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The X-Wing Technique
Once you have mastered scanning, naked pairs, and hidden pairs, most puzzles fall quickly. Then, on a harder grid, everything stalls: no single is forced, no simple pair narrows anything, and the board just sits there. This is the moment the X-Wing was made for. It is one of the first true pattern-based techniques, and seeing it is a real step up in your solving. This guide explains what the X-Wing is, why it works, and how to apply it.
Before You Begin: You Need Candidates
The X-Wing is impossible to spot in your head. It is built on pencil marks, the small candidate digits you jot into each empty cell to record which numbers could still legally go there. Every intermediate technique, the X-Wing included, is really a statement about how those candidates line up across the grid. So before you go hunting, make sure every open cell shows its candidates. In Samuraiku you can turn on pencil marks with a tap, and its hints will name the technique, the X-Wing among them, when one is available. If candidate marks are still new to you, review the basics first.
The Pattern in Plain Terms
Here is the app's definition, worth memorizing: a digit lines up in a rectangle across two rows and two columns. That pattern means it can't appear elsewhere in those columns (or rows). That single sentence is the whole idea. The rest is learning to recognize the rectangle.
Work with the row-based version first. Pick a candidate digit, say a 4. Scan the rows for one where that digit appears as a candidate in exactly two cells, no more, and note which two columns those cells sit in. Now find a second row where the same digit again appears in exactly two cells, and, crucially, in the same two columns. When that happens, the four cells, sitting at the corners of two rows and two columns, form a rectangle. That rectangle is your X-Wing.
The payoff is the elimination. Because of that rectangle, the digit can be removed as a candidate from every other cell in those two columns, all the cells above, below, and between the corners. Those eliminations often break a stuck puzzle wide open, exposing a fresh naked single a move or two later.
The technique is perfectly symmetric. In the column-based version you look for a digit that appears in exactly two cells in each of two columns, aligned on the same two rows. The four corners again form a rectangle, but this time you eliminate the digit from the other cells along those two rows. Same shape, axis swapped.
Why the X-Wing Works
The logic is airtight, which is what makes the X-Wing a legitimate solving step rather than a guess. Take the row-based case with our two rows, each holding the digit in only two possible spots, both in the same pair of columns, say columns 3 and 7. In each of those rows the digit must land in column 3 or column 7, its only candidates there.
Now consider how it can resolve. If the first row places the digit in column 3, then, to avoid repeating it, the second row is forced into column 7. If the first row instead uses column 7, the second must use column 3. Either way, both columns end up containing that digit within these two rows. Since each column may hold the digit only once, both are now fully accounted for. That is why the digit cannot appear anywhere else in columns 3 and 7, and why you can safely erase it from every other cell in them.
How to Spot and Apply It
Reach for the X-Wing when the easy moves dry up on a moderately hard puzzle. The trick is to hunt digit by digit rather than cell by cell. Here is a reliable routine:
- Choose a single candidate digit to focus on, from 1 to 9.
- Scan every row and note only the rows where that digit appears as a candidate in exactly two cells.
- Among those rows, look for a pair whose two candidate cells sit in the same two columns.
- Confirm the four cells form a clean rectangle across two rows and two columns.
- Eliminate that digit from every other cell in those two columns.
- Find nothing? Repeat the scan looking at columns instead of rows, eliminating along the two rows.
- Move to the next digit and run through again.
It takes patience at first, but the shape becomes easy to recognize once you learn to notice rows and columns where a digit has only two homes left.
Relation to the Swordfish
The X-Wing has a bigger sibling worth knowing about. The Swordfish extends the same idea from a 2×2 pattern to a 3×3 one: three rows in which a digit is confined to the same three columns, letting you eliminate it from those three columns elsewhere. The X-Wing sits at the intermediate-to-advanced level and the Swordfish just beyond it, but if you understand why the X-Wing works, the Swordfish feels like a natural next step rather than a new concept. Both belong to the same family of other solving techniques that carry you past the beginner stage.
The X-Wing rewards a particular kind of patience: instead of asking "what goes in this cell?" you ask "where can this digit still live?" That shift, from filling cells to tracking a single number's remaining homes, is the doorway to advanced Sudoku. Take a stuck puzzle, pick a digit, and go looking for the rectangle. The first time an X-Wing unlocks a board that had you stalled, the pattern will be burned into your eye for good.