You've mastered X-Wing and Y-Wing, but some level 7-8 puzzles still resist? The W-Wing is the natural next step after these two techniques.
The W-Wing belongs to the advanced techniques family, alongside the Y-Wing, the XY-Chain and X-Cycles. It combines two ideas you already know: bivalue cells (seen with the Y-Wing) and the strong link or conjugate pair (seen with the X-Wing). Once these two notions are understood, the W-Wing becomes surprisingly easy to spot.
The W-Wing principle (two identical bivalue cells connected by a strong link), how to spot the configuration, and the Domino33 method to find it efficiently in a grid. The full video gives you 3 practical examples from real puzzles.
🎬 The full Domino33 video on the W-Wing
Before the written content, here's the full video: theory illustrated with 3 practical examples, followed by the search method:
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Part 1
What is a W-Wing?
The two ingredients of a W-Wing
A W-Wing relies on two elements that must be present simultaneously in the grid:
- Two identical bivalue cells: two cells, not necessarily neighbours, that contain exactly the same 2 candidates (for example {2,7} and {2,7})
- A strong link (conjugate pair) on one of the two candidates, somewhere else in the grid: a candidate that appears in exactly 2 cells of the same row, column or box
For the technique to work, each of the two bivalue cells must see one end of the strong link (be in the same row, column or box as one of the two link cells).
The elimination logic
Let's call the two shared candidates X and Y, and assume the strong link is on X. Reason it out: if the first bivalue cell equals X, then it prevents the end of the strong link it sees from being X, so the other end of the link must be X (that's the very definition of a strong link). That other end then prevents the second bivalue cell from being X, so the second bivalue cell equals Y.
And if the first bivalue cell equals Y directly, it's even simpler: it's already Y.
In both cases, at least one of the two bivalue cells always equals Y. Consequence: any cell that sees both bivalue cells simultaneously cannot contain Y. It can therefore be eliminated.
The Y-Wing links 3 directly neighbouring cells through their shared candidates. The W-Wing uses only 2 identical bivalue cells, which can be far apart in the grid: it's the strong link, located elsewhere, that bridges them.
Schematic example
Here's a simplified diagram. Two bivalue cells {2,7} are present on the same row (at the bottom), and a strong link on candidate 2 connects two cells on another row (at the top), each in the same column as one of the bivalue cells. Candidate 7 can be eliminated from cells that see both bivalue cells:
| 2 Strong link | 2 Strong link | |||||||
| {2,7} | ✗ 7 | ✗ 7 | ✗ 7 | ✗ 7 | {2,7} | |||
The cells between the two bivalues, on the same row, see both: candidate 7 (Y) can be eliminated there.
The video develops this diagram over 3 examples taken from real puzzles, with configurations where the strong link is found in a row, a column or a box.
Part 2
The search method
As with the Y-Wing, knowing the theory isn't enough: you need to know how to spot it quickly in a real grid.
Step 1 — Spot pairs of identical bivalue cells
Scan the grid looking for two bivalue cells that share exactly the same 2 candidates. Unlike the Y-Wing, they don't need to be neighbours: they can be anywhere in the grid.
Step 2 — Look for a strong link on one of the two candidates
For each of the two candidates in the pair, check whether there's a row, column or box where that candidate appears in exactly 2 cells (a strong link). This is often the longest step: focus first on candidates that look rare in the grid.
Step 3 — Verify the connection
Once a strong link is found, check that each bivalue cell sees a different end of the link. If so: you've got a W-Wing. All that's left is to eliminate the other candidate from any cell that sees both bivalue cells.
Many people look for the strong link first, across the whole grid: that's tedious. The right approach: start from pairs of identical bivalue cells, then look for the strong link only for the candidates of that specific pair. This drastically narrows the search.
🎬 See the method in action
In the video, the method is walked through on 3 real grids with different configurations (strong link in a row, a column, a box). It's the best way to build the reflex.
Part 3
Application quiz
Have you got the theory and the method down? Test your knowledge with this 4-question quiz. Good luck!
❓ Frequently asked questions
A W-Wing involves 4 cells in total: two identical bivalue cells (the same 2 candidates) and a conjugate pair (strong link) on one of the two candidates, connecting the two bivalue cells.
The Y-Wing links 3 directly neighbouring cells through their shared candidates. The W-Wing uses 2 identical bivalue cells that do not need to be neighbours, connected indirectly by a strong link (conjugate pair) located elsewhere in the grid.
A strong link exists when a candidate appears in exactly 2 cells of the same unit (row, column or box). One of the two cells must necessarily contain that candidate in the final solution.
The W-Wing typically appears in puzzles of level 7 and above, similar to the Y-Wing. It's one of the advanced techniques to master to progress towards expertise, alongside the XYZ-Wing and the Sashimi X-Wing.
📋 Summary
The essentials of the W-Wing
- Configuration: 2 identical bivalue cells {X,Y} + 1 strong link (conjugate pair) on X
- Requirement: each bivalue cell sees a different end of the strong link
- Action: eliminate Y from any cell that sees both bivalue cells simultaneously
- Starting point: spot pairs of identical bivalue cells, wherever they are in the grid
- Appears at level: grids 7+ (hard to expert)
- Related techniques: Y-Wing, XYZ-Wing, Sashimi X-Wing
The W-Wing combines two notions already seen separately (bivalue cells and strong link): that's what makes it a natural technique to learn right after the Y-Wing. Regular practice on real puzzles remains the best way to build the reflex.
📘 Go further with the Domino33 books
Every technique on this site is covered step by step in the Domino33 memento, available in English — with the Sudoku Solver Pro software included.
