Sudoku Solver

Expert

W-Wing

A fan-favorite "secret shortcut" using two identical pairs connected by a Strong Link.

The W-Wing is a fan-favorite Sudoku strategy because it feels like a secret shortcut.

It’s part of the "Wing" family (alongside the Y-Wing and X-Wing), but it’s unique because it uses identically marked cells that are linked together by a third party.

While it sounds technical, the logic is very "if-this-then-that" and is incredibly satisfying to find.

Interactive Example

1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1
1 2 3 4 5 6 7 8 9
7
1 2 3 4 5 6 7 8 9
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1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
8
1 2 3 4 5 6 7 8 9
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1 2 3 4 5 6 7 8 9
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1 2 3 4 5 6 7 8 9
9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
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1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
2
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
4
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
5
1 2 3 4 5 6 7 8 9
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1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
2
1 2 3 4 5 6 7 8 9
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1 2 3 4 5 6 7 8 9
1
1 2 3 4 5 6 7 8 9
7
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
4
1 2 3 4 5 6 7 8 9
8
1 2 3 4 5 6 7 8 9
2
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
3
1 2 3 4 5 6 7 8 9
1
1 2 3 4 5 6 7 8 9
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1 2 3 4 5 6 7 8 9
6
1 2 3 4 5 6 7 8 9
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1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
8
1 2 3 4 5 6 7 8 9
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1 2 3 4 5 6 7 8 9
5
1 2 3 4 5 6 7 8 9
4
1 2 3 4 5 6 7 8 9
2
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
7
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
4
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1
1 2 3 4 5 6 7 8 9
8
1 2 3 4 5 6 7 8 9
9
1 2 3 4 5 6 7 8 9
3
1 2 3 4 5 6 7 8 9
8
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
6
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
2
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
7
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
6
1 2 3 4 5 6 7 8 9
8
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
6
1 2 3 4 5 6 7 8 9
1
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
2
1 2 3 4 5 6 7 8 9
8
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
9
1 2 3 4 5 6 7 8 9

Click "Apply Logic" to see the strategy in action.

Real Example Explanation

In the interactive example above, look at the pair {2, 3}:

  1. The Wings:
    • Wing A: R1C1 contains only {2, 3}.
    • Wing B: R8C3 contains only {2, 3}.
    • They are far apart, but they hold the same potential values.
  2. The Connector (Strong Link):
    • We need to link them using one of the values (let's say 2).
    • Look at Row 6. The number 2 appears only twice: at R6C1 and R6C3.
    • R6C1 sees Wing A (same Column 1).
    • R6C3 sees Wing B (same Column 3).
    • This Row 6 Strong Link acts as a "Bridge".
  3. The Logic:
    • If Wing A is 3 -> Then it's 3.
    • If Wing A is NOT 3 -> Then it must be 2.
      • If Wing A is 2 -> R6C1 cannot be 2 (Column).
      • If R6C1 is not 2 -> R6C3 MUST be 2 (Row Strong Link).
      • If R6C3 is 2 -> Wing B cannot be 2... so Wing B must be 3.
    • Result: Either Wing A is 3, or Wing B is 3. They cannot both be 2.
  4. The Elimination:
    • Since one of the Wings is guaranteed to be a 3, any cell that sees BOTH Wings cannot contain a 3.
    • R8C1 sees Wing A (Column 1) and Wing B (Row 8). We can safely remove 3 from R8C1.

The Logic: The "Domino Effect"

Let's break down why this works using the "Domino Effect".

  1. The Choice: We look at the link (the row/col with only two candidates). Since there are only two spots, one of them must be true.
  2. The Chain Reaction:
    • If the first link end is true, it "sees" Wing A and forces it to be the other number.
    • If the second link end is true, it "sees" Wing B and forces it to be the other number.
  3. The Conclusion: No matter which end of the link is correct, at least one of our identical twins must be the "other" number (e.g., the 3).

How to Identify a W-Wing

  1. Find Identical Pairs: Scan for two bivalue cells with the exact same candidates (e.g., {A, B}). They should not see each other.
  2. Pick a "Linking" Number: Choose one of the two numbers (e.g., A).
  3. Find the Strong Link: Look for a row, column, or box where Candidate A appears only twice.
  4. Check the "Sight Lines": One end of the Strong Link must see Wing A, and the other end must see Wing B.

The "Kill Zone" (Eliminations)

Since we have proven that either Wing A or Wing B (or both!) must be the value B, any cell that can see both twins at the same time cannot be B.

Action: Find any cell that shares a row/column/box with Wing A AND Wing B. If it has the candidate B, delete it!

Why "W-Wing"?

It is named because the path of the logic zig-zags across the board, somewhat resembling the letter "W" (Wing -> Link End -> Link End -> Wing).

[!TIP] Pro Tip: W-Wings are the easiest way to solve puzzles that seem "stuck" with lots of pairs. If you see two {1, 2} cells far apart, don't ignore them—look for a row or column that only has two 1s or two 2s and see if they link up!