Calculating all of the subsets of a set of numbers

What you want is called a Powerset. Here is a simple implementation of it:

public static Set<Set<Integer>> powerSet(Set<Integer> originalSet) {
        Set<Set<Integer>> sets = new HashSet<Set<Integer>>();
        if (originalSet.isEmpty()) {
            sets.add(new HashSet<Integer>());
            return sets;
        }
        List<Integer> list = new ArrayList<Integer>(originalSet);
        Integer head = list.get(0);
        Set<Integer> rest = new HashSet<Integer>(list.subList(1, list.size()));
        for (Set<Integer> set : powerSet(rest)) {
            Set<Integer> newSet = new HashSet<Integer>();
            newSet.add(head);
            newSet.addAll(set);
            sets.add(newSet);
            sets.add(set);
        }
        return sets;
    }

I will give you an example to explain how the algorithm works for the powerset of {1, 2, 3}:

• Remove {1}, and execute powerset for {2, 3};
  • Remove {2}, and execute powerset for {3};
    • Remove {3}, and execute powerset for {};
      • Powerset of {} is {{}};
    • Powerset of {3} is 3 combined with {{}} = { {}, {3} };
  • Powerset of {2, 3} is {2} combined with { {}, {3} } = { {}, {3}, {2}, {2, 3} };
• Powerset of {1, 2, 3} is {1} combined with { {}, {3}, {2}, {2, 3} } = { {}, {3}, {2}, {2, 3}, {1}, {3, 1}, {2, 1}, {2, 3, 1} }.