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X-Wing in Sudoku: the strategy explained with an example

An X-Wing in Sudoku is a pattern on one digit: in two rows, that digit can go in only two cells each, and those cells sit in the same two columns. The four cells form a rectangle. The digit must occupy two opposite corners, so it can be removed from every other cell in those two columns. The same works with rows and columns swapped.

Why an X-Wing works

Look at row 2 in the diagram. Its 4 goes either in column 3 or in column 8. If it is in column 3, row 7's 4 cannot also be in column 3, so it must be in column 8. If row 2's 4 is in column 8, row 7's is in column 3. Either way, columns 3 and 8 each get their 4 from rows 2 and 7, so no other cell in those two columns can hold a 4.

Note the direction: the pattern is found in the rows, and the eliminations happen in the columns. For a column-based X-Wing it is the other way round.

How to find an X-Wing

1. Pick one digit and look only at its candidates.
2. Find rows where it appears exactly twice. Note which columns those two cells are in.
3. Look for a second such row with the same two columns. That's the rectangle.
4. Remove the digit from the other cells of those two columns. Then repeat the search with columns instead of rows.

A real example

Here is an X-Wing found by Camera Sudoku's Smart Hint. In rows 6 and 9, the digit 4 can only go in columns 4 and 7: the four yellow 4s. That removes the two other 4 candidates in column 4, circled in red. Column 7 has no other 4 candidates left, so nothing changes there.

Finned X-Wing, Swordfish and Jellyfish

• Finned X-Wing: almost an X-Wing, but one row has an extra candidate or two (the fin) in the same box as one of the corners. Eliminations are then limited to cells that also see the fin.
• Swordfish: three rows whose candidates for the digit lie in the same three columns. Each row needs only two or three of them.
• Jellyfish: the same with four rows and four columns.

Smart Hint knows all of these, including the finned versions, and names the exact pattern it found.

Common mistakes

• A row with three candidates. Each of the two rows must have the digit in exactly two cells. A third candidate breaks the X-Wing (though it may make a Finned X-Wing or a Swordfish).
• Columns that don't match. Columns 3 and 8 in one row and 3 and 9 in the other is not an X-Wing.
• Eliminating in the wrong direction. Found in rows, eliminate in columns, and vice versa.

Practise it

X-Wings show up in harder puzzles, so try Intermediate and Expert levels. When stuck, open only the first hint stage: if it says X-Wing, find the rectangle yourself before revealing more. The strategies guide shows where X-Wing sits on the ladder from singles to chains.