sudokly
Advanced technique

X-Wing

An X-wing is a pattern where a digit appears as a candidate in exactly two cells of two different rows, and those four cells line up across the same two columns. The digit must occupy diagonal corners of the rectangle, so it can be eliminated from those two columns outside the four cells.
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X-wing is the first technique that spans the whole grid for a single digit. It is also the simplest of the fish family. Get comfortable with it and swordfish and jellyfish follow the same shape.

How it works

Pick a digit X. Find two rows where X has exactly two candidate cells. If the four candidate cells across those two rows line up across the same two columns, you have an X-wing.

Each of the two rows must place X in one of its two candidate cells. Whichever way the puzzle resolves, X will occupy a diagonal pair of the four rectangle corners: top-left and bottom-right, or top-right and bottom-left.

Either way, each of the two columns gets exactly one X at a rectangle corner. So X cannot live anywhere else in those two columns. Erase it from every other cell in those two columns.

✗✗✗✗✗✗✗✗✗✗✗✗✗✗6666DIGIT 6 RECTANGLE. ELIMINATIONS DOWN BOTH COLUMNS
Digit 6 in rows 2 and 7 sits only in columns 3 and 8. Erase 6 from the rest of those two columns.

When to look for it

After pointing pairs and box-line reduction stop producing eliminations. The candidate sets need to be tight, so always make sure pencil marks are clean before you scan.

Track digits that have only two or three candidate cells per row. Those are the digits worth checking. Anything with four or more candidate cells per row is not X-wing fuel.

Step-by-step example

  1. Pick a digit, say 6. List the rows where 6 has exactly two candidate cells remaining.
  2. For each pair of such rows, check whether the two candidate columns are the same in both rows.
  3. When the columns match, you have an X-wing.
  4. Erase the digit from every other cell in those two columns.
  5. Re-scan for singles. X-wings usually unlock one immediate placement that cascades.

Tips for spotting it

  • Pick digits that already appear in seven or eight of the nine rows. Their remaining homes are tightly constrained.
  • Use a finger or cursor to trace columns across the two candidate rows. Misaligned columns kill the pattern.
  • X-wings produce eliminations in the columns (or rows, if pivoted), never in the four corner cells.
  • Re-mark the affected columns after the eliminations. Singles often appear immediately.

Common mistakes

  • Counting cells with more than two candidates for the digit. X-wing requires exactly two per row.
  • Eliminating in the rows. The eliminations sweep the two columns.
  • Confusing X-wing with a naked pair. Naked pair sits inside one unit; X-wing spans two rows and two columns.
  • Skipping the pivot. Half of all X-wings live in columns.

Practise it

Hard sudoku contains an X-wing more often than you would think. Mark candidates fully, walk every digit through the rows, and look for two rows with matching two-cell candidate columns. Once X-wing is reflex, move on to swordfish.

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