1. ## 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
$w(A)$

2. 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.

3. Originally Posted by ThePerfectHacker
this was an AIME 1983 problem.
Was it an AIME or maybe a Putman in the late ‘80’s ?

4. Originally Posted by Plato
Was it an AIME or maybe a Putman in the late ‘80’s ?
No it was AIME I am sure of it. They had those back then.

5. Sorry, but i cannot find the solution, can anybody place it here, please?

6. Ok, I found the solution, thank you very much for the information