Beyond Basic Sudoku: Advanced Techniques
Once you’ve mastered the fundamentals of sudoku, you may find yourself stuck on harder puzzles where basic scanning and elimination aren’t enough. This guide introduces 10 advanced techniques that expert solvers use to crack even the most challenging puzzles.
Before You Begin: Prerequisites
These advanced techniques assume you’re comfortable with:
- Pencil marks (candidates): Marking possible numbers in each cell
- Naked singles: Cells with only one possible candidate
- Hidden singles: Numbers that can only go in one place in a row/column/box
- Naked pairs/triples: Sets of cells that must contain specific numbers
If you’re not familiar with these basics, start with our Beginner’s Guide first.
1. X-Wing
What It Is
X-Wing is a pattern-based elimination technique that works across rows or columns.
The Pattern
Look for a number that appears as a candidate in exactly two cells in two different rows (or columns), and these cells align perfectly in columns (or rows).
How to Apply
Row 2: Candidate 5 in columns 3 and 7
Row 6: Candidate 5 in columns 3 and 7
Result: Eliminate all other 5s from columns 3 and 7
Why It Works: The 5 in row 2 MUST be in either column 3 or 7. Same for row 6. If row 2 has it in column 3, row 6 must have it in column 7, and vice versa. Either way, no other cells in those columns can contain 5.
When to Use
- You have two rows (or columns) with exactly two possible positions for a number
- These positions align perfectly in the perpendicular direction
2. Swordfish
What It Is
Swordfish is an extended version of X-Wing, working with three rows or columns instead of two.
The Pattern
A candidate appears in exactly 2-3 cells in each of three rows, and all these cells fall within the same three columns.
How to Apply
Row 1: Candidate 7 in columns 2, 5, 8
Row 4: Candidate 7 in columns 2, 5
Row 9: Candidate 7 in columns 5, 8
Result: Eliminate all other 7s from columns 2, 5, and 8
Pro Tip
Swordfish is rare but powerful. When basic techniques fail, systematically check each number for this pattern.
3. XY-Wing
What It Is
XY-Wing uses three cells to eliminate candidates from related cells through logical chains.
The Pattern
You need three cells:
- Pivot: A cell with exactly two candidates (let’s say XY)
- Pincer 1: Shares a group with pivot, has candidates XZ
- Pincer 2: Shares a different group with pivot, has candidates YZ
How to Apply
If a cell sees both pincers, you can eliminate candidate Z from it.
Logic:
- If pivot is X, then Pincer 2 must be Z
- If pivot is Y, then Pincer 1 must be Z
- Either way, any cell seeing both pincers cannot be Z
Example
Pivot (R5C5): [3,6]
Pincer 1 (R5C2): [3,8] (same row as pivot)
Pincer 2 (R2C5): [6,8] (same column as pivot)
Eliminate 8 from any cell that sees both R5C2 and R2C5
4. Simple Coloring
What It Is
A technique that uses color logic to eliminate candidates by marking cells in two alternating colors.
How to Apply
- Pick a candidate number that appears in exactly two cells per group
- Color one cell blue, the other red
- Continue coloring connected cells in alternating colors
- Apply elimination rules:
- If two cells of the same color see each other → That color is wrong
- If one color sees a cell with that candidate → Eliminate from that cell
When to Use
Works best with candidates that form long chains across the grid.
5. XYZ-Wing
What It Is
An extension of XY-Wing that uses a pivot with three candidates instead of two.
The Pattern
- Pivot: Has three candidates (XYZ)
- Pincer 1: Shares a group with pivot, has candidates XZ
- Pincer 2: Shares a group with pivot, has candidates YZ
How to Apply
Eliminate Z from any cell that sees all three cells (pivot and both pincers).
Logic: One of these three cells must be Z, so any cell seeing all three cannot be Z.
6. Remote Pairs
What It Is
Uses a chain of cells with identical pairs of candidates to make eliminations.
The Pattern
Find cells with the same two candidates (e.g., [4,7]) forming a chain where:
- Each cell in the chain shares a group with the next cell
- The chain has an even number of cells
How to Apply
The chain alternates between the two numbers. Any cell that sees both ends of the chain can have those candidates eliminated.
7. Unique Rectangles
What It Is
A technique that exploits the fact that sudoku puzzles should have only one solution.
The Pattern
Four cells forming a rectangle within two boxes, two rows, and two columns. Three cells have the same two candidates [X,Y], and the fourth has additional candidates.
How to Apply
If completing the pattern with [X,Y] would create multiple solutions, eliminate X and Y from the fourth cell.
Note: Only works when you know the puzzle has a unique solution (all properly constructed puzzles do).
8. Forcing Chains
What It Is
Follow the logical consequences of placing a candidate in a cell. If both possibilities lead to the same conclusion, that conclusion must be true.
How to Apply
- Pick a cell with two candidates (e.g., [2,5])
- Assume it’s 2 and follow the logical chain
- Assume it’s 5 and follow that chain
- If both chains eliminate the same candidate elsewhere, make that elimination
Warning
This is time-consuming. Use only when other techniques fail.
9. Aligned Pair Exclusion (APE)
What It Is
When two cells in a box can only contain two specific candidates, and these cells align in a row or column, you can make eliminations.
How to Apply
Box 1: Cells R1C1 and R1C2 can only be [3,8]
These cells align in Row 1
If another box also has aligned pairs for [3,8] in Row 1:
You can deduce which box has which number
10. Sue de Coq
What It Is
An advanced technique combining box and line interactions with exactly five cells.
The Pattern
In a single box, you need:
- Two cells in the same row/column with candidates from a set (e.g., [2,6,7])
- Three other cells in the box with candidates from another set (e.g., [2,5,6])
- The union of both sets has exactly 5 numbers
How to Apply
Complex eliminations can be made based on how these numbers must distribute across the five cells.
Note: This is one of the most advanced techniques and rarely needed.
How to Practice These Techniques
1. Learn One at a Time
Don’t try to master all 10 at once:
- Week 1-2: X-Wing and basic coloring
- Week 3-4: XY-Wing and Swordfish
- Month 2: More advanced techniques
2. Use the Right Tools
The Sudoku Master app helps you practice:
- Hint system shows which technique to use
- Candidate highlighting makes patterns visible
- Technique explanations teach while you play
- Progressive difficulty introduces techniques gradually
3. Solve with Purpose
When practicing:
- Before using a technique, explain to yourself why it works
- Document interesting puzzles that required advanced techniques
- Time yourself to build speed alongside understanding
4. Join the Community
- Share puzzles that required specific techniques
- Learn from others’ solving approaches
- Participate in timed challenges
When to Use Each Technique
Here’s a decision flowchart:
1. Can I place any definite numbers? → Place them
2. Are there hidden singles? → Find them
3. Are there naked pairs/triples? → Eliminate candidates
4. Can I spot an X-Wing? → Apply elimination
5. Is there an XY-Wing pattern? → Make eliminations
6. Can I use coloring? → Follow color logic
7. More complex patterns? → Try Swordfish, XYZ-Wing
8. Still stuck? → Forcing chains or seek hints
Common Mistakes When Learning Advanced Techniques
1. Applying Techniques Incorrectly
Solution: Double-check pattern requirements before making eliminations. One wrong elimination can make a puzzle unsolvable.
2. Missing Simpler Solutions
Solution: Always exhaust basic techniques before trying advanced ones. Often what seems like an advanced puzzle has a simple move you overlooked.
3. Not Maintaining Candidates
Solution: Keep pencil marks updated. Advanced techniques rely on accurate candidate tracking.
4. Giving Up Too Quickly
Solution: Expert puzzles can take 45-90 minutes. Take breaks and return with fresh eyes.
The Psychology of Advanced Solving
Pattern Recognition
Your brain will start recognizing these patterns automatically after 20-30 puzzles using each technique. Initially, systematically check for each pattern.
Patience Pays Off
Expert puzzles are meant to be challenging. The satisfaction of solving without hints is worth the investment.
Learn from Every Puzzle
Each puzzle teaches something:
- Which techniques appeared?
- Where did you get stuck?
- What did you learn?
Beyond Techniques: Becoming an Expert
1. Speed and Accuracy
Expert solvers balance both:
- Fast candidate elimination
- Careful verification of conclusions
- Systematic pattern checking
2. Intuition Development
After hundreds of puzzles:
- You’ll “feel” where to look
- Patterns jump out naturally
- Solving becomes more fluid
3. Embracing Difficulty
The hardest puzzles provide the most growth. Don’t shy away from “Expert” or “Evil” difficulty levels.
Conclusion
Advanced sudoku techniques transform puzzle-solving from trial-and-error into pure logic. While the learning curve is steep, each technique you master opens new puzzles to conquer.
Remember:
- Start with X-Wing and XY-Wing
- Practice each technique deliberately
- Keep candidates updated
- Be patient with yourself
- Enjoy the journey to mastery
Ready to put these techniques into practice? Download Sudoku Master and challenge yourself with expert-level puzzles that will put your new skills to the test!
Which advanced technique do you find most useful? Share your experiences in the comments!