Sudoku Strategies

Sudoku becomes much easier when you stop looking at it as a grid of empty cells and start looking at it as a system of possibilities.

Every solving technique follows the same basic principle: use the numbers already placed to eliminate impossible candidates until only valid positions remain.

Beginner strategies often reveal a number directly. More advanced techniques help you remove candidates, create new constraints, and uncover placements several steps later.

You do not need to memorise every strategy before playing. Start with the simplest techniques and add more as your puzzles become harder.

Before learning strategies: understand candidates

A candidate is a number that could still legally fit in an empty cell.

Suppose a cell's row, column, and box already contain 1, 2, 3, 4, 6, and 9.

The remaining possibilities might be:

Those are the cell's candidates.

In digital Sudoku, candidates are usually recorded using notes. On paper, they are traditionally written as small pencil marks inside a cell.

Candidates are important because many Sudoku strategies do not immediately tell you which number belongs in a cell. Instead, they help you determine which numbers cannot go there.

As candidates disappear, the correct placement becomes easier to identify.

1. Scanning

Scanning is the most fundamental Sudoku strategy.

It simply means systematically looking across rows, columns, and boxes for useful constraints.

Scan by area

Look for rows, columns, and boxes that already contain many clues. Areas with fewer empty cells usually have fewer remaining possibilities.

Scan by number

Choose one digit — for example, 7 — and look at every 7 already placed on the grid.

Each existing 7 eliminates cells in its row, column, and box from containing another 7.

Following those restrictions across the puzzle can reveal the only possible position for the next 7.

2. Full house

A full house is the simplest possible Sudoku deduction.

It occurs when a row, column, or box has only one empty cell.

No candidate analysis is required because every other number already appears in the unit.

3. Naked singles

A naked single occurs when one empty cell has only one possible candidate.

Imagine a cell where the surrounding row, column, and box eliminate every number except 4.

Therefore the cell must contain 4.

The difference between a full house and a naked single is subtle:

• a full house is found because an entire unit is missing only one number;
• a naked single is found because a particular cell has only one legal candidate.

4. Hidden singles

A hidden single occurs when a particular number can appear in only one cell within a row, column, or box.

The cell itself may still show several candidates.

If 7 appears nowhere else as a candidate inside that box, then Cell C must contain 7.

The 7 is "hidden" among the other candidates in the cell.

Instead of asking what number belongs in this cell?, ask where can this number go in this row, column, or box?

5. Cross-hatching

Cross-hatching is a practical way to find hidden singles inside boxes.

Suppose you want to place a 5 in a particular 3×3 box.

Look at the rows and columns crossing that box.

If a row already contains a 5, every cell where that row passes through the target box is eliminated.

Do the same for columns.

After eliminating those positions, you may find that only one cell remains where 5 can legally appear.

6. Naked pairs

A naked pair occurs when two cells in the same row, column, or box contain exactly the same two candidates.

Because those two cells must eventually contain 3 and 8 in some order, no other cell in that unit can contain either number.

You can therefore eliminate 3 and 8 from the candidates of every other cell in the row, column, or box.

7. Hidden pairs

A hidden pair works from the opposite direction.

Imagine a row where the numbers 2 and 6 can only appear in two particular cells.

If no other cell in the row can contain 2 or 6, then those two cells must eventually contain 2 and 6.

The other candidates can be removed from those cells.

8. Naked triples

A naked triple extends the same idea used by naked pairs.

If three cells in the same unit contain candidates drawn exclusively from the same three numbers, those numbers must occupy those three cells.

Together, these cells contain only 2, 5, and 7.

Therefore those numbers can be removed from every other cell in the same unit.

9. Hidden triples

A hidden triple is the inverse pattern.

Three numbers may appear as candidates in only three cells of a row, column, or box.

Those cells may contain several other candidates, but if the three target numbers have nowhere else to go, the extra candidates can be removed.

Hidden triples are considerably harder to spot than naked singles or pairs because they require comparing candidate positions across an entire unit.

10. Pointing pairs and triples

A pointing pair or pointing triple occurs when all possible positions for a number inside a 3×3 box lie on the same row or column.

Suppose every possible location for 4 inside a box lies on the same row.

You may not know exactly which of those cells contains 4, but you do know that the 4 for that box must appear somewhere on that row.

Therefore, no cell outside the box but still on the same row can contain 4.

11. Box-line reduction

Box-line reduction is closely related to pointing pairs, but the reasoning begins from the row or column instead of the box.

Suppose a number can appear in several cells within a row, but every one of those candidates lies inside the same 3×3 box.

That means the number for that row must be somewhere inside that box.

As a result, you can remove the same candidate from other cells in that box that are not part of the row.

12. X-Wing

The X-Wing is one of the best-known intermediate-to-advanced Sudoku techniques.

It involves one candidate appearing in exactly two positions in two different rows, with those positions aligned in the same two columns.

        C2      C7

Row 3    X       X

Row 8    X       X

Suppose those four positions represent every possible location for the number 5 in Row 3 and Row 8.

Whichever way the two 5s are eventually placed, one will occupy Column 2 and the other Column 7.

Therefore, every other candidate 5 in those two columns can be eliminated.

13. Swordfish

A Swordfish extends the idea behind an X-Wing.

Instead of using two rows and two columns, a Swordfish generally involves a candidate restricted across three rows and three columns.

If a number can only appear in specific aligned positions across those units, the pattern can eliminate the same candidate elsewhere in the affected columns or rows.

Swordfish patterns are significantly harder to find manually and are normally encountered in difficult or expert-level Sudoku.

14. Candidate chains

As Sudoku becomes more difficult, you may encounter situations where no single unit provides enough information.

Candidate chains analyse relationships between possibilities across multiple cells.

• if this cell is 4, another cell cannot be 4;
• if that cell cannot be 4, a third cell must be 4;
• that conclusion may eliminate 4 somewhere else.

Different advanced techniques formalise particular kinds of chains.

The details can become complex, but the underlying concept remains logical implication rather than guessing.

Which Sudoku strategies should beginners learn first?

What should you do when no strategy seems to work?

Before searching for an advanced pattern, check the fundamentals again.

A missed single is much more common than an exotic technique.

1. Rescan every row with only a few empty cells.
2. Rescan every column with only a few empty cells.
3. Check nearly completed boxes.
4. Look for cells with only one candidate.
5. Search each unit for hidden singles.
6. Update notes affected by your latest placements.
7. Look for pairs or locked candidates.
8. Only then move toward advanced patterns.

Sudoku often becomes difficult because one small deduction has been overlooked.

Should you use notes for every Sudoku?

Not necessarily.

Easy puzzles can often be solved without filling every candidate. Adding too many notes too early can sometimes make the grid harder to read.

For Hard and Expert Sudoku, accurate candidate tracking becomes much more valuable because many advanced strategies depend on relationships between candidates.

Are advanced Sudoku strategies guessing?

No.

Techniques such as X-Wings, Swordfish, and candidate chains may involve reasoning about possibilities, but they still produce logical conclusions.

Guessing means selecting a candidate without enough information and continuing under the assumption that it is correct.

Logical strategies instead demonstrate that a candidate must be true, cannot be true, or is constrained in a way that allows further eliminations.

The most important Sudoku strategy

Learning named techniques is useful, but the most important skill is developing a systematic solving process.

Do not jump randomly around the board looking for inspiration. Work methodically.

Every placement changes the candidate structure of the puzzle, so after making progress, return to simple techniques first.

Build your strategy toolkit gradually

You do not need to memorise dozens of named patterns to enjoy Sudoku.

Start with:

Those techniques alone can take you through a large range of puzzles.

When you start encountering grids where those methods no longer produce progress, add more advanced techniques one at a time.

Over time, patterns that initially require deliberate candidate analysis begin to become visually familiar.

Frequently asked questions