X-Wing

An X-Wing is the smallest standard Fish pattern in Sudoku.

It follows one candidate digit across two rows and two columns. If two rows can place that digit only in the same two columns, those rows must supply the digit to those columns.

The result:

The digit can be removed from the same columns everywhere outside the two source rows.

Rows and columns can swap roles.

The useful way to think about X-Wing is not “four corners make a rectangle.”

It is:

2 base sets require 2 placements, and all of those placements are covered by 2 cover sets.

That idea scales directly into Swordfish and larger Fish.

Quick rule

For a row-based X-Wing:

1. Choose one digit X.
2. Find two rows where every candidate X is contained in the same two columns.
3. Those rows are the base sets.
4. The two columns are the cover sets.
5. Remove X from the cover columns outside the base rows.

For a column-based X-Wing, swap rows and columns.

A simple X-Wing

Suppose candidate 5 appears in row 2 only at:

• r2c4
• r2c8

and in row 7 only at:

• r7c4
• r7c8

Row 2 must place one 5.

Row 7 must place one 5.

Both placements are restricted to columns 4 and 8.

So columns 4 and 8 will receive their 5s from rows 2 and 7.

Candidate 5 can therefore be removed from every other cell in columns 4 and 8.

We do not need to know which diagonal is correct.

The two possible arrangements are:

• r2c4 = 5 and r7c8 = 5;
• r2c8 = 5 and r7c4 = 5.

Both arrangements produce the same outside conclusion.

Why X-Wing works

The Fish proof is a counting argument.

Two base rows each require one copy of the Fish digit.

That gives us two required placements.

Every possible source position for those placements lies inside two cover columns.

A Sudoku column can contain the digit only once.

Therefore the two required placements consume the two cover columns.

No third candidate for the digit can survive in either cover column.

This base/cover explanation is more reusable than memorizing a rectangular picture.

Step-by-step board example

Column-based X-Wing

Transpose the entire pattern.

If columns 3 and 9 can place candidate 7 only in rows 2 and 6, then:

• columns 3 and 9 are the base sets;
• rows 2 and 6 are the cover sets.

Candidate 7 can be removed from those rows outside the two base columns.

X-Wing vs a random rectangle

Four equal candidates can visually form a rectangle without proving an X-Wing.

The key question is not:

Do these four cells make corners?

It is:

In each base row, are all candidates for this digit contained in the two proposed cover columns?

If row 2 also contains candidate 5 at c1, then rows 2 and 7 are not restricted to the same two cover columns and the basic X-Wing proof fails.

X-Wing vs Locked Candidates

Both follow one digit.

Locked Candidates

The restriction lives at a box-line intersection.

X-Wing

The restriction connects two rows and two columns across the grid.

This makes X-Wing a natural first advanced step after digit-first intersection scanning.

X-Wing vs Swordfish

The Fish rule scales by size.

X-Wing

2 base sets → 2 cover sets.

Swordfish

3 base sets → 3 cover sets.

Jellyfish

4 base sets → 4 cover sets.

The geometry becomes less tidy as Fish get larger, which is why base/cover-set thinking is important.

How to search for X-Wings

Use a digit filter.

1. Choose one digit

Candidates with relatively sparse positions are easiest.

2. Scan rows with two positions

Mentally record the column pair.

Example:

r2 → c4/c8

3. Look for a matching row

If another row is:

r7 → c4/c8

test the X-Wing.

4. Check the cover columns

If candidate X exists elsewhere in either cover column, you have a productive elimination.

5. Repeat with columns

If no row-based pattern appears, transpose the scan.

What an X-Wing often unlocks

The Fish itself rarely solves a cell.

A useful sequence might be:

X-Wing
↓
remove candidate 5
↓
Hidden Single 5
↓
peer updates
↓
Locked Candidates

As always, stop searching for advanced patterns immediately after the elimination and re-scan the changed units.

Common mistakes

Searching several digits at once

Fish are single-digit patterns.

Treating any rectangle as an X-Wing

Verify the complete source candidate sets.

Eliminating from the base rows

For a row-based X-Wing, eliminations occur in the cover columns outside the base rows.

Choosing rows with an extra source candidate

That breaks the basic Fish condition.

Expecting the pattern to choose a diagonal

It does not need to. Both possible diagonals produce the same elimination.

Recognition drill

With one digit highlighted, translate sparse rows into position pairs:

r2 → c4/c8
r5 → c1/c6
r7 → c4/c8

You should immediately notice the repeated c4/c8.

This is often faster than visually hunting rectangles.

FAQ

Is X-Wing a Wing technique?

No. Despite the name, X-Wing is a Fish.

Must the four source cells be in four different boxes?

No. The basic proof depends on rows and columns, not box distribution.

Can X-Wing run from columns?

Yes.

Does X-Wing require guessing which diagonal is true?

No. The elimination is valid under either diagonal arrangement.

What to learn next

Learn Swordfish while the base/cover idea is fresh.

Then compare X-Wing with Skyscraper, where two same-digit conjugate pairs share only one aligned side instead of forming a complete Fish.