Template:Weeklyproblem
Problem of the Week
For 
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 
is 
and for 
it is simply 
. Find the sum of all such alternating sums for 
.
