Sudoku Advanced Techniques: X-Wing, Swordfish & Y-Wing Explained

You have worked through scanning, naked singles, hidden singles, naked pairs, pointing pairs, and box-line reduction. The grid has gone completely quiet. No eliminations remain. The puzzle still has empty cells.

This is the moment advanced techniques were made for.

X-Wing, Swordfish, and Y-Wing are different in kind from the techniques below them. They do not look at one row, one column, or one box at a time. They look across multiple rows and columns simultaneously and prove that a digit cannot appear in certain cells — even when you cannot directly place it yet. Each technique is a forced elimination: once you see the pattern, the logic is airtight.

These three techniques handle the vast majority of hard and expert-rated published Sudoku puzzles. [VERIFY]

Before You Start

Make sure you have already applied everything below:

• All naked and hidden singles.
• Naked pairs and triples.
• Pointing pairs (box → row/column).
• Box-line reduction (row/column → box).

If any of those still have moves, use them first. Advanced techniques become visible only when the easier ones are truly exhausted.

Technique 1: X-Wing

The X-Wing is the technique that separates intermediate solvers from advanced ones. The logic feels surprising the first time, but it becomes second nature quickly.

Here is the situation you are looking for: a digit you cannot place, even after pointing pairs and naked pairs. The digit still appears in too many cells to resolve directly. X-Wing looks across two rows and two columns simultaneously and proves where the digit cannot go.

Pick a digit. Find two rows where that digit can only go in exactly two cells each — and both rows share the same two candidate columns.

Those four cells form a rectangle. Think about what must happen. Row A needs the digit — it can go in column X or column Y. Row B also needs it — same two columns. Two outcomes are possible:

• Row A gets the digit in column X, Row B gets it in column Y.
• Row A gets it in column Y, Row B gets it in column X.

Either way, column X gets exactly one occurrence of the digit from these two rows, and column Y gets exactly one occurrence. That means no other cell in column X or column Y needs to hold the digit. Remove it from every other cell in those two columns.

Worked example — X-Wing on digit 7:

Scanning pencilmarks for digit 7:

• Row 2: 7 is a candidate only at R2C3 and R2C7.
• Row 5: 7 is a candidate only at R5C3 and R5C7.

Both rows share the same two columns — C3 and C7. This is an X-Wing.

Conclusion: digit 7 must land in C3 and C7 from these two rows (in some order). Rows 1, 4, and 8 already have digit 7 placed elsewhere, so their cells in C3 and C7 carry no pencilmark 7 — nothing to erase there. For the remaining open rows: remove 7 from R3C3 and R3C7 (row 3 has pencilmark 7 in both target columns), R6C7 (row 6 has a pencilmark 7 in column 7), R7C3 (row 7 has a pencilmark 7 in column 3), and R9C3 (row 9 has a pencilmark 7 in column 3). Five genuine eliminations.

How to search for X-Wings:

1. Pick a digit — start with digits appearing 5–7 times already placed.
2. For each row, count how many cells can hold the digit. Note rows where the count is exactly 2.
3. Check whether two such rows share the same two candidate columns.
4. If they do, eliminate the digit from all other cells in those two columns.

Column-based X-Wings work identically in reverse: find two columns where a digit has exactly two candidates each, all in the same two rows. Eliminate from those two rows.

Technique 2: Swordfish

Swordfish is the three-row extension of X-Wing. The same logic, stretched across three rows and three columns.

The setup: Find three rows where a digit appears in exactly two or three candidate cells per row, and those cells collectively span exactly three columns — no more, no fewer. Eliminate the digit from all other cells in those three columns.

Why it works: The three rows collectively must place the digit in one of those three columns each. Each column receives exactly one occurrence of the digit from this set of three rows. So no other cell in those three columns can hold the digit.

Worked example — Swordfish on digit 4:

Scanning pencilmarks for digit 4:

• Row 2: candidates at R2C3 and R2C7.
• Row 5: candidates at R5C3 and R5C9.
• Row 8: candidates at R8C7 and R8C9.

Those three rows collectively span exactly three columns — C3, C7, and C9. That is a Swordfish.

Conclusion: digit 4 must land in C3, C7, and C9 from these three rows (one per column). Remove 4 from every other cell in column 3 (all rows except 2, 5, 8), every other cell in column 7 (all rows except 2, 5, 8), and every other cell in column 9 (all rows except 2, 5, 8).

How to search for Swordfish:

1. Pick a digit.
2. List rows where that digit has exactly 2 or 3 candidate cells.
3. Check whether any three of those rows span exactly three columns collectively.
4. If they do, eliminate the digit from all other cells in those three columns.

Technique 3: Y-Wing (XY-Wing)

Y-Wing works differently from X-Wing and Swordfish. Instead of scanning across rows and columns for a repeated pattern, it traces a chain of logic through three specific cells. This makes Y-Wing harder to spot, but the logic is equally airtight.

You need three bivalue cells — cells with exactly two candidates each. Call the candidates A, B, and C.

The setup:

1. Find a pivot cell with candidates {A, B}.
2. Find two pincer cells that each see the pivot (share a row, column, or box with it): one with {A, C}, one with {B, C}.
3. Trace the logic: the pivot must be A or B. If it is A, the pincer with {A, C} cannot be A and becomes C. If it is B, the pincer with {B, C} cannot be B and becomes C. Either way, one of the two pincers holds C.
4. Any cell that sees both pincers cannot be C — eliminate it.

Worked example — Y-Wing on digit 8:

• Pivot: R5C5 holds candidates {2, 5}.
• Pincer 1: R5C2 holds candidates {2, 8}. Shares row 5 with the pivot.
• Pincer 2: R2C5 holds candidates {5, 8}. Shares column 5 with the pivot.

Walk through it: R5C5 is either 2 or 5.

• If R5C5 = 2 → R5C2 cannot be 2, so R5C2 = 8.
• If R5C5 = 5 → R2C5 cannot be 5, so R2C5 = 8.

Either way, digit 8 lands in one of the two pincers. Now look for cells that see both pincers: R2C2 sees R5C2 through column 2 and sees R2C5 through row 2. It sees both pincers. Remove 8 from R2C2.

How to search for Y-Wings:

1. Find all bivalue cells (exactly two candidates).
2. For each bivalue cell, treat it as a potential pivot.
3. Check whether two other bivalue cells each share a group with the pivot and together cover three distinct digits (A, B on pivot; A, C on one pincer; B, C on the other).
4. Find any cell that sees both pincers — it cannot hold the shared digit C.

The Full Solving Sequence

Working through every difficulty level systematically:

1. Scan (30–60 seconds). Fill any naked singles you spot immediately.
2. Add pencilmarks to all remaining empty cells.
3. Naked and hidden singles — clear every cell/group with a forced placement. Update pencilmarks after each.
4. Naked pairs and triples — remove locked candidates from shared groups.
5. Pointing pairs and box-line reduction — eliminate candidates locked to one line or box.
6. Look for X-Wings — pick each digit and find two rows where it appears in exactly two cells, both in the same two columns. Eliminate from those columns.
7. Look for Swordfish — find three rows where a digit’s candidates collectively span only three columns. Eliminate from those three columns.
8. Look for Y-Wings — find a bivalue pivot cell, then look for two bivalue pincers each sharing a group with it. Any cell that sees both pincers can remove the pincers’ shared digit.

After each technique finds an elimination, cycle back to step 3. A single X-Wing elimination can unlock a cascade of naked singles that finishes the puzzle.

Recap Checklist

After finishing this guide, you should be able to:

• Recognize when a puzzle is ready for advanced techniques (intermediate techniques exhausted, grid still has pencilmarks with no obvious move).
• Find an X-Wing: two rows where a digit has exactly two candidates each, both in the same two columns — and eliminate that digit from those two columns.
• Find a column-based X-Wing: the reverse — two columns, same two rows.
• Find a Swordfish: three rows where a digit’s candidates collectively span exactly three columns — and eliminate from those three columns.
• Find a Y-Wing: a pivot bivalue cell with two pincer bivalue cells, each sharing a group with the pivot, with a shared digit C in both pincers — and eliminate C from any cell that sees both pincers.
• Return to naked/hidden singles after every advanced elimination, since one chain often unlocks a cascade.

Frequently Asked Questions

Q: Is there a technique beyond Swordfish?
Yes — Jellyfish, which extends the pattern to four rows and four columns. After Jellyfish, the techniques branch into Alternating Inference Chains (AIC) and other chain-based logic. Many published puzzles at hard and expert difficulty can be solved without going beyond Y-Wing, though this varies by publisher and rating system. [VERIFY]

Q: X-Wing feels like luck — how do I actually spot it reliably?
Scan by digit, not by cell. Pick digit 7. Go row by row and count how many cells can hold 7. Write down every row with exactly two candidates. Then compare those rows pairwise to see if any share the same two columns. Once this becomes a systematic habit, X-Wings appear consistently.

Q: Can Y-Wing work across boxes, not just rows and columns?
Yes. A pincer “sees” the pivot if it shares a row, column, or box. The pivot’s connection to each pincer can be different — one via row, one via column, one via box — as long as each pincer sees the pivot.

Q: How do I know if a hard puzzle needs advanced techniques or if I missed something intermediate?
Re-run pointing pairs and box-line reduction one more time before advancing. Intermediate eliminations are easy to miss on a crowded grid. If those truly yield nothing, the puzzle requires at least X-Wing.

What to Try Next

• Sudoku Series Hub — Full technique overview and level chooser.
• The X-Wing Technique: Deep Dive — Extra X-Wing examples, the column-based variant, and common pitfalls.
• How to Solve Nonograms — Master picture-logic puzzles with the overlap method.
• How to Solve Logic Grid Puzzles — Deduction chains and elimination grids explained.

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