X-Wing Sudoku Technique

The X-Wing Sudoku technique is the first pattern that works on a single digit spread across four cells, and it is the gateway to every fish pattern above it. It ignores what else is in those cells entirely: only the positions of one candidate matter.

What the pattern is

Take one digit. Find two rows in which that digit fits in exactly two cells each, and where both rows use the same pair of columns. The four cells form a rectangle — the corners of the X-Wing.

Whichever way the digit falls, it takes one corner in the top row and one in the bottom row, and those two corners are always in different columns. So both columns end up holding the digit inside the rectangle. Every other cell in those two columns loses the digit.

The pattern is symmetric. Swap the words row and column and it still works: two columns where the digit fits in exactly two cells each, sharing the same two rows, clear the digit from the rest of those rows.

When to look for it

• When singles, pairs and box interactions have all run dry and the grid still has plenty of blanks.
• When a digit is already scarce — three or four placements of it usually leave the rest tightly confined.
• Always scan one digit at a time. Trying to see an X-Wing while looking at full pencil marks is much harder than sweeping digit by digit.

How to apply it, step by step

1. Choose a digit that is missing from four or more rows.
2. For each row, mark the columns where that digit is still possible. Keep only the rows with exactly two.
3. Compare those rows in pairs. You want two rows whose column pairs are identical.
4. If you find a match, you have an X-Wing on the four intersections.
5. Delete the digit from every other cell in those two columns.
6. Repeat the whole sweep with rows and columns swapped, then move to the next digit.

A worked example

Positions where digit 5 is still possible, row by row. A dot means the cell is solved or cannot take a 5:

      c1 c2 c3 c4 c5 c6 c7 c8 c9
r2:    .  .  5  .  .  .  .  5  .
r4:    5  .  5  .  .  5  .  .  .
r7:    .  .  5  .  .  .  .  5  .
r9:    .  .  5  .  .  .  .  5  5

Rows 2 and 7 each hold the 5 in exactly two cells, and both use columns 3 and 8. That is an X-Wing on r2c3, r2c8, r7c3, r7c8.

If r2c3 is the 5, then r7c3 is not, so row 7 puts its 5 at r7c8. If instead r2c8 is the 5, row 7 puts its 5 at r7c3. Either way one 5 sits in column 3 and one in column 8, both inside the rectangle.

So column 3 and column 8 are finished with the digit 5. Erase it from r4c3, from r9c3 and from r9c8. Row 4 is now down to r4c1 and r4c6, and row 9 is down to r9c9 — a placement.

Common mistakes

• Accepting three positions. A row with three possible cells for the digit is not part of a plain X-Wing. That shape belongs to the finned patterns instead.
• Mismatched columns. Both rows must use the same two columns. Overlapping in only one column proves nothing.
• Eliminating in the wrong direction. Row-based X-Wings clear columns, not rows. The corners themselves are never eliminated.
• Stopping at one digit. X-Wings are common for scarce digits, so finish the sweep for all nine before you conclude the grid is stuck.

The same logic extended to three rows and three columns is a Swordfish, and to four of each is a Jellyfish. Learning the X-Wing properly makes both of them free.

Where you meet it

The X-Wing is the first of the tough techniques and the usual reason a Hard puzzle refuses to fall to basics alone. Expect to need it on hard classic Sudoku, often more than once in the same grid.