Very interesting problem

• Sep 19th 2007, 01:27 PM
Ununuquantium
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
$w(A)$
• Sep 19th 2007, 06:07 PM
ThePerfectHacker
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.
• Sep 19th 2007, 06:29 PM
Plato
Quote:

Originally Posted by ThePerfectHacker
this was an AIME 1983 problem.

Was it an AIME or maybe a Putman in the late ‘80’s ?
• Sep 19th 2007, 06:35 PM
ThePerfectHacker
Quote:

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.
• Sep 20th 2007, 12:07 AM
Ununuquantium
Sorry, but i cannot find the solution, can anybody place it here, please?
• Sep 20th 2007, 09:14 AM
Ununuquantium
Ok, I found the solution, thank you very much for the information