Using a 10-element multiset of $\{1, 2, 5, 10, 20, 50, 100\}$, what's the largest range of consecutive integer values that can be produced (note that $0$ isn't counted)?
For example, I could take ten ones to get a range of $1$ to $10$, which would give me an answer of $10 - 1 = 9$. I can't seem to do any better than $9$. Can someone please help me with this problem? I don't think that ten ones is the answer because it seems too simple.