As you progress to harder Sudoku puzzles, basic techniques like naked singles and hidden pairs may not be enough. Advanced strategies help you break through tough spots and solve even the most challenging grids. Below, you’ll find explanations, bullet-point summaries, and links to in-depth guides for each technique, along with tips on when to use them.
Pointing Pairs and Pointing Triples
When to use: After naked and hidden singles stop working, pointing pairs are usually the next technique that opens up progress on Medium and Hard puzzles.
How they work: When a candidate number appears in only two (or three) cells within a 3×3 box, and all of those cells lie in the same row or column, that number cannot go anywhere else in that row or column outside the box. You can safely eliminate it from all other cells in that row or column.
The logic is simple: the digit must land somewhere in the box. If the only legal positions within the box all share a row (or column), then the digit occupies that row or column — it just hasn’t been placed yet. Anything in the same row or column outside the box is therefore ruled out.
Example: In the top-left 3×3 box, suppose candidate 4 appears only in row 2 (cells at columns 1 and 3). You can eliminate candidate 4 from every other cell in row 2 outside that box.
Key points:
- Requires complete pencil marks to spot reliably.
- Pointing pairs appear in almost every Medium and Hard puzzle.
- Always re-scan for naked singles after each pointing pair elimination — they frequently cascade.
- For a full walkthrough, see Pointing Pair and Pointing Triple.
X-Wing
When to use: X-Wing is the first “fish” pattern and the go-to technique when a candidate is confined to the same two columns in exactly two rows (or two rows in exactly two columns).
How it works: Imagine candidate digit 7 appears in exactly two cells in row 2 (columns 4 and 8) and also in exactly two cells in row 7 (also columns 4 and 8). This forms a rectangle. Since 7 must be placed in one of the two cells in row 2 and one of the two cells in row 7, and those four cells collectively occupy only columns 4 and 8, digit 7 cannot appear anywhere else in columns 4 or 8. Eliminate 7 from every other cell in those two columns.
Key points:
- X-Wing works on rows eliminating from columns, and on columns eliminating from rows — both directions are valid.
- Always verify the candidate appears in exactly two cells per row (not three or more).
- Common in Hard and Expert puzzles.
- See the full guide: X-Wing technique.
Swordfish
When to use:
Use when a candidate appears in up to three rows and three columns, forming a pattern similar to X-Wing but larger.
How it works:
- If a candidate appears in three rows (or columns), and in each row (or column) it is limited to the same three columns (or rows), it can be eliminated from other cells in those columns (or rows).
Key points:
- Advanced version of X-Wing.
- Useful for very challenging puzzles.
Y-Wing
When to use:
Use when you find three cells (pivot and two pincers) with two candidates each, forming a specific pattern.
How it works:
- The pivot cell shares a candidate with each pincer.
- If both pincers see a common cell, a candidate can be eliminated from that cell.
Key points:
- Great for breaking through when other techniques stall.
- Requires careful scanning for the pivot and pincers.
XY-Wing
When to use:
Use when three cells form a pivot and two pincers, each with two candidates, and the pivot shares a candidate with each pincer.
How it works:
- Allows you to eliminate a candidate from any cell that sees both pincers.
Key points:
- Similar to Y-Wing, but with more complex logic.
- Effective in advanced puzzles.
XYZ-Wing
When to use:
Use when three cells contain three candidates between them, with one cell (the pivot) containing all three candidates.
How it works:
- If the two other cells (the pincers) each share two candidates with the pivot, you can eliminate the third candidate from any cell that sees all three.
Key points:
- Useful for eliminating stubborn candidates.
- Appears in hard and expert puzzles.
Jellyfish
When to use:
Use when a candidate appears in four rows and four columns, forming a jellyfish pattern.
How it works:
- Extends the logic of X-Wing and Swordfish.
- Eliminates candidates from other cells in those columns or rows.
Key points:
- Rare but powerful.
- Typically found in the hardest puzzles.
Unique Rectangle
When to use:
Use when you spot a rectangle of four cells that could lead to multiple solutions.
How it works:
- Prevents the puzzle from having more than one solution by eliminating candidates that would create ambiguity.
Key points:
- Ensures puzzle uniqueness.
- Useful for avoiding dead ends.
Coloring
When to use:
Use when you can create chains of strong links between candidates.
How it works:
- Assign colors to linked candidates.
- Contradictions or patterns allow you to eliminate candidates.
Key points:
- Great for complex eliminations.
- Requires careful tracking of chains.
Chains (AIC, Nice Loops)
When to use:
Use when you can form alternating inference chains between candidates.
How it works:
- Chains of strong and weak links lead to eliminations or placements.
Key points:
- Powerful for breaking through tough puzzles.
- Advanced technique for experienced solvers.
Finned X-Wing / Finned Swordfish
When to use:
Use when an X-Wing or Swordfish pattern is disrupted by an extra candidate (the “fin”).
How it works:
- The presence of the fin allows for additional eliminations.
Key points:
- Advanced variation of fish patterns.
- Useful for expert puzzles.
BUG (Bivalue Universal Grave)
When to use:
Use when the grid is filled with only bivalue cells except for one.
How it works:
- Recognize and resolve the situation to avoid multiple solutions.
Key points:
- Ensures puzzle uniqueness.
- Rare but important for advanced solvers.
ALS (Almost Locked Sets)
When to use:
Use when you find overlapping sets of candidates in a unit.
How it works:
- Allows for complex eliminations based on the interaction of locked sets.
Key points:
- Very advanced technique.
- Useful for the hardest puzzles.
When to Use Advanced Techniques
- Pointing Pairs/Triples, X-Wing, and Swordfish: Use when basic eliminations stall and you notice repeating candidate patterns.
- Y-Wing, XY-Wing, XYZ-Wing: Use when you spot cells with two or three candidates forming a pivot and pincers.
- Coloring, Chains, ALS, and Unique Rectangle: Use when the puzzle seems stuck and you need to break through with more complex logic.
- Jellyfish, Finned Fish, and BUG: Use in the most challenging puzzles, often at the expert or evil level.
Decision Framework: Which Technique to Try Next
When you are stuck, use this sequence to decide which advanced technique to look for:
| Step | Check For | Difficulty Tier |
|---|---|---|
| 1 | Naked/hidden singles, pairs, triples | Beginner–Intermediate |
| 2 | Pointing pairs/triples, box-line reduction | Medium |
| 3 | X-Wing (fish across 2 rows × 2 cols) | Hard |
| 4 | Swordfish (3 rows × 3 cols fish) | Hard–Expert |
| 5 | XY-Wing, XYZ-Wing (wing eliminations) | Expert |
| 6 | Coloring / simple chains | Expert |
| 7 | Unique Rectangle variants | Expert–Evil |
| 8 | AIC / ALS / advanced chains | Evil |
Work through the list in order. The technique that solves your puzzle is the simplest one that applies — never jump to chains when an X-Wing would do.
For a structured learning path through all these techniques, visit the technique progression guide or start practising individual techniques in practice mode.