✈️ X-Wing

X-Wing is the first genuinely advanced Sudoku technique — the point where many solvers begin to feel the puzzle has crossed from "working it out logically" into something that feels almost magical. It exploits a structural pattern in how a single digit is distributed across rows and columns, and it eliminates candidates in cells that appear to have nothing to do with each other.

What is an X-Wing?

An X-Wing occurs when a specific digit appears as a candidate in exactly two cells in each of two different rows, and those four cells form a rectangle — the two cells in row A are in the same two columns as the two cells in row B. This creates four cells arranged in a rectangular pattern whose diagonals cross like the letter "X" — hence the name.

When this pattern exists, the digit can be eliminated from all other cells in those two columns.

Step-by-step guide

Choose a digit to analyse — typically one with few remaining candidates on the board.
Scan each row and note which rows have this digit appearing as a candidate in exactly two cells. Record the column positions of those cells.
Compare row pairs. Find two rows where the digit appears in exactly two cells each, and those cells are in the same two columns (e.g., both rows have the digit only in columns 3 and 8).
You have an X-Wing. The four cells at the corners of this rectangle form the pattern.
Eliminate the digit from all other cells in the two columns involved — every cell in column 3 and column 8 that is not one of the four X-Wing corners.
Check for new deductions — eliminations often create Naked Singles, Hidden Singles, or new Naked Pairs.

Digit 5 forms an X-Wing in rows 2 and 5 (blue), columns B and E — amber cells hold the 5s, red ✗5 cells have candidate 5 eliminated

Why does it work?

Consider digit 5 with an X-Wing in row 2 (columns B and E) and row 5 (columns B and E). Digit 5 must appear somewhere in row 2, so it goes in either column B or column E of that row. The same applies to row 5.

Now consider column B. It will receive a 5 from either row 2 or row 5. That satisfies column B's requirement for digit 5. No other row can place a 5 in column B — if it did, column B would have two 5s, which is illegal. The same logic applies identically to column E.

Therefore, 5 can be eliminated from all cells in column B and column E that are not in rows 2 or 5. The logic is airtight: the four X-Wing cells are the only candidates in their respective rows, and they entirely cover both columns.

Column-based X-Wing

X-Wing can also be found using columns as the base instead of rows:

Find a digit that appears in exactly two cells in each of two columns.
If those cells are in the same two rows, you have an X-Wing.
Eliminate the digit from all other cells in those two rows.

The logic is completely symmetrical — row-based and column-based X-Wings are equally valid.

Swordfish — the three-row extension

Swordfish extends X-Wing to three rows and three columns. A digit forms a Swordfish when it appears as a candidate in exactly 2 or 3 cells in each of three rows, and all those cells fall within the same three columns. When this holds, the digit can be eliminated from all other cells in those three columns.

Swordfish is considerably rarer than X-Wing and usually appears only on Expert or Evil puzzles. The concept is identical — just scaled up by one dimension.

Common mistakes

Applying X-Wing when rows have more than two candidates. X-Wing requires exactly two candidate cells per row. If a row has the digit in three cells, it cannot be the base of an X-Wing.
Eliminating from the wrong cells. For a row-based X-Wing, only eliminate from the two columns. Do not eliminate from the rows themselves — the X-Wing cells in those rows are the very cells that will hold the digit.
Not checking both orientations. Always scan for both row-based and column-based X-Wings for each digit.
Jumping to X-Wing before exhausting simpler techniques. X-Wing is only needed when Naked Singles, Hidden Singles, and Naked Pairs have all been exhausted.

Practical tips for SudokuStreak

In pencil mode, for each digit scan each row and note which rows have exactly two candidates. Then compare pairs of such rows to see if they share the same two columns.
X-Wing is often the breakthrough technique on Hard puzzles that seem stuck after Hidden Singles.
After applying X-Wing elimination, immediately check the affected columns for new Hidden Singles or Naked Pairs.
On Evil difficulty, expect to use X-Wing (or its Swordfish extension) as a regular tool rather than an occasional trick.