X-Wing Sudoku Technique Explained for 2026

You’ll be able to: recognize a row-based or column-based X-Wing for one digit, eliminate that digit in the correct perpendicular houses, and tell the pattern apart from broken conjugates and Swordfish-sized setups.

You’ll need: full candidate marking for the digit you’re scanning, comfort with conjugate pairs (exactly two candidates for one digit in one row, column, or box), and the habit of naming which lines define the fish before you erase pencil marks.

X-Wing is the smallest fish: one digit d, two parallel defining lines (rows or columns), and two perpendicular tracks (columns or rows) so that every candidate for d in those two lines sits on only those two tracks—forming a rectangle at the four intersections. Same counting story as Swordfish, but 2×2 instead of 3×3.

It is the usual first step where single-digit line logic forces constraints across a second direction: you are no longer only looking “along one row,” but at how two rows jointly pin two columns.

Video walkthrough

In plain terms (what the video is proving)

You can see the four missing-number corners on the grid, but X-Wing is counting, not admiring the shape.

1. Two rows each still need the digit once. In each row, that digit may appear only in two cells, and both rows use the same two columns—call them C1 and C2.
2. Those two row-placements cannot land in the same column—that would be two copies of the digit in one column—so one fish row takes C1 and the other takes C2.
3. Now pretend the digit also appeared in C1 but outside the two fish rows. That would use up C1’s copy of the digit without using either fish row in C1, so both fish rows would have to place the digit in C2 instead—two copies in C2, which is impossible. The same argument works if you start with C2.
4. So every candidate for the digit in C1 or C2 that lies outside the fish rows is eliminated.

You still do not know which corner of the rectangle is true—only that “outside along those columns” is impossible.

Pattern (row-based first)

Fix digit d. Pick two different rows such that every cell in those rows that still has d as a candidate lies in exactly two columns—call them C1 and C2.

Equivalently: in each of the two rows, d appears as a candidate in exactly two cells, and those two column indices are the same pair in both rows. The four cells R_a C1, R_a C2, R_b C1, R_b C2 are the rectangle’s corners.

Column dual (swap the roles): two columns confine d to two rows only → eliminate d from the rest of those rows outside the two defining columns. If you mix defining lines and elimination direction, the move will not match the pattern.

Sanity checks before you call it X-Wing:

• In each defining row (or column), d has no third candidate cell—otherwise the line is not a conjugate pair for d.
• The perpendicular coordinates match across both lines so the four corners are the only intersections of those lines with the two tracks.

Logic (why the elimination is sound)

Row-based story: The two defining rows must place d twice total—once per row. All candidates for d in those rows live in columns C1 and C2, so both copies of d land in the 2×2 intersection. Those two placements must use both columns C1 and C2 (two rows cannot share a column for d), so C1 gets d from one defining row and C2 from the other. Therefore d cannot appear elsewhere in C1 or C2: if d sat in one of those columns outside the two defining rows, neither defining row could still place d in that column, so both would have to use the other column of the pair—impossible. Hence eliminate d from all other rows in C1 and C2.

Transpose the words “row” and “column” for the column-based case.

This is the same pigeonhole picture as Swordfish, with two lines and two tracks instead of three.

Reach for X-Wing when a digit’s map shows two parallel lines each locked to the same two perpendicular tracks while simpler singles and intersections are exhausted. If you need three lines before the perpendicular footprint closes, you are closer to Swordfish; if a defining line still shows d in three cells, the rectangle is not a conjugate X-Wing yet.

Worked sketch

Row-based (map coordinates to your own sheet):

• Rows 2 and 7 each contain 5 as a candidate only in columns 3 and 8.
• Corners: R2C3, R2C8, R7C3, R7C8.

Whatever placement 5 takes in row 2, row 7 must still place 5 in the other column of the pair so both rows satisfy their row constraint and the two column constraints stay consistent. So 5 in columns 3 and 8 is confined to rows 2 and 7; eliminate 5 from every other row in columns 3 and 8—without guessing which corner is true.

        col3   col8
row2     *5*----*5*
row7     *5*----*5*

row-based X-Wing on digit 5
=> eliminate 5 from columns 3 & 8 outside rows 2 and 7

After the trim, re-scan for naked singles; a second digit may collapse to another fish once its map simplifies.

Practice note: X-Wing lives or dies on honest “exactly two per line” counts—Sudoku Face Off keeps pencil marks stable and can highlight one digit so conjugates do not drift.

Common confusions

• “Almost two” in a defining line: three d candidates in one row breaks the conjugate premise; you may be heading toward Swordfish, or the pattern may not be ready yet—finish intersections instead of forcing a rectangle.
• Corners without conjugates: the two defining lines must each contain only the two corner cells as d candidates—not two cells in one row plus a stray d elsewhere in that row.
• Eliminating in the wrong house: for a row-based X-Wing, strikethroughs belong in the two columns, on cells outside the two defining rows. For column-based, strike d along the two rows outside the two defining columns—not inside the defining lines unless a different tactic says so.
• Rectangle-shaped marks alone: the pattern is conjugate counting, not geometry—confirm each defining line has exactly two candidates for d and they line up on the same two tracks.
• Expecting the rectangle to pick the winner: X-Wing does not tell you which corner holds the digit; it only clears false candidates outside the two rows on the two fish columns (or the transpose for column-based fish).

Recap

• X-Wing = one digit, two parallel defining lines, two perpendicular tracks, and no candidates for d in the defining lines outside those tracks.
• Eliminations hit the perpendicular units (columns for a row-based fish), outside the defining parallel lines.
• If the footprint needs three parallel lines, step up to Swordfish reasoning; if a line still has three d marks, do not name it X-Wing yet.

Check your understanding

1. You have a row-based X-Wing on digit 4 using rows 1 and 6 and columns 2 and 9. Where do you eliminate 4?
   Answer: From columns 2 and 9 in every row except 1 and 6.

2. Digit 7 appears in row 3 only in columns 1 and 4, but in row 8 it appears in columns 1, 4, and 6. Is that an X-Wing on 7 across rows 3 and 8?
   Answer: No—row 8 is not conjugate for 7; treat it as a different pattern or reduce candidates first.

3. Two columns each have digit 7 as a candidate only in rows 5 and 9. Where do you eliminate 7 for the column-based X-Wing?
   Answer: From rows 5 and 9 in every column except the two defining columns (eliminate along those rows outside the two columns that form the fish).

For the longer treatment with Swordfish side by side, read Advanced Sudoku Techniques: Mastering X-Wing and Swordfish. For wing logic after fish, open learn the XY-Wing method. For study order and hard-puzzle context, use how to solve hard Sudoku and the strategies hub.