You are right; there are 131,072 possibilities. Just have a computer go through them each week and see which ones match the weekly total. I'm sure there are nic

You are right; there are 131,072 possibilities. Just have a computer go through them each week and see which ones match the weekly total. I'm sure there are nicer ways in terms of mathematical beauty, but if your friend is just trying to get work done, it doesn't really matter. Computers are fast.