User:Piphi/AoPS Wiki

Problem of the Week

1983 AIME, Problem 13

For $\{1, 2, 3, \ldots, n\}$ and each of its non-empty subsets a unique alternating sum is defined as follows. Arrange the numbers in the subset in decreasing order and then, beginning with the largest, alternately add and subtract successive numbers. For example, the alternating sum for $\{1, 2, 3, 6,9\}$ is $9-6+3-2+1=5$ and for $\{5\}$ it is simply $5$. Find the sum of all such alternating sums for $n=7$.

Statistics

It is Thursday November 14, 2024, 06:17 (GMT).
There have been 235,287 edits to 10,582 articles since January, 2006.

3,315 files have been uploaded. There are 248,942 users registered.