1/9 of 17 horses. There needs to be 18 horses present for them to be distributed evenly.
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  3. #3
    Bar0n janvdl's Avatar
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    Hmm, i think ive seen this solution before, u have to add 1 to the number of horses. But then when u add the number of distributed horses again you get 17 instead of 18.

    Can someone explain why this happens?
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by janvdl View Post
    Hmm, i think ive seen this solution before, u have to add 1 to the number of horses. But then when u add the number of distributed horses again you get 17 instead of 18.

    Can someone explain why this happens?
    The will only allocates 17/18 th of the noblemans horses, always leaving
    1/18 th of his horses unallocated. So if he leaves a number of horses not
    divisible by 18 they cannot be allocated according to the will.

    By adding one of his own horses to the estate the executor can now allocate
    the horses according to the will, and there will be one horse unallocated
    which he can keep.

    RonL
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