What makes a good puzzle?

This space is about puzzles, so to start with, we should talk about what makes something a puzzle. A puzzle is a toy, game or problem that requires ingenuity or knowledge to solve. But there has to be more to it than that, right. Counting all the potholes in Blackburn Lancashire UK (there are 4,000 according to the Beatles in "A Day in the Life") is a problem that would require knowledge to solve, but that doesn't sound like something I would enjoy spending my free time answering. Certainly there has to be something like an enjoyable journey of discovery in the process of solving a puzzle. Some examples of what I mean: trying a jigsaw puzzle piece in several places before making it fit, solving a riddle to the location of a treasure, or finding the correct path through a maze. What about such a journey separates a mediocre puzzle from a truly great one? I think it must be a mix of "solvability" and difficulty. A great puzzle must require a tough, non-trivial journey (not just counting potholes) without seeming to be too tough.

For BabelDoKu puzzles, I vary the number of empty cells to make a puzzle either easy (not many empty cells to begin with) or hard. I also choose the difficulty of the words, clues and quotations used in my puzzles to add another dimension of difficulty.