W-Wing in Sudoku: How to Find & Use This Advanced Technique

Home › Blog › W-Wing

Published April 13, 2026 · 10 min read

You’ve mastered Naked Pairs, learned the XY-Wing, and perhaps even tackled the XYZ-Wing. But there’s another powerful pattern hiding in your pencil marks: the W-Wing.

The W-Wing is an advanced elimination technique that uses two bi-value cells with the same pair of candidates, connected not by a shared row, column, or box, but by a strong link (conjugate pair) on one of the candidates. It’s one of the most elegant chain-based patterns in sudoku.

In this guide we explain exactly what a W-Wing is, walk through the logic step by step, show a real example with before-and-after diagrams, and compare it with the XY-Wing family.

✅ What is a W-Wing in Sudoku?

A W-Wing is an advanced candidate-elimination technique that uses exactly two bi-value cells containing the same pair of candidates, connected by a strong link (conjugate pair) on one of those candidates.

The name “W-Wing” comes from the shape of the logical chain: bi-value cell → strong link endpoint → strong link endpoint → bi-value cell — forming a “W” pattern across the grid.

🔗 Understanding strong links

Before diving into the W-Wing, you need to understand what a strong link (also called a conjugate pair) is:

Strong links are the backbone of chain-based techniques. In a W-Wing, the strong link acts as a “bridge” between two bi-value cells that don’t see each other directly.

🧠 How the W-Wing works (the logic)

Consider two bi-value cells, both containing candidates {3, 7}:

• Cell A (R3C2): candidates {3, 7}
• Cell B (R8C1): candidates {3, 7}

These cells don’t see each other (different row, column, and box). But in Row 5, digit 3 appears in exactly two cells — R5C1 and R5C2 — forming a strong link on 3. Crucially, R5C2 sees Cell A (same column), and R5C1 sees Cell B (same column).

Now trace the two possibilities:

• If Cell A = 7: At least one bi-value cell is 7. Done.
• If Cell A = 3: R5C2 sees Cell A and shares Column 2, so R5C2 cannot be 3. The strong link in Row 5 means the other cell (R5C1) must be 3. R5C1 sees Cell B (same column), so Cell B cannot be 3 — Cell B must be 7.

Either way, at least one of Cell A or Cell B is 7. Any cell that sees both bi-value cells can never be 7, because it would conflict with whichever one holds the 7.

🔎 Step-by-step example

Let’s walk through a real W-Wing. The two bi-value cells are R3C2 and R8C1, both with candidates {3, 7}. The strong link on digit 3 runs through Row 5 at cells R5C1 and R5C2.

Step 1: Identify the bi-value pair

• Cell A — R3C2: candidates {3, 7}.
• Cell B — R8C1: candidates {3, 7}.
• They share the same two candidates but don’t see each other ✔

Step 2: Find the strong link

• In Row 5, digit 3 appears in exactly two cells: R5C1 and R5C2 — a conjugate pair (strong link) on 3.
• R5C2 sees Cell A (both in Column 2) ✔
• R5C1 sees Cell B (both in Column 1) ✔

Step 3: Find the elimination targets

Which cells see both Cell A (R3C2) and Cell B (R8C1), and contain candidate 7?

• R1C1 — {2,3,4,6,7,8}: sees Cell A via Box 1, sees Cell B via Column 1. Eliminate 7 → {2,3,4,6,8}.
• R2C1 — {2,3,4,6,7,8}: sees Cell A via Box 1, sees Cell B via Column 1. Eliminate 7 → {2,3,4,6,8}.
• R7C2 — {2,3,4,5,7}: sees Cell A via Column 2, sees Cell B via Box 7. Eliminate 7 → {2,3,4,5}.
• R9C2 — {2,5,7,9}: sees Cell A via Column 2, sees Cell B via Box 7. Eliminate 7 → {2,5,9}.

Four eliminations from a single W-Wing!

Step 4: Continue solving

With four fewer 7-candidates in Columns 1–2, further techniques can now make progress. The cascade of reduced candidates often unlocks Hidden Singles or Naked Pairs that were previously hidden.

🕵️ How to spot a W-Wing

🔄 W-Wing vs XY-Wing

Both techniques produce candidate eliminations, but the structure is quite different.

The key difference: the XY-Wing connects cells through direct unit-sharing, while the W-Wing bridges cells through a logical chain (strong link). This makes the W-Wing harder to spot but applicable in positions where no XY-Wing exists.

⚠️ Common mistakes to avoid

1. Using bi-value cells that see each other

If the two cells see each other, they form a Naked Pair, not a W-Wing. The W-Wing requires cells in different units connected by the chain.

2. Confusing weak and strong links

The connecting link must be strong — the candidate appears in exactly two cells in its unit. If it appears in three or more cells, the either/or guarantee breaks and the elimination is invalid.

3. Wrong elimination digit

You eliminate the candidate that is not the link digit. If the strong link is on digit 3, you eliminate the other digit (7 in our example) — not 3.

4. Elimination cells must see both bi-value cells

Don’t eliminate from cells that only see one of the two bi-value cells. Both must be visible for the logic to hold.

📅 When to look for W-Wings

1. Basic techniques: Naked Singles, Hidden Singles, Full House.
2. Intermediate techniques: Naked Pairs, Hidden Pairs, Naked Triples, Pointing Pairs, Box/Line Reduction.
3. Advanced techniques: X-Wing, Swordfish, XY-Wing, XYZ-Wing.
4. Expert techniques: W-Wing, Jellyfish, Simple Colouring, ALS chains.

🚀 Beyond the W-Wing

The W-Wing is part of a broader family of chain-based techniques:

Once you’re comfortable with the W-Wing, you’re ready for longer chains like remote pairs and X-chains. The fundamental skill — tracing either/or logic through connected cells — is the same.

🎯 Practise W-Wings

• Fill in all pencil marks: W-Wings require knowing every candidate in every cell.
• Scan for matching bi-value pairs: Two cells with {4,8}, {2,5}, etc. in different boxes are prime targets.
• Check conjugate pairs: For each candidate in the pair, look for rows/columns where it appears in exactly two cells.
• Verify with the solver: Use our sudoku solver to confirm your findings.