This comprehensive guide covers all major Sudoku solving strategies, from beginner to advanced levels. Each technique is explained with detailed descriptions, examples, and tips for recognizing when to apply them. Master these strategies to solve any Sudoku puzzle through pure logic.
đĄ Key Principle: Every Sudoku puzzle can be solved using logical deduction alone - no guessing required! The techniques below provide a systematic approach to finding the solution.
A naked single is a cell that has only one possible candidate number remaining. This is the most fundamental Sudoku technique and the first thing you should look for in any puzzle.
How to identify:
Look at an empty cell
Check which numbers already exist in its row
Check which numbers already exist in its column
Check which numbers already exist in its 3x3 box
If only one number (1-9) is missing from all three units, that's your answer
Example:
If a cell's row contains {1,2,3,4,5,6,7,8}, its column contains {1,2,3,5,6,7,8,9}, and its box contains {2,3,4,5,6,7,8,9}, then the only number that doesn't appear in any of these units is 1. Therefore, this cell must be 1.
đĒ Practice Tip: Scan the grid systematically - check each row, then each column, then each box. Naked singles are most common at the start of a puzzle and after placing each new number.
2. Hidden Singles Beginner
What is it?
A hidden single occurs when a specific number can only be placed in one position within a row, column, or box, even if that cell has multiple candidates.
How to identify:
Pick a number (e.g., 5)
Look at a specific row, column, or box
Check all empty cells in that unit to see where 5 could go
If only one cell can contain 5, place it there
Repeat for all numbers 1-9 in all rows, columns, and boxes
Example:
In a particular box, the number 7 is missing. Looking at all empty cells in this box, you notice that six cells already have 7 eliminated (because 7 appears in their rows or columns). Only one cell remains where 7 could possibly go - that's a hidden single.
đĒ Practice Tip: Use the "scanning" approach - pick a number and systematically check each box, row, and column for hidden singles of that number.
3. Cross-Hatching / Scanning Beginner
What is it?
Cross-hatching is a visual technique where you scan rows and columns to determine where a specific number must be placed in a box.
How to use it:
Choose a number (e.g., 4)
Find boxes where 4 has been placed
Draw imaginary lines through the rows and columns containing those 4s
Look at boxes where 4 hasn't been placed yet
The intersecting lines eliminate certain cells, often leaving only one possible position
This technique works best with numbers that appear frequently in the given clues.
Intermediate Strategies
4. Naked Pairs Intermediate
What is it?
When two cells in the same row, column, or box both contain exactly the same two candidates (and only those two), they form a naked pair. These two numbers must occupy these two cells.
How to use it:
Find two cells in the same unit (row/column/box) with identical candidate pairs, like {3,7}
Even though you don't know which cell gets 3 and which gets 7, you know these cells must contain 3 and 7
Remove 3 and 7 from all other cells in that same unit
Example:
In row 5, cells A and B both have candidates {2,8}. This means 2 and 8 must go in these two cells. You can now eliminate 2 and 8 from all other cells in row 5.
đĒ Practice Tip: Look for cells with only two candidates first, then check if any pairs match. This technique also extends to Naked Triples (three cells with the same three candidates) and Naked Quads.
5. Hidden Pairs Intermediate
What is it?
When two candidates can only appear in two specific cells within a row, column, or box (and nowhere else in that unit), those cells must contain those two numbers, even if they have other candidates.
How to identify:
Look at a row, column, or box
Find two numbers that can only go in the same two cells within that unit
Remove all other candidates from those two cells
Example:
In box 3, the numbers 1 and 6 can only appear in cells X and Y (and nowhere else in that box). Cell X might have candidates {1,4,6,9} and cell Y might have {1,2,6,8}, but since 1 and 6 must go in these cells, you can remove the other candidates, leaving X={1,6} and Y={1,6}.
6. Pointing Pairs/Triples Intermediate
What is it?
When a candidate in a box is limited to a single row or column within that box, that candidate can be eliminated from the rest of that row or column outside the box.
How to identify:
Look at a candidate number within a box
If that candidate only appears in one row or column within the box (in 2 or 3 cells)
Eliminate that candidate from the rest of that row or column outside the box
Example:
In box 1 (top-left), the candidate 9 only appears in the top row of the box (in 2 cells). This means 9 must be in one of those two cells. Therefore, you can eliminate 9 from all other cells in the top row that are outside box 1.
đĒ Practice Tip: This technique is also called "box/line reduction" or "intersection removal." It creates a powerful interaction between boxes and rows/columns.
7. Box/Line Reduction Intermediate
What is it?
The opposite of pointing pairs. When all candidates for a number in a row or column are confined to a single box, that candidate can be eliminated from other cells in that box.
How to identify:
Look at a row or column
Find a candidate that only appears in one box within that row/column
Eliminate that candidate from other cells in that box (outside the row/column)
Example:
In row 4, all the 5s are confined to box 5 (middle box). This means 5 in box 5 must be in row 4. You can eliminate 5 from all other cells in box 5 that aren't in row 4.
Advanced Strategies
8. Naked Triples/Quads Advanced
What is it?
An extension of naked pairs. When three cells in the same unit contain only three specific candidates (distributed among them), or four cells contain only four candidates, those candidates belong to those cells.
How to identify:
Find three cells in the same unit where the combined candidates contain exactly three numbers
The cells might have {1,2}, {2,3}, {1,3} or {1,2,3}, {2,3}, {1,2} etc.
These three numbers must go in these three cells
Remove these three candidates from all other cells in the unit
Example:
Three cells in column 7 have candidates: {4,9}, {4,6}, {6,9}. These three cells must contain 4, 6, and 9. Remove 4, 6, and 9 from all other cells in column 7.
9. X-Wing Advanced
What is it?
X-Wing is a powerful technique that works across two rows (or columns). When a candidate appears in exactly two positions in two different rows, and these positions are in the same columns, eliminations can be made in those columns.
How to identify:
Pick a candidate number (e.g., 3)
Find two rows where 3 appears in exactly two cells each
Check if these four cells align to form a rectangle (same column positions)
If yes, eliminate 3 from all other cells in those two columns
Why it works:
If 3 must appear once in each of the two rows, and there are only two possible positions (the corners of the rectangle), then 3 must occupy two diagonally opposite corners. Either way, 3 is locked into those two columns, so it can be eliminated elsewhere in those columns.
Example:
Row 2 has candidate 7 in columns 3 and 8. Row 6 has candidate 7 in columns 3 and 8. This forms an X-Wing. You can eliminate 7 from all other cells in columns 3 and 8.
đĒ Practice Tip: X-Wing can also work with columns and rows reversed (two columns, eliminations in rows). Look for candidates that appear exactly twice in two different rows/columns.
10. Y-Wing Advanced
What is it?
Y-Wing involves three cells forming a Y-shape: one "pivot" cell and two "wing" cells. The pivot has two candidates, and each wing shares one candidate with the pivot and has one common candidate with the other wing.
Structure:
Pivot cell: {A,B}
Wing 1: {A,C} (shares A with pivot)
Wing 2: {B,C} (shares B with pivot)
Both wings share candidate C
How to use it:
Any cell that can "see" both wing cells (is in the same row, column, or box as both wings) cannot be C. Why? If the pivot is A, then Wing 2 must be C. If the pivot is B, then Wing 1 must be C. Either way, C must be in one of the wings.
Example:
Pivot at R5C5: {3,7}. Wing 1 at R5C2: {3,8}. Wing 2 at R8C5: {7,8}. Any cell that sees both R5C2 and R8C5 cannot be 8.
11. Swordfish Advanced
What is it?
Swordfish is an extension of X-Wing involving three rows and three columns instead of two. It's a rare but powerful technique for difficult puzzles.
How to identify:
Pick a candidate number
Find three rows where this candidate appears in 2 or 3 positions
If these positions align to three columns, you have a Swordfish
Eliminate the candidate from all other cells in those three columns
Example:
Candidate 5 appears: Row 1 in columns 2,5,9; Row 4 in columns 2,9; Row 8 in columns 5,9. These align to columns 2, 5, and 9, forming a Swordfish. Eliminate 5 from all other cells in columns 2, 5, and 9.
Expert Strategies
12. XYZ-Wing Expert
What is it?
Similar to Y-Wing but involves three candidates instead of two. The pivot cell has three candidates {X,Y,Z}, and the wing cells each have two of these three candidates.
Pattern:
Pivot: {X,Y,Z}
Wing 1: {X,Y} or {X,Z} or {Y,Z}
Wing 2: {X,Y} or {X,Z} or {Y,Z}
Any cell that sees all three cells (pivot and both wings) cannot contain the common candidate that appears in all three cells.
13. Unique Rectangles Expert
What is it?
A technique based on the assumption that a well-formed Sudoku has only one solution. When you find four cells forming a rectangle with the same two candidates, you can make eliminations to prevent multiple solutions.
Requirements:
Four cells form a rectangle (two rows, two columns, two boxes)
All four cells contain the same two candidates {A,B}
This would create a "deadly pattern" with multiple solutions
To prevent this, eliminate candidates to avoid the pattern
Note: This technique assumes the puzzle has a unique solution, which is standard for published Sudoku puzzles.
14. Jellyfish Expert
What is it?
Jellyfish is an extension of X-Wing and Swordfish, involving four rows and four columns. It's extremely rare but useful for the hardest puzzles.
How it works:
When a candidate appears in 2-4 positions in four different rows, and these positions align with four columns, eliminations can be made in those columns (and vice versa).
Due to its rarity and complexity, Jellyfish is typically only needed for extremely difficult puzzles.
Strategy Selection and Practice Tips
Order of Application
When solving a puzzle, apply techniques in this order for maximum efficiency:
Naked Pairs/Triples - Scan for matching candidates
Hidden Pairs/Triples - More time-consuming
X-Wing - For harder puzzles
Y-Wing - When simpler methods don't work
Advanced Techniques - Only for expert puzzles
General Practice Tips
Maintain Clean Candidates: Always update your pencil marks after placing a number. Incorrect candidates lead to mistakes.
Be Systematic: Don't jump randomly between techniques. Complete one pass of simple techniques before moving to complex ones.
Use Our Solver: When stuck, use the "Human Solve" feature to see which technique applies next and learn from it.
Practice Pattern Recognition: The more puzzles you solve, the faster you'll recognize which patterns to look for.
Start Easy: Master basic techniques on easy puzzles before attempting expert-level challenges.
Take Notes: Keep track of which techniques you find most useful and which need more practice.
Learn from Every Puzzle: After solving (or getting help), review which techniques were needed and why.
Difficulty Level Guide
Easy Puzzles: Can be solved using only Naked Singles and Hidden Singles
Medium Puzzles: Require Naked/Hidden Pairs and Pointing Pairs
Hard Puzzles: Need X-Wing, Y-Wing, and Naked Triples
Expert Puzzles: Require Swordfish, XYZ-Wing, and advanced techniques
Evil Puzzles: May need Jellyfish, Unique Rectangles, and complex chains
đ¯ Ready to Practice? Try our Online Sudoku Solver with generated puzzles at various difficulty levels. Use the "Human Solve" feature to see these strategies in action!
Mastering Sudoku strategies takes time and practice, but every technique you learn makes you a better solver. Start with the basic strategies, practice them until they become second nature, then gradually add intermediate and advanced techniques to your toolkit. Our online solver with the "Human Solve" feature is an excellent training tool that shows you exactly which strategies to apply and when.
Remember: every Sudoku puzzle, no matter how difficult, can be solved through logical deduction using these strategies. Happy solving!