It has recently been stated that an invention must be (a) useful, (b) novel and (c) not obvious to one skilled in the art. For the purposes of this discussion we can forget crass utility, obviously. In analogy uniqueness of fit of a piece in the puzzle may be equated to a kind of conditioned novelty. The finding of a fit is an exclusive event. An ordinary invention leaves the field open for other and different ways of accomplishing the same end.
The solution of any problem, once it has been recognized, is indeed disgustingly obvious. In a jigsaw puzzle, the fact that a piece actually fits as expected proves that the guess that it would fit was correct. In real life many conditions that are usually considered to be obvious go untested for want of a proper criterion.
As an analogue the pieces of a jigsaw puzzle, when spread out face up on a table, may be thought of as the contents of a finite long-term memory that has been somehow inherited. Looking over the array of pieces is like thinking over the many comparatively unrelated memories in my mind. My psyche, like a demented mouse, goes poking about among the pieces, looking for shapes and colors that might fit the memory (just acquired) of other pieces. As I look at the pieces I am simultaneously putting memories of the pieces into my short-term memory for possible future retrieval. When trial proves that two pieces fit then the fun begins.