Swordfish
Swordfish is X-Wing extended to three lines: a digit that in three rows can only go in the same three columns can be removed from the rest of the columns.
Learn the techniqueX-Wing
An X-Wing is four cells that form a rectangle: in two rows or columns a digit can only go in the same two places. Then the digit can be removed from the rest of the crossing lines.
See the technique in practice
Work through the examples step by step. Each step explains what you see on the puzzle and why the conclusion holds.
Example:
- We follow digit 6 through column 4. The notes show that 6 can only go in two cells there.
- Then we check column 6 the same way. Here too, digit 6 can only go in two cells.
- Now we see the pattern. The four cells lie in pairs in row 1 and row 9, so they form the corners of a rectangle. If you draw lines between the corners, you get an X. That is why the technique is called X-Wing.
- Both column 4 and column 6 must get digit 6 in one of their two corners. The two cannot use the same row, because then it would get 6 twice. Instead, the digits end up in two corners that lie diagonally across from each other.
- Both rows thus get digit 6 somewhere inside the rectangle. No other cells in row 1 or row 9 can then contain 6, and we remove it from the notes in row 9, column 7.
How to recognize the pattern
An X-Wing consists of four cells that form the corners of a rectangle. The starting point is one digit that in two different rows has only two possible placements, and those placements lie in the same two columns. If you draw lines between the four cells, you get a cross, and that cross is what gave the technique its name.
The digit must go in one diagonal pair of corners, because each row should have the digit exactly once. Whichever diagonal is correct, both columns get their copy of the digit in one of the corners. Therefore, the digit can be removed from all other cells in the two columns. The pattern works equally well mirrored, with columns as the starting point and removals in the rows.
Step-by-step procedure
- Choose a digit and find rows where the digit has only two possible placements.
- Look for two such rows where the placements lie in the same two columns, so the four cells form a rectangle.
- Check that neither of the two rows has a third possibility for the digit.
- Remove the digit from all other cells in the two columns.
- Repeat with columns as the starting point and removals in the rows.
Common mistakes
- Removing in the rows when the base is rows. The removals always apply to the other direction, that is, the columns covering the rectangle.
- Accepting a row with three possibilities. The base requires exactly two possible placements in each of the two rows.
- Removing in the corners. The four cells in the rectangle keep their candidates, because that is where the digit should go.
When do you need the technique?
At Hard level you must see multiple units in context: digits that form rectangles across multiple rows, chains of linked cells and boxes that lock each other. The techniques still only remove candidates, but these are exactly the eliminations that open up the puzzle.
Try it on your own puzzle
Enter your puzzle in the Sudoku Solver and it will find the next step and explain the technique behind it.
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