It is my experience that almost all published sudoku puzzles can be solved by applying to each element the various logic techniques derived from the basic rules--that all nine numbers be present in each 9-element column and row, and non-overlapping 3x3 square. However, occasionally, after partially solving a puzzle, I can complete the solution only by trial and error. Is it true that some puzzles can be completed after a certain point only by trial and error, or, am I ignorant of some advanced logic????

If someone wants to see an example of what I mean, complete the puzzle below---the x's are unfilled elements. You should be able to easily solve this to the point where only the four corner 3x3 blocks remain completely unfilled. Then I think you become stuck without guessing and trying an entry in some remaining unfilled element.

6 x x x 5 4 x x x

x 2 x x 9 8 4 6 x

3 x 4 2 7 6 x 5 x

x x x 8 x 5 1 4 6

4 1 6 x x x x 8 x

8 5 2 4 x 1 x x x

x x x 9 8 2 5 x 4

x x x 5 4 3 6 7 x

x 4 x 6 1 7 x x 3