Sudoku Solving Strategies — Complete Overview
One of the most frustrating moments in sudoku is being stuck without knowing what to try next. This guide presents all core solving strategies in order of complexity — from the simplest techniques that solve every easy puzzle to the advanced methods needed for expert grids. Use it as a reference whenever you need to know what to try, and follow the links to deep-dive guides for each technique.
Level 1: Beginner Strategies
These techniques alone are sufficient to solve every Easy-difficulty puzzle. If you are new to sudoku, master these before attempting anything else. They are not "too basic" — even experienced solvers use them on every puzzle, at every difficulty.
Last Remaining Cell
The simplest pattern: a row, column, or box has exactly one empty cell. The missing digit — the one not yet present in that group — is the answer. No elimination or pencil marks needed. Simply scan for rows, columns, and boxes with eight of nine cells already filled. This pattern is abundant at the start of easy puzzles and appears regularly throughout medium ones.
Naked Single
An empty cell has only one possible digit after checking its row, column, and box. Eliminate every digit already present in those three groups from your candidate list. Whatever remains is the answer. On easy puzzles, at least one naked single is always available. Naked singles disappear quickly on hard puzzles, but a single elimination step often creates a new one elsewhere. See: Naked Singles in depth →
Digit Scanning (Cross-Hatching)
Pick a digit — say, 6. Find every 6 already placed on the grid. For each 3×3 box that doesn't yet have a 6, draw imaginary horizontal and vertical lines through each existing 6. Any cell that a line crosses is eliminated. If only one cell in the box escapes all lines, that cell must be 6. Scanning works fastest for digits that already appear most frequently on the board — more placements mean more eliminations. See: Scanning Method →
How to Apply Elimination Systematically
All of the above techniques are expressions of the same underlying logic: elimination. Every digit present in a cell's row, column, or box is ruled out as a candidate for that cell. Understanding elimination deeply means you can learn any technique quickly — they are all just different ways of performing eliminations that basic cell-by-cell checking cannot find. See: The Elimination Method →
Level 2: Intermediate Strategies
Medium puzzles require these techniques. You'll exhaust naked singles and basic scanning partway through, then need hidden singles to continue. Naked pairs become essential as puzzles grow harder.
Hidden Single
A digit can only go in one cell within a row, column, or box — even though that cell appears to have multiple candidates. The uniqueness is "hidden" because you discover it by examining the group rather than the individual cell. To find hidden singles: pick a digit, find an incomplete group, and check which of the group's empty cells could hold that digit. If exactly one cell remains after cross-referencing rows, columns, and boxes, place the digit there. Hidden singles are the bridge between easy and medium solving — mastering them is the most important skill jump in sudoku. See: Hidden Singles →
Naked Pair
Two cells in the same group each contain exactly the same two candidates — and only those two. One cell must hold digit A and the other must hold digit B, though we don't yet know which is which. This certainty means neither A nor B can go anywhere else in that group. Eliminate both digits from every other cell in the row, column, or box. Naked pairs frequently trigger cascade eliminations that unlock stuck puzzles. See: Naked Pairs →
Naked Triple
Three cells in the same group collectively contain only three distinct candidates. Each cell doesn't need all three — the union of candidates across all three cells must be exactly three digits. Eliminate all three digits from every other cell in that group. Naked triples are rarer than naked pairs but apply the same logic at larger scale.
Hidden Pair
Two digits can only appear in the same two cells within a group. Those cells may have other candidates, but since the two digits are locked into those two cells, all other candidates in those cells can be removed. Hidden pairs are harder to spot than naked pairs because you're looking at the group from the digit's perspective rather than the cell's perspective. They're one of the most powerful stuck-breakers on hard puzzles.
Level 3: Advanced Strategies
Hard puzzles require at least some of these. Expert and Evil puzzles may require all of them, plus techniques beyond the scope of this guide.
Pointing Pair / Pointing Triple
All candidates for a digit within a box are confined to a single row or column inside that box. Because the digit must land somewhere in the box, and all valid positions are in one line, no other cell on that line — outside the box — can hold the digit. This is a box-to-line elimination, working outward from the box. See: Pointing Pairs →
Box-Line Reduction
The inverse of pointing pairs. All candidates for a digit within a row or column fall inside a single box. Because the digit must go somewhere in that line, and all valid positions are within one box, no other cell in that box can hold the digit. This is a line-to-box elimination, working inward from the line. See: Box-Line Reduction →
X-Wing
A digit appears as a candidate in exactly two cells in each of two different rows, and the candidate cells in both rows align in the same two columns. The digit must land in one of two diagonal arrangements — which means it cannot appear anywhere else in those two columns. Eliminate the digit from all other cells in both columns. X-Wing is the simplest "fish" pattern and one of the first advanced techniques needed for expert-level puzzles.
Swordfish
An extension of X-Wing using three rows and three columns instead of two. A digit appears in at most three cells per row, and those cells are all within the same three columns. The digit is confined to a 3×3 sub-pattern of the grid, allowing elimination from all other cells in those three columns. Swordfish is rare but decisive when it appears.
The Technique Stack: Why Order Matters
The most common mistake experienced solvers make is applying complex techniques while simpler ones are still available. An X-Wing search is wasted effort if a naked pair was sitting unnoticed — the pair would have unlocked the position faster and with less mental overhead.
Always exhaust the current level before moving to the next. The reason is both logical and practical: simpler techniques are faster to apply, and their eliminations often make higher-level patterns visible. A pointing pair might reduce a cell's candidates to two, creating a naked pair that wouldn't have been visible before. Working in order ensures you never skip a shortcut.
When stuck, the systematic approach is:
- Verify pencil marks are fully up to date — stale candidates are the most common cause of apparent "stuck" states.
- Re-scan for naked singles everywhere — they appear in unexpected places after eliminations.
- Scan all digits for hidden singles, box by box, then row by row, then column by column.
- Look for naked and hidden pairs in every group.
- Check all boxes for pointing pairs. Check all lines for box-line reductions.
- Only then consider X-Wing and beyond.
How to Practice Each Technique Deliberately
Knowing a technique and applying it fluently are different things. Deliberate practice accelerates the gap between them.
For naked singles: Solve easy puzzles and time yourself. The goal is to spot naked singles without consciously running the three-group check — your eye should jump to constrained cells automatically. After 20–30 easy puzzles this starts to happen. See: Easy puzzle guide →
For hidden singles: Solve medium puzzles and pause each time you find a hidden single. Note which group it was in (row, column, or box) and which perspective revealed it. Box-based hidden singles are the hardest to see; practice scanning boxes digit by digit until it feels natural. See: Medium puzzle guide →
For naked pairs: After setting up pencil marks on a hard puzzle, go through every group and look only for pairs — ignore everything else. This focused search, done in isolation, builds the pattern recognition faster than finding pairs incidentally during general solving.
For pointing pairs and box-line reduction: These are best practiced systematically. Pick a digit, then go through every box on the grid asking the pointing pair question. Then go through every line asking the box-line question. One full pass through all digits for both techniques takes time initially, but the pattern becomes fast and intuitive within a few sessions.
Difficulty Level Guide
| Difficulty | Strategies Required |
|---|---|
| Easy | Last remaining cell, naked singles, digit scanning |
| Medium | + Hidden singles |
| Hard | + Naked pairs, pointing pairs, box-line reduction |
| Expert | + Hidden pairs, naked triples, sometimes X-Wing |
| Evil | + X-Wing, Swordfish, and more advanced fish patterns |
This table represents typical requirements — individual puzzles vary. An "easy" puzzle might occasionally require a hidden single; a "hard" puzzle might be solvable with only naked pairs. The difficulty grading reflects what techniques are typically needed on average, not what is required in every case.