Techniques for solving Sudoku
Sudoku is a puzzle involving logic – no arithmetic or guessing is required!
The basic idea of completing puzzles is to find cells (the small squares) where you are sure that only one value is a valid placement. If you’ve not played Sudoku before, take a look at our guide to how to start. Below are the most common techniques you can use once you’ve covered the basics.
The majority of Sudokus of the type seen in newspapers can be solved with use of just two easy techniques. Computer programs that assist players can make these kinds of puzzles very quick to solve, because they help to make it obvious where the next placement can be.
- Technique 1 : Single Position
- Technique 2 : Single Candidate
Many of the techniques that follow don’t actually provide you with a direct placement, but help you by allowing you to cross out one or more pencilmarks. If you can remove all of the possibles leaving just one remaining value, you can be certain that's the one to fill in.
Going a little further, there are some extra techniques which help you to find either valid placements, or to help you to remove some of the pencilmarks. These are obviously quite tricky to manage without using pencilmarks!
- Technique 3 : Candidate Lines
- Technique 4 : Double Pairs
- Technique 5 : Multiple Lines
These techniques make use of looking at your group of pencilmarks for the line or block. These are trickier to use because it takes a while to understand them, but once you have got the hang of the techchnique you can use them to crack quite difficult puzzles.
- Technique 6 : Naked Pairs/Triples
- Technique 7 : Hidden Pairs/Triples
Going to the extreme, there are some extra techniques mark you out as an a Sudoku Master! These involve using more complex patterns to see more ways to remove candidates. While it is possible to do these on paper, features of computer programs such as our free Sudoku of the Day app make these just a bit easier to see!
- Technique 8 : X-Wing
- Technique 9 : Swordfish
- Technique 10 : Forcing Chains
So, armed with all of these potential techniques, you'll be able to solve all possible Sudoku?
Well, maybe, maybe not.
The vast majority of puzzles don't require the trickier techniques, but there are some which just aren't solvable by simple logic alone, and require various forms of guessing to solve. Some argue that guessing is a form of logic, but it does often mean a lot of erasing!
Nishio is a form of guessing, where you look for a guess causing a contradiction, meaning that you can rule it out. Going on from this, it is possible to solve entire Sudoku puzzles from guesses alone, but it can take a long time!
You can learn about how we use these techniques to helpfully rate the difficulty of our puzzles.