The XY-Wing Technique in Sudoku Explained

When to reach for it

The XY-Wing is an advanced move for hard and extreme boards, the kind where singles, pairs, and even the X-Wing have run dry. Unlike those techniques, which work inside a single row, column, or box, the XY-Wing links three separate cells scattered around the grid. That reach is exactly what makes it valuable. When a board has stalled and every simple elimination is exhausted, an XY-Wing can remove a candidate sitting far from any of the cells that prove it should go, and that one removal is often enough to restart the whole chain of logic that carries you to the finish.

The three cells

Every XY-Wing is built from three cells that each hold exactly two candidates. One cell is the pivot. It shares a row, column, or box with each of the other two, which are called the pincers. The magic is in how their candidates overlap. Label the pivot two candidates X and Y. One pincer must hold X together with a third value Z, so it reads X and Z. The other pincer must hold Y together with that same Z, so it reads Y and Z. The pivot can see both pincers, but the two pincers do not need to see each other at all, which is what lets the pattern span the board.

The forcing that makes it work

Whatever value the pivot finally takes, one of the pincers is forced to become Z. If the pivot resolves to X, the first pincer can no longer be X, so it must fall back to Z. If the pivot resolves to Y instead, the second pincer can no longer be Y, so it too must become Z. There is no third option for the pivot, so one of the two pincers is always going to end up as Z. That certainty is the entire payoff. Any cell that can see both pincers at once cannot possibly be Z, because one of those pincers is about to claim the value for itself.

A worked example with coordinates

Suppose the pivot sits at r5c5 with candidates 4 and 7, so X is 4 and Y is 7. Along its row you find a pincer at r5c2 reading 4 and 9, which makes Z equal to 9. Down its column you find the second pincer at r2c5 reading 7 and 9, the same Z. Now look for cells that see both pincers. The cell r2c2 shares row 2 with r2c5 and shares column 2 with r5c2, so it sees both at once. Since one of those pincers must become 9, r2c2 can never be 9, and you can strike 9 from its notes with complete confidence, even though nothing in r2c2 itself pointed to that removal.

How to find an XY-Wing

1. Keep clean, complete Notes, since the whole pattern lives in cells with exactly two candidates.
2. Find a pivot cell holding two candidates, X and Y.
3. Look for a pincer it can see that reads X and Z, then a second pincer it can see that reads Y and Z.
4. Confirm both pincers share the same Z, the value that is never in the pivot.
5. Remove Z from every cell that sees both pincers at the same time.

Common mistakes and taking it slow

Two errors trip up newcomers. The first is forgetting that the pincers must not share Z with the pivot; the pivot holds X and Y only, never Z, or the logic collapses. The second is eliminating Z from a cell that sees just one pincer, when the guarantee is only that one of the two is Z, not any particular one, so the removal is valid only for cells that see both. When an elimination does not seem to work, check those two conditions first. Beyond that, the XY-Wing simply rewards patience. Trace the forcing by hand once or twice until the conclusion feels obvious rather than memorized, then load an Extreme board in Shapedoku, keep your Notes tidy, and hunt for a two-candidate pivot with its two matching pincers. Finding your first one in the wild is a genuine pleasure.

How it differs from the X-Wing

It helps to see exactly where the XY-Wing goes beyond the X-Wing you already know. An X-Wing works with a single value locked into a rectangle of four cells across two rows and two columns, and it eliminates that one value from the lines it dominates. The XY-Wing, by contrast, juggles three different values across three cells and eliminates a value that never even appears in the pivot. That is a genuinely different kind of reasoning: instead of one value pinned in a neat shape, you are following a short chain of implications from cell to cell. Because the pincers only need to see the pivot and not each other, the pattern can stretch across the board in ways an X-Wing cannot, which is exactly why it clears candidates the earlier technique simply cannot reach. Learning both gives you two very different tools rather than two versions of the same one.