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Math Help - Very interesting problem

  1. #1
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    Very interesting problem

    Integer number n\geqslant 1 is given. For every subset (not empty) A of set \lbrace 1, 2, 3, 4,...n \rbrace we assing number w(A) in such a way: if numbers a_{1}>a_{2}>a_{3}>...>a_{k} are all elements of set A, therefore:
    w(A)=a_{1}-a_{2}+a_{3}-...+(-1)^{k+1}a_{k}
    Count the sum of all 2^{n}-1 numbers
    w(A)
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  2. #2
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    I solved this problem some time ago I forgot what I did. But anyway, you can look up the official solution because this was an AIME 1983 problem.
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  3. #3
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    Quote Originally Posted by ThePerfectHacker View Post
    this was an AIME 1983 problem.
    Was it an AIME or maybe a Putman in the late 80s ?
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  4. #4
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    Quote Originally Posted by Plato View Post
    Was it an AIME or maybe a Putman in the late 80s ?
    No it was AIME I am sure of it. They had those back then.
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  5. #5
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    Sorry, but i cannot find the solution, can anybody place it here, please?
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  6. #6
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    Ok, I found the solution, thank you very much for the information
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