Let $D$ be set of denominations and $m$ the largest element of $D$. We say that $c$ is a counterexample if the greedy algorithm gives an answer different from the optimal one.
Now, apparently, if for a given set $D$, the greedy algorithm does not return an optimal solution, then the smallest $c$ will be smaller than $2m-1$.
Is this really true? How can we prove it? If not, is there a relatively small range to look for the smallest counterexample?