A greedy algorithm is used to make change for a given amount using a set of coin denominations. For denominations {1, 5, 10, 25} and an amount of 30, it works correctly. However, for denominations {1, 4, 6} and an amount of 8, it fails to find the optimal solution (e.g., 4+4 vs 6+1+1). What is the fundamental reason for this failure, which is a common debugging point for greedy algorithms?