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Thread: [SOLVED] Can anyone help?

  1. #1

    Exclamation [SOLVED] Can anyone help?

    I was wondering if there is any kind of formula that will allow me to do this:
    I have about 20 numbers. I want a combination of some of the numbers to add up to be (let's say) $25,768.45. I don't have to use all the numbers to make them add up to that number. I can use 2 or I can use all 20. Is there any kind of formula I can use to help me do this? The numbers are all big and the final number I need them to add up to is big too so I've just been plugging in numbers and guessing but it is taking forever AND I cannot make it work. I realize it may not work, but I thought maybe there is a trick or a shortcut to this. Thanks. Sorry if this makes no sense!
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  2. #2
    MHF Contributor

    Aug 2006
    Given a set of twenty numbers, there are a maximum of $\displaystyle 2^{20} - 1 = 1048575$ possible sums. (There may be several equal sums, but that is the number of different sums.) Given the power of today’s computers, it should be possible to actually check out each possible sum. But there is no mathematical formula to do this for an arbitrary set.
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