What makes a unique sudoku?

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It gets messy very quickly: http://en.wikipedia.org/wiki/Latin_square

I believe that the editors' personality subtly comes through in which puzzles they select for publication. Will Shortz' Sudokus , the diifficult ones at least, have a slightly different feel than those of other authors. The difficult ones in his second book felt more complex than ones you would see on websites and newspapers. He may have run out of good ones because some of the final dificult ones in his third book were easy and reminded me of others'.

Anxiled: The link you gave in another thread with the solving strategies answers my questions. From what the programmers are discussing in the forum on that site, it is clear that the programs to produce unique puzzles do in fact add numbers one by one and try to solve it after each one. I guess if your solving algorithm is fast at determining whether the solution is unique, this is not a problem.

Also, apparently there are algorithms that imitate a human trying to solve a puzzle. These are applied once a unique puzzle is already generated, and give a score to each move depending on how easy it is. This allows an approximate difficulty level to be assigned automatically, though the only true test is to have people actually try to solve it.