Solving Sudoku : Guessing
If you’ve tried everything else you can think of, and a few quick Nishio attempts haven’t yielded a result (or completed the grid), then you may need to break down and make a guess. Most good Sudoku puzzles won’t require you to guess, but it may just be that there’s another logical technique out there you haven’t used, or it might just be a puzzle which really does require a guess!
First of all, if you have to make a guess, at least try to make a guess in a place with limited options, that will open up a whole new set of cells for you.
Next, be aware that even after making your guess, you might still have lots of hard work ahead of you before you get close to either completing the puzzle, or knowing that it was the wrong guess!
Finally, and here’s the worst part, one guess might not be enough! It might be that along the route to completion you have to make several guesses, each one leading you down a different path with different choices to make. Better have an eraser handy!
If multiple guesses are required, you’ll find yourself needing to track back if you find you did make a wrong turn (and end up in a dead end). For that reason, a guess-based technique that follows from Nishio is known as “Ariadne’s Thread” – meaning following guesses, but each time you find an error backtrack to your last choice, and take a different path, like Ariadne of legend! Yes, you’ll eventually get to the end of the Sudoku, but it could take a very long time with a great deal of wrong turns! Working things out with logic is much simpler when you can! (Ariadne was the daughter of the Cretan King Minos, who helped Theseus by giving him a sword with which to kill the Minotaur, and a thread which he used to find his way back out of the labyrinth, winding the thread back up every time he made a decision ending in a dead-end, and taking a different path.)
The technique of guessing (or trial and error) is also known as bifurcation – and many computer based solvers only include this technique! That may seem strange, but it is very easy for a computer program to brute-force run through each of the guesses to complete the puzzle, and trivial for it to backtrack to a previous choice – humans just don’t work this way! (But then, we can make deductive leaps of logic that computers can’t… yet!)