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Math Help - number of ways to add integers

  1. #1
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    number of ways to add integers

    In how many ways can six integers from 1 to 60 add up to 60?
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  2. #2
    Super Member Matt Westwood's Avatar
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    Do they have to be different? In other words, will "10+10+10+10+10+10" do as an option?
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  3. #3
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    yes

    They are supposed to be different.

    it is a question about the lottery.
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  4. #4
    Super Member Matt Westwood's Avatar
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    The full mathematical analysis of this is complicated and requires the use of generating functions. An interesting treatise on this subject is given in Polya & Szego's "Problems and Theorems in Analysis" (Springer-Verlag 1924, reprinted 1970).

    However, it's my guess that this question is being asked from a somewhat more basic level than postgrad (we never did generating functions even in my MMath course) so I presume the question you're being asked to solve requires a more basic technique, such as hunting for the solutions by exhaustion.

    So, I'd start by going:

    1+2+3+4+5+(whatever 60-1-2-3-4-5 is)

    1+2+3+4+6+(whatever 60-1-2-3-4-6 is, I'll leave you to do the tricky technical higher mathematics here)

    1+2+3+4+7+ ... etc.

    Long job, but let's face it, it's Saturday night and you're doing maths so it's not as if you've got a date or anything.
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  5. #5
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    Edit: Sorry, I am an idiot, please disregard this

    Long job, but let's face it, it's Saturday night and you're doing maths so it's not as if you've got a date or anything.
    It seems to me that this might be a very long job, as I think there are infinitely many. If we call the sum of the first 5 integers x then a 6th integer 60-x will always exist to make 60. The restriction that integers can't be repeated doesn't seem severe enough to prevent this being the case, although I haven't proved this.
    Last edited by badgerigar; July 26th 2008 at 04:46 PM. Reason: I am an idiot
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