The problem is NP-Hard. Even determining if there is ANY subset of the problem that sums to the desired number is NP-Hard (known as the subset sum problem), and there is no known polynomial solution to it.
Thus, you should look for an exponantial solution, such as a backtracking one - generate all possible combinations, and check if they are valid.
You can use trimming to get your search faster (for example, if you generate a partial subset of sum 13, no need to check other subsets which are supersets of this subset, since they will definetly won't lead to a solution.
pseudo code:
findValidSubsets(sum,arr,idx,currSolution):
if (sum == 0):
print currSolution
if (sum < 0): //trim the search, it won't be succesful
return
//one possibility: don't take the current candidate
findPermutations(sum,arr,idx+1,currSolution)
//second poassibility: take the current candidate
currSolution.add(arr[idx])
findPermutations(sum-arr[idx],arr,idx+1,currSolution)
//clean up before returning:
currSolution.removeLast()
Complexity is O(2^n) - need to generate at worst case all 2^n possible subsets
Invoke with findValidSubsets(desiredSum,myArray,0,[]), where [] is an empty initial list
