Algorithm to determine possible groups of items

Question

I am scratching my head trying to do this and it\'s eating me up. I know it is not THAT complex. I have a number of items, this number can be equal or greater than three. Then I

Answer 1

In pseudocode:

List results;

void YourAnswer(int n) {
    GeneratePossiblities("", [3, 4, 5, 6, 7], n);
}

void GeneratePossibilities(String partialResult, List buildingBlocks, int n) {
    if (n == 0) {
        // We have a solution
        results.Add(partialResult);
    } else if (buildingBlocks.IsEmpty()) {
        // Dead-end: there is no solution that starts with the partial result we have and contains only the remaining building blocks
        return;
    } else {
        int first = buildingBlocks.First();
        buildingBlocks.PopFirst();
        for (int i = 0, i < n/first; i++) {
          GeneratePossibilities(partialResult + " " + i + "groups of " + first,
                                buildingBlocks, 
                                n - i * first);
        }
    }
}

The first two cases are pretty straight-forward. The third one, you figure out (for example) how many groups of size 3 there are - that can be any number between 0 and n/3, and then recursively the function with [4, 5, 6, 7], etc.