Solving Sudoku - Trial and Error (Ariadne's Thread, Backtracking, Guessing)

There are some that would argue trial and error is not a logical technique, and is no better than guessing. Although it's not a technique I like to use, I do consider it logical. When further moves seem impossible, trial and error may be the only way forward. Indeed, some Sudoku puzzles cannot be completed without it.

The technique involves selecting one candidate for a cell - without any particular reason for that selection - and then seeing whether the puzzle can then be completed. If it can, well done (although, there could also be other solutions - test the other candidates too.) If not, the trial and error move, and any subsequent moves, are undone, and a different choice is made. For some Sudoku puzzles, it may be necessary to use trial and error several times. For others, it may be required only once.

In order to better manage the complexity, it's usual, if possible, to choose a cell with only two candidates, but that doesn't have to be the case.

It's worth noting, that this technique alone will always generate a solution if the Sudoku puzzle can be solved, no other technique can guarantee that. But when used alone, it becomes the equivalent of a brute-force attack.