Past level 7, the basic techniques stop being enough. You pencil in your candidates, you hunt for pairs, triples and alignments, and the grid does not budge an inch.
The W-Wing is one of the few techniques that unlock those grids. It has to be known and mastered to make progress on level 8 grids and above, and its great quality is being both simple to grasp and formidably effective.
The four ingredients of a W-Wing, the two-branch reasoning behind it, and the search method for finding one in a real grid. Both Domino33 videos are embedded, theory first and search second.
Part 1
The four ingredients
A W-Wing is four elements that must all be present, no more and no less:
- Two identical bivalue cells: two cells holding exactly the same two candidates, for instance {5,8}
- They do not see each other: no shared row, no shared column, no shared box
- A strong link on one of the two digits, elsewhere in the grid
- Each end of the link sees one of the two bivalue cells
Reminder: what is a strong link?
A strong link, or conjugate pair, exists when a digit has only two possible locations left within one unit. One of the two must take it. That certainty is what drives the whole argument.
🎬 The Domino33 video on W-Wing theory
Tutorial 12-1 introduces the technique and its variants through three detailed examples.
▶ English audio track and English subtitles: pick either from the ⚙️ icon.
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▶ Subscribe for freeA worked example
Here is a grid where every condition is met. Only the useful candidates are shown:
R1C1 and R5C5 hold {5,8} · the 8 of row 3 has only two possible locations, R3C1 and R3C5
Let us check the four ingredients. R1C1 and R5C5 both hold {5,8}, and they do not see each other: different rows, different columns, different boxes. On row 3, the 8 has only two possible locations left, R3C1 and R3C5: that is our strong link. Finally, R3C1 sees R1C1 through column 1, and R3C5 sees R5C5 through column 5.
Part 2
The two-branch reasoning
The whole technique rests on a case split. The strong link guarantees that one of its two ends holds the 8. Let us look at both possibilities.
- If R3C1 = 8, then column 1 has its 8, so R1C1 can no longer be 8. Being bivalue, R1C1 = 5.
- If R3C5 = 8, then column 5 has its 8, so R5C5 can no longer be 8. Being bivalue, R5C5 = 5.
Look at the conclusion: in both cases, at least one of the two bivalue cells is a 5. You do not know which one, and you do not need to.
All that is left is to draw the consequence: any cell that sees both R1C1 and R5C5 cannot hold a 5.
R1C5 sees R1C1 by the row and R5C5 by the column · R5C1 sees R5C5 by the row and R1C1 by the column
Two candidates eliminated, without a single digit being placed. On a level 8 grid, this kind of elimination is often the one that restarts the whole solve.
The strong link forces one or the other bivalue cell to take the second digit. So you eliminate that second digit in the intersection, meaning the cells that see both of them at once.
W-Wing, X-Wing, Y-Wing: do not mix them up
- The X-Wing works on a single digit laid out as a rectangle across two rows and two columns
- The Y-Wing links three neighbouring cells through their shared candidates, around a pivot
- The W-Wing links two identical, distant cells through a strong link located elsewhere
Part 3
The search method
Step 1, List your bivalue cells
Spot every cell with exactly two candidates and group them by digit pair. All the {5,8} together, all the {2,6} together. On a level 8 grid there are often a good fifteen of them.
Step 2, Keep the pairs that do not see each other
Within each group, keep only the cell pairs with no shared row, column or box. Two cells that see each other form a different pattern, not a W-Wing.
Step 3, Hunt for the strong link
Take one of the two digits, then sweep rows, columns and boxes looking for a unit where that digit has only two locations. If one end sees the first bivalue cell and the other end sees the second, the pattern is complete.
Step 4, Eliminate in the intersection
Find the cells that see both bivalue cells at once, and remove the second digit there, the one that does not carry the strong link.
Do not hunt for the strong link at random. Start from the two bivalue cells and look only at the units crossing one or the other. The useful strong link is almost always close by, rarely at the far end of the grid.
🎬 The Domino33 video on the search method
Tutorial 12-2 follows on from the first and is devoted entirely to searching for a W-Wing pattern, with a worked example.
▶ English audio track and English subtitles: pick either from the ⚙️ icon.
🎬 Both W-Wing tutorials
Theory in 12-1, searching in 12-2. Watching them back to back is the fastest way to build the reflex.
🎬 On a real grid
The diagrams above isolate the pattern. Here is the same technique on a full grid, at the point where it stalls. Step through it at your own pace.
A real position: unique solution, exact candidates, verified eliminations.
🎮 Put it into practice right away
Four grids from the book are playable online, free and with no sign-up. When you get stuck, the simulator reads your grid and tells you which technique to use, without ever giving the answer away.
Play a grid now →Exercise
Your turn
Here is a position with a W-Wing. Only the useful candidates are shown.
Two identical bivalue cells that do not see each other, and a strong link on one of their two digits.
Part 4
Practice quiz
Four questions to check what you have learned. Good luck!
❓ Frequently asked questions
Four in total: two bivalue cells holding exactly the same two candidates, and the two ends of a strong link on one of those two digits. Each end of the link must see one of the two bivalue cells.
The Y-Wing links three directly neighbouring cells through their shared candidates, around a pivot cell. The W-Wing uses two identical bivalue cells that do not need to be neighbours, connected indirectly by a strong link located elsewhere in the grid.
A strong link exists when a digit has only two possible locations left within one unit, row, column or box. One of those two cells must contain that digit in the final solution.
It becomes useful from level 8 grids onwards. It is an elaborate technique, alongside XY-Chains and X-Cycles, and it assumes the six basic techniques and strategic ones such as the X-Wing are already mastered.
📋 Summary
W-Wing essentials
- Setup: 2 identical bivalue cells that do not see each other, plus a strong link
- The strong link: sits on one of the 2 digits, and each end sees one of the 2 cells
- The conclusion: at least one of the 2 bivalues takes the second digit
- Action: eliminate that second digit from the cells seeing both bivalues
- Starting point: list the bivalue cells and group them by digit pair
- Related techniques: Y-Wing, Swordfish, XY-Chain
The W-Wing belongs to the elaborate techniques, alongside XY-Chains and X-Cycles. It naturally extends the Y-Wing and the X-Wing, and it assumes the six basic techniques are already in place, because without properly maintained candidates none of these patterns is visible.
📘 Go further with the Domino33 books
The W-Wing and every other technique on this site are covered step by step in the Domino33 memento, available in English.
This technique is one of the 6 advanced techniques. See them all in the order to tackle them, split into two families, with the method that makes them automatic.