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Thread: Hello I Like Math

  1. #1
    Jul 2014

    Hello I Like Math

    I think math is fun. Problem is that I do not always know how to do what I am trying to. I must now rely on my fellow man to take his time, for free, and choose to give it away rather than sell it. I appreciate communities and their ability to come together to work a problem.

    I have a problem. I will try to describe it the best way I can. I am not just looking for someone to do the work, I also want to know what this type of math is called and how it works.

    So here is the problem:

    I am trying to figure out the best order in which to subtract a list of numbers from a specific constant number to offer the best efficient solution. So as to minimize waste.

    Can someone please help me with the methods, theories, whatever for doing this?

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  2. #2
    MHF Contributor
    Nov 2013

    Re: Hello I Like Math

    assuming the list is just random numbers the quickest method would be as follows.

    Let your list be

    $a_{0,i},~i=1,N$ (the reason for the zero will become apparent)

    now form a new list


    i.e. we add adjacent pairs of numbers from the 0th list to come up with the 1st list.
    Repeat to form $a_{2,k}, a_{3,k}$, etc. until there is only a single number left.

    This number is the sum of all the numbers on your list.

    Subtract this from your constant.

    To make this a bit clearer consider

    $a_0=\{ 1, 3, -2, 7, 13, -5, -1, 6\}$

    we form

    $a_1=\{ (1+3), (-2+7), (13-5),(-1+6) \} =\{ 4, 5, 8, 5 \}$

    $a_2 = \{ (4+5), (8+5) \}=\{ 9, 13 \}$

    $a_3 = \{ (9+13) \} = \{ 22 \}$

    so subtract 22 from your constant.
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