Sudoku for Beginners: 5 Solving Techniques in Order of Difficulty

A well-made Sudoku never requires guessing. Every number can be found with logic. The trick is knowing which techniques to try and in what order. This guide covers the five techniques that solve the vast majority of easy and medium puzzles.

The rules in one sentence

Fill the 9×9 grid so that every row, every column and every 3×3 box contains the digits 1 to 9 exactly once.

Those three groups (rows, columns and boxes) are sometimes called "units." Every technique below is about finding which digit a unit is still missing and where it can go.

A fun fact: a classic Sudoku needs at least 17 starting clues to have a single unique solution. Mathematicians proved in 2012 that no 16-clue puzzle with a unique solution exists.

Technique 1: Cross-hatching (scanning)

Pick a digit, say 5. Look at one 3×3 box that does not have a 5 yet. Now look across the rows and down the columns that pass through that box. Every row or column that already contains a 5 elsewhere rules out the squares it crosses inside your box.

If only one empty square in the box survives, the 5 must go there.

Run through each digit from 1 to 9 this way. On easy puzzles, cross-hatching alone can fill most of the grid.

Technique 2: Naked single

Sometimes a square can only be one digit. Look at a single empty square and list every digit already present in its row, column and box. If eight different digits appear, the missing ninth digit goes in that square.

This is called a naked single because the answer is "visible" from the square itself.

Technique 3: Hidden single

A hidden single is the opposite view. Instead of asking "what can go in this square?", you ask "where can this digit go in this unit?"

For example, in a particular row, the digit 7 might fit in only one square because the other empty squares in that row are blocked by 7s in their columns or boxes. Even if that square could hold other digits in theory, the 7 has nowhere else to go, so it goes there.

Hidden singles are the most common technique in medium puzzles.

Technique 4: Pencil marks

When scanning stops working, start writing small candidates (possible digits) in each empty square. It feels slow, but it turns the puzzle from memory work into clear bookkeeping. Many apps can fill in candidates for you; doing it by hand at least a few times will help you understand the techniques that follow.

Update candidates every time you place a digit: remove that digit from every square in the same row, column and box.

Technique 5: Naked pairs

Look for two squares in the same unit that both have exactly the same two candidates, for example {3, 8} and {3, 8}.

Those two squares must hold the 3 and the 8 between them, in some order. That means no other square in that unit can be 3 or 8. Remove those candidates from the rest of the unit, and new singles will often appear.

The same logic extends to three squares sharing three candidates (naked triples), but pairs are by far the most common.

Bonus: Pointing pairs

If, inside one box, a digit's only candidates sit in the same row (or column), then that digit must be in that row within the box. You can remove it as a candidate from the rest of that row outside the box. This is called a pointing pair, and it often breaks a medium puzzle open.

Which technique to try when you are stuck

1. Cross-hatch every digit again. It is easy to miss one.
2. Check every row, column and box for hidden singles.
3. Fill in pencil marks if you have not.
4. Look for naked pairs.
5. Look for pointing pairs.

Working through this checklist in order solves most puzzles labeled easy or medium. Harder puzzles use more advanced patterns, but they all build on these five ideas.

Habits that help

• Never guess. A guess that turns out wrong can corrupt the whole grid before you notice.
• Double-check before writing in ink. Most mistakes come from missing a digit already in a unit.
• Take a short break when stuck. Fresh eyes spot singles you looked straight past.