# Very interesting problem

• Sep 19th 2007, 12:27 PM
Ununuquantium
Very interesting problem
Integer number \$\displaystyle n\geqslant 1\$ is given. For every subset (not empty) \$\displaystyle A\$ of set \$\displaystyle \lbrace 1, 2, 3, 4,...n \rbrace\$ we assing number \$\displaystyle w(A)\$ in such a way: if numbers \$\displaystyle a_{1}>a_{2}>a_{3}>...>a_{k}\$ are all elements of set \$\displaystyle A\$, therefore:
\$\displaystyle w(A)=a_{1}-a_{2}+a_{3}-...+(-1)^{k+1}a_{k}\$
Count the sum of all \$\displaystyle 2^{n}-1\$ numbers
\$\displaystyle w(A)\$
• Sep 19th 2007, 05:07 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, 05:29 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, 05:35 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 19th 2007, 11:07 PM
Ununuquantium
Sorry, but i cannot find the solution, can anybody place it here, please?
• Sep 20th 2007, 08:14 AM
Ununuquantium
Ok, I found the solution, thank you very much for the information