How to solve Sudoku without guessing

First, understand the one rule

A standard Sudoku contains nine rows, nine columns and nine 3×3 boxes. Your goal is to place the digits 1 to 9 so that each digit appears exactly once in every row, once in every column and once in every box. The printed numbers are givens; they cannot be changed.

You never need arithmetic. A 7 is not larger or more powerful than a 2—it is simply one of nine symbols. Solving means ruling out places where a symbol cannot go until one legal position remains.

A calm five-pass solving method

1. Scan for nearly complete units. Look for a row, column or box with six or more givens. List the missing digits mentally and check where each can fit.
2. Place naked singles. When a cell has only one candidate after checking its row, column and box, place it. A new number often creates another single nearby.
3. Find hidden singles. Pick one missing digit and inspect a whole row, column or box. If that digit has only one possible cell in the unit, place it—even if that cell has several candidates.
4. Add useful pencil marks. When the easy placements stop, note candidates in the emptiest areas. Begin with cells that have two or three possibilities; they reveal patterns more clearly than crowded cells.
5. Repeat before escalating. Every placement changes three units. Rescan its row, column and box before reaching for pairs or advanced techniques.

Worked example: make the first placement

Consider the grid below. Focus on row 5, column 5—the green central cell. Row 5 already contains 4, 8, 3 and 1. Column 5 already contains 7, 9, 6, 2, 1 and 8. The centre box also contains 6, 8, 3 and 2. Every digit except 5 is blocked, so the cell must be 5.

What to scan after every placement

Beginners often jump to another part of the board after entering a number. That misses the most productive follow-up. A placed number immediately affects exactly three units, so use this short loop:

• Check the row for a new missing digit or single candidate.
• Check the column for a digit that now has only one position.
• Check the box for another forced placement.

If nothing appears, move to another nearly complete unit. This disciplined loop is faster and more accurate than scanning the whole board at random.

When should you use notes?

Do not fill every empty square with all possible candidates at the beginning. It takes time, adds visual noise and makes transcription errors more likely. Start with direct scanning. Add notes when you reach a point where no naked or hidden singles are visible.

Good notes are complete enough to trust but limited enough to read. If a cell can be 2 or 7, record both. When you place a 2 in the same row, remove 2 from that note immediately. Our player does not automatically remove every note because checking candidates is part of the solving process.

A sensible technique ladder

Use the simplest technique that moves the puzzle forward. A useful order is:

1. Scanning and cross-hatching
2. Naked singles
3. Hidden singles
4. Naked or hidden pairs
5. Locked candidates
6. Fish and chain techniques, such as X-Wing

Easy puzzles may need only the first three. Harder puzzles often alternate between a small elimination and a fresh run of singles. Advanced techniques are not a badge of honour; they are tools for specific patterns.

Four mistakes that make Sudoku feel harder

Guessing between two candidates

A guess can create a contradiction much later, making it difficult to find the original mistake. If a cell has two candidates, leave both and inspect the rest of the unit.

Checking only the row

A candidate must be legal in its row, column and box. Skipping one constraint is the most common cause of an incorrect entry.

Leaving stale notes

Candidate notes are promises about what remains possible. Update them whenever you place a number in the same row, column or box.

Using a hint without studying it

If you request a hint, pause before continuing. Check why the supplied number is forced and name the technique. One studied hint teaches more than several automatic fills.