Advanced Sudoku Techniques: X-Wing, Swordfish, and More
If you've mastered the five basic strategies but still get stuck on hard or evil puzzles, this guide is for you.
These techniques require more careful scanning, but they unlock puzzles that seem impossible at first glance.
1. X-Wing
X-Wing is one of the most famous advanced sudoku techniques. It works on a single digit across four cells forming a rectangle.
How to find one: Pick a digit. Find two rows where that digit can only go in exactly the same two columns. Those four cells form an X-Wing.
What you can eliminate: Since the digit must be in one of the two cells in each row, it cannot appear in any other row in those two columns. Eliminate it from all other cells in those columns.
X-Wings can also work on columns instead of rows — same logic, rotated 90 degrees.
2. Swordfish
Swordfish is the three-row version of X-Wing. Instead of two rows and two columns, it uses three rows and three columns.
How to find one: Pick a digit. Find three rows where that digit can only go in the same set of three columns. Those nine cells form a Swordfish.
What you can eliminate: The digit must appear once in each of the three rows, using three of the nine cells. So it can be eliminated from every other cell in those three columns.
Swordfish is harder to spot than X-Wing because you need to scan more rows at once, but it's equally powerful.
3. XY-Wing
XY-Wing uses three cells: one pivot and two wings. Each cell has exactly two candidates, and they share candidates in a specific pattern.
How to find one: Look for a cell with candidates {X, Y}. Then find two other cells that "see" the pivot (same row, column, or box), where one has candidates {X, Z} and the other has {Y, Z}.
What you can eliminate: Any cell that sees both wings cannot contain Z. Since X and Y are mutually exclusive, one wing must be Z, eliminating Z from any cell that sees both.
XY-Wing is often the key to unlocking hard puzzles where X-Wing and Swordfish don't apply.
4. XYZ-Wing
XYZ-Wing is an extension of XY-Wing. This time, the pivot has three candidates {X, Y, Z}, and the two wings have {X, Z} and {Y, Z}.
What you can eliminate: Z can be eliminated from any cell that sees all three of the pivot and both wings — typically the three cells that share the pivot's box.
XYZ-Wings are relatively rare but devastating when they appear.
5. Forcing Chains
Forcing chains are the nuclear option. Instead of looking for a pattern, you follow a logical chain: "If cell A is X, then cell B must be Y, then cell C cannot be Z..."
How to use it: Pick a cell with two candidates. Assume one value, then follow the implications. If you hit a contradiction, the original assumption was wrong — so the other value must be correct.
Forcing chains are slow but reliable. They can crack any puzzle, no matter how hard, if you're patient enough to follow the chain.
When to use which technique
Advanced techniques aren't always necessary. Here's a rough guide:
- Easy puzzles: Naked singles and scanning are enough.
- Medium puzzles: Add hidden singles and block elimination.
- Hard puzzles: X-Wing and naked pairs are usually required.
- Evil puzzles: Swordfish, XY-Wing, and sometimes forcing chains.
Tip: Don't jump to advanced techniques too early. Try the basic strategies first — many "hard" puzzles can be solved without them if you scan carefully.
How to practice
The best way to learn these techniques is deliberate practice:
- Print or open a hard puzzle.
- Fill in all candidates (pencil marks) in every empty cell.
- Spend 10 minutes looking for X-Wings. Don't move on until you find one or give up.
- Next session, look for Swordfish. Then XY-Wing.
- Keep a log of which techniques you use to solve each puzzle.
Try a hard printable puzzle from our library, or challenge yourself with an evil-level puzzle on the site.
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