There's an old joke. It was said that English automobiles of the 1950's came equipped with a walnut inlayed toolbox containing many hammers. These ranged in size from a small jeweler's hammer up through a heavy, concrete shattering, sledge. It was said that when something in the automobile stopped working that one should begin by pounding on it with the smallest hammer. If that didn't solve the problem then one should move up to the next larger size. And so on, using ever larger hammers, until the sledge, which would reduce the automobile to a heap of shattered parts that could easily be hauled away – because the original problem was obviously insolvable.
Fuzz testing of software is somewhat like that old English automotive technique, but often without the benefit of an orderly sequence.
