ok we have the integers 0,1,2...,9
to make the sum equal to 4 we have options
4 + 0 = 4
3 + 1 = 4
2 + 2 = 4 (not possible as we cant have duplicates)
and that is all
so new we can divide this into cases.
case # 1 (4 and 0 are the largest 2 elements):
if 0 is second largest element we have no element less than it so the only subset possible is {0, 4} so 1 option
case # 2 (3 and 1 as 2 max elements):
now we obviously have 0 which we can add such that it does not mess with the max elements as any element >= 2 it would mess up the "second-largest = 1" so we have two options one with zero and one without zero {0,1,3}, {1,3}
so adding up the cases we have 3 satisfying subsets