If you want a hard sudoku try . . . | . . 3 | . 6 . . . . | . . . | . 1 . . 9 7 | 5 . . | . 8 . ---------------------- . . . | . 9 . | 2 . . . . 8 | . 7 . | 4 . . . . 3 | . 6 . | . . . ---------------------- . 1 . | . . 2 | 8 9 . . 4 . | . . . | . . . . 5 . | 1 . . | . . . I believe that this one cannot be solved without trial and error (aka guesswork). Here's another almost completed example: 193 852 746 854 763 912 672 419 853 938 147 625 246 ... 371 517 236 489 78. 6.. .34 465 3.. .97 32. .74 .68 This is easily completed by making a guess. But I cannot see any way to complete it without making a guess. There is much discussion about whether every sudoku can be solved without resorting to trial and error. I think the above examples show that some sudokus require guesswork, but that's not a proof. None of the puzzles given in newspapers will require guesswork, but there are several levels of difficulty beyond what you find in published newspapers and books. Somebody on a forum quoted the NP-completeness result as being a proof that sudokus requiring guesswork exist. Solving sudoku is NP-complete, as has been mentioned before (see the wikipedia entry). The argument goes that an NP-complete problem requires a non-deterministic algorithm, which is one that has to make a random choice somewhere. This random choice is the guess. Is this a valid argument? I don't know enough about NP-completeness. Gary McGuire