How to Solve Sudoku: Advanced Techniques That Actually Work

Stuck on a hard grid where the easy scans run dry? Learning how to solve sudoku with advanced techniques is what gets you past that wall. This guide covers pointing pairs, X-Wing, Swordfish, and XY-Wing — the real methods experts use, explained step by step. Keep a tough sudoku puzzle to play open and try each one as you go.

Key takeaways

Advanced techniques rely on pencil marks — the candidate numbers in each empty cell.
Pointing pairs and box-line reduction remove candidates between boxes and lines.
X-Wing uses two rows and two columns to eliminate a candidate from intersecting lines.
Swordfish is X-Wing scaled up to three rows and three columns.
XY-Wing chains three linked cells to eliminate a candidate they all see.

Before you go advanced: pencil marks

Every advanced technique depends on accurate pencil marks. A pencil mark is the list of candidate digits that could still legally go in an empty cell.

Fill in candidates only after you’ve exhausted the basics — naked singles (a cell with one candidate) and hidden singles (a digit that fits only one cell in a unit). Without clean pencil marks, the patterns below won’t appear.

If your candidates are wrong, every advanced step will be wrong too. Double-check them before hunting for patterns.

Pointing pairs and pointing triples

This is the gentlest of the sudoku advanced techniques, so start here. A pointing pair happens when a candidate within a single box is restricted to one row or one column inside that box.

If the only places a 4 can go in a box all sit in the same row, then 4 must be somewhere in that row inside the box. So you can remove 4 as a candidate from the rest of that row outside the box.

Find a candidate that appears only in one line within a box.
Eliminate that candidate from the same line in neighboring boxes.
The same logic with three cells is a pointing triple.

Box-line reduction

This is the mirror image of a pointing pair. Here, a candidate within a row or column is confined to a single box.

Suppose every spot for a 7 in one row falls inside the same box. Then 7 in that box must be in that row, so you can remove 7 from the other cells of that box.

Pointing pairs work box-to-line; box-line reduction works line-to-box. Together they clear a surprising number of candidates.

Naked and hidden subsets

Subsets are pairs, triples, or quads of cells that lock candidates together.

Naked pairs

If two cells in the same unit contain exactly the same two candidates — say 3 and 8 — those two digits must occupy those two cells. You can remove 3 and 8 from every other cell in that unit.

Hidden pairs

If two candidates appear in only two cells of a unit (even if those cells hold other candidates too), those two cells must hold those two digits. Remove all other candidates from those two cells.

The same idea scales to naked and hidden triples and quads. Subsets are the workhorses between basic solving and the heavier fish techniques.

The X-Wing technique

The X-Wing is the famous one, and once it clicks it’s very satisfying. It works on a single candidate digit across two rows and two columns.

Look for a candidate — say 5 — that appears in exactly two cells in one row, and in exactly two cells in another row, where those cells share the same two columns. The four cells form the corners of a rectangle.

How the X-Wing eliminates candidates

Because of the rectangle, the 5s must sit on one of the two diagonals. Either way, 5 occupies both of those columns within those two rows. So you can remove 5 from every other cell in those two columns.

The X-Wing also works the other way around: two columns sharing two rows let you eliminate the candidate from those two rows. This x-wing sudoku pattern is one of the most reliable ways to break a stuck grid.

The Swordfish technique

Swordfish is X-Wing scaled up by one. Instead of two rows and two columns, it uses three.

Find a candidate that appears in three rows, where in each row it’s limited to cells within the same three columns (each row uses two or three of those columns). The candidate is then locked into those three columns across those three rows.

That lets you remove the candidate from any other cell in those three columns. The sudoku swordfish is rarer and harder to spot than X-Wing, so scan carefully and verify before erasing anything.

Pick one candidate digit to test.
Check whether it confines to three columns across three rows (or three rows across three columns).
Eliminate that candidate from the rest of those three lines.

The XY-Wing technique

The XY-Wing is a short chain of three cells, each holding exactly two candidates. It’s powerful because it doesn’t rely on a single digit.

You need a “pivot” cell with candidates XY, and two “wing” cells: one with XZ and one with YZ. The pivot must share a unit (row, column, or box) with each wing.

Why XY-Wing works

Whatever the pivot turns out to be, one of the wings will be forced to Z. So any cell that both wings can “see” — that shares a unit with both XZ and YZ cells — cannot contain Z. Remove Z from those shared cells.

Take it slow: confirm the three cells are bivalue (two candidates each) and that the Z elimination targets a cell seen by both wings.

A practical order of operations

When a puzzle stalls, work through the techniques from simplest to hardest. This keeps you from over-thinking.

Re-scan for naked and hidden singles.
Apply pointing pairs and box-line reduction.
Hunt for naked and hidden pairs, triples, and quads.
Look for an X-Wing on each digit.
Try Swordfish and XY-Wing only if the grid is still stuck.

Often one elimination from a simpler technique reopens easier moves, so loop back to the top after each success.

Frequently asked questions

What is the hardest sudoku technique to learn?

Most solvers find Swordfish and chain-based methods like XY-Wing the hardest, because the patterns span more cells and are easy to misread. X-Wing is usually the first “advanced” technique people master.

How does the X-Wing technique work in sudoku?

Find a candidate that appears in only two cells in each of two rows, and those cells share the same two columns, forming a rectangle. The candidate must occupy those columns within those rows, so you can remove it from the rest of both columns.

What is the difference between X-Wing and Swordfish?

X-Wing uses two rows and two columns; Swordfish uses three rows and three columns. Both lock a single candidate into specific lines so you can eliminate it elsewhere. Swordfish is the larger, harder-to-spot version.

Do I need pencil marks for advanced sudoku techniques?

Yes. Every advanced technique reads patterns in the candidate numbers of empty cells. Without accurate pencil marks, you can’t spot pointing pairs, X-Wings, or chains.

What is an XY-Wing in sudoku?

An XY-Wing is three two-candidate cells: a pivot with XY and two wings with XZ and YZ. One wing is always forced to Z, so any cell that both wings can see cannot contain Z and you can remove it.

Practice until the patterns pop

Now you know how to solve sudoku with advanced techniques: clean pencil marks first, then pointing pairs, subsets, X-Wing, Swordfish, and XY-Wing. The patterns get faster to spot with practice. Load a hard sudoku game and try one technique per puzzle. When your brain needs a reset, the Chrome Dino game is a fun palate cleanser.