Strategy

How to solve Sudoku

Good solvers do not rely on inspiration. They follow a loop: try the simplest idea, then the next, and only then the hard ones.

The solving loop

1. Scan for singles. Look for hidden singles and naked singles. Place every digit you find.
2. Write notes. When no single is visible, fill in candidates for all empty cells (how to use notes).
3. Use simple eliminations. Look for naked pairs, hidden pairs, pointing pairs and box-line reduction.
4. Go back to singles. Every elimination may create a new single. Place digits, update notes and repeat.
5. Try bigger patterns. Only now look for triples, X-Wing and Swordfish.
6. Last resort: chains. XY-Wing and coloring solve the toughest puzzles.

The order matters. Easier techniques are faster to spot, so they should be tried first. A good rule: never look for a harder technique while an easier one still applies.

Where to scan first

• Rows, columns and boxes with the most filled cells: they have the fewest open spots.
• Digits that already appear many times: they have the fewest places left.
• Cells with only two candidates: they are the best starting points for pairs and wings.

What to do when you are stuck

1. Check your notes for missing eliminations. After each placement, remove that digit from its row, column and box.
2. Check for a wrong digit. If a cell ends up with no candidates, you made a mistake earlier.
3. Go through each technique in order, one unit at a time.
4. Use the step-by-step solver to see which technique applies. Then look for it on your own.

Why guessing fails

Guessing in Sudoku means placing a digit without proof. If it is wrong, you may fill many cells before you notice, and then you cannot tell where the error began. A proper puzzle is designed to be solved by logic, so there is always a deduction, even when it is hard to see.