Fish & Wings
Swordfish
A Swordfish removes one digit from three columns at once. It appears when, in three rows, the digit has only two or three possible cells each and all of those cells lie in the same three columns: each row must put the digit in a different one of those columns, so the three columns are used up and the digit can be removed from every other cell in them. It is the X-Wing argument with three rows instead of two, and it works the same way with rows and columns swapped.
What you need to see on the grid
Hunt a Swordfish one digit at a time, once singles, subsets and X-Wing have stopped producing moves and the digit is down to a few places in most rows. Four terms carry the whole method:
- Base rows
- The three rows you build on. In each one the digit must have two or three candidate cells: one place is a Hidden Single you should simply play, four places can never fit into three columns. The rows need not be neighbours or share a band of boxes.
- Cover columns
- The three columns that, between them, hold every candidate of the digit from the base rows. Eliminations happen only in these columns, and only outside the base rows.
- The 2-2-2 and mixed shapes
- Nine candidates in a neat 3×3 block are rare. Three rows with two places each, or a mix such as 2-3-2 like the example below, make a complete Swordfish as long as all their places fall in exactly three columns.
- The column version
- Swap the roles: three base columns whose candidates fall into three cover rows, and the digit then leaves the rest of those rows. The steps are identical with "row" and "column" exchanged.
How to apply it, step by step
One example runs through all five steps: the digit 7, part-way through a hard puzzle. Every diagram shows the whole grid. The cells a step needs are filled in; the others are left blank and hatched, so you know you can ignore them.
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Step 1Pick one digit and list its places, row by row
Choose a digit and read the grid one row at a time, noting every cell where that digit is still a candidate. Here row 2 leaves 7 just two places, R2C2 and R2C6 — write it down as "R2: C2, C6".
Do the same for every row where the digit is not placed yet. It is mechanical work, and it only holds if your pencil marks are up to date: a candidate you forgot to erase is a place that does not exist.
Only row 2 matters here. 7 is a candidate in exactly two of its cells: R2C2 and R2C6. C1 C2 C3 C4 C5 C6 C7 C8 C9 R1 R2 1 4 8 3 2 5 6 R3 R4 R5 R6 R7 R8 R9 - Digit already on the grid
- Row being read
- A place for 7
- Candidate 7, the digit studied
- Not needed for this step
Filled in: row 2. The other 72 cells are left blank: they are not needed for this step. Nothing is removed yet: this step only reads the grid.
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Step 2Keep the rows where it has two or three places
Sort the rows by how many places the digit has left. A row with two or three places can serve as a base row. A row with four or more cannot: four cells of one row always sit in four different columns.
Row 1 already has its 7, at R1C7, so it is out of the count. Row 2 (step 1) has two places, and rows 4, 5 and 8 have two, three and two: these four rows stay on the list. Rows 3, 6, 7 and 9 give 7 four places each and drop out.
Rows 2 to 9 in full, and the 7 already placed in row 1. Kept rows 2, 4, 5 and 8 have two, two, three and two places for 7; rows 3, 6, 7 and 9 have four each. C1 C2 C3 C4 C5 C6 C7 C8 C9 R1 7 R2 1 4 8 3 2 5 6 R3 2 9 8 4 R4 8 9 5 4 2 3 R5 9 2 4 R6 2 6 1 9 R7 R8 6 9 5 3 2 R9 3 5 4 8 - Digit already on the grid
- Kept: two or three places for 7
- A place for 7 in a kept row
- Candidate 7, the digit studied
- Not needed for this step
Filled in: rows 2, 3, 4, 5, 6, 7, 8 and 9; cell R1C7. The other 8 cells are left blank: they are not needed for this step. Nothing is removed yet: this step only reads the grid.
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Step 3Find three rows whose places use only three columns
Among the kept rows, look for three whose places for the digit, taken together, fall in exactly three columns. Rows 2, 5 and 8 do: their 7s sit only in columns 2, 6 and 8. These are the base rows; columns 2, 6 and 8 are the cover columns.
No row has to reach all three columns — here they have two, three and two places, and a 2-2-2 trio works just as well. Row 4 cannot join any trio: its 7 in column 4 always adds a fourth column.
Technique: Swordfish
Base rows 2, 5 and 8 keep 7 inside columns 2, 6 and 8. Those three columns are shown top to bottom, because the next step clears them; row 4 is shown because it reaches column 4. C1 C2 C3 C4 C5 C6 C7 C8 C9 R1 3 R2 1 4 8 3 2 5 6 R3 2 8 R4 8 9 5 4 2 3 R5 9 2 4 R6 9 R7 R8 6 9 5 3 2 R9 4 - Digit already on the grid
- Base rows
- Cover columns
- A place for 7 in a base row
- Candidate 7, the digit studied
- Not needed for this step
Filled in: rows 2, 4, 5 and 8; columns 2, 6 and 8. The other 30 cells are left blank: they are not needed for this step. Nothing is removed yet: this step only reads the grid.
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Step 4Remove the digit from the rest of those three columns
Each base row must contain a 7, and it can only go into one of the cover columns. Two base rows cannot both use the same column, because a column holds 7 only once — so rows 2, 5 and 8 use up columns 2, 6 and 8 between them, one column each, even though we do not yet know which row takes which.
Every other cell of those three columns therefore loses 7: R4C2 and R9C2 in column 2, R6C6 in column 6, R7C8 and R9C8 in column 8. Check all nine cells of each cover column, not only the rows you happened to look at. The base rows keep all their candidates: the 7s are still somewhere among them.
Technique: Swordfish
The base rows and the cover columns, every cell of them. 7 leaves the five cover-column cells outside the base rows that still list it. C1 C2 C3 C4 C5 C6 C7 C8 C9 R1 3 R2 1 4 8 3 2 5 6 R3 2 8 R4 5 2 R5 9 2 4 R6 9 R7 R8 6 9 5 3 2 R9 4 - Digit already on the grid
- Base rows
- Cover columns
- A place for 7 in a base row
- Candidate 7, the digit studied
- Candidate removed
- Not needed for this step
Filled in: rows 2, 5 and 8; columns 2, 6 and 8. The other 36 cells are left blank: they are not needed for this step. Removed: 7 from R4C2, R6C6, R7C8, R9C2 and R9C8.
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Step 5Collect what the elimination unlocks
A Swordfish never places a digit by itself, so look at the cells it just cleared. Row 4 had two places for 7, C2 and C4. With R4C2 gone, R4C4 is the only cell left for 7 in the row: a Hidden Single.
Check every row, column and box that lost a candidate before you move on — that is where a Swordfish pays you back.
Technique: Hidden Single
Row 4 after the Swordfish. 7 now fits only R4C4. C1 C2 C3 C4 C5 C6 C7 C8 C9 R1 R2 R3 R4 8 7 9 5 4 2 3 R5 R6 R7 R8 R9 - Digit already on the grid
- Row 4: one place left for 7
- The cell that must be 7
- Candidate 7, the digit studied
- Digit placed
- Not needed for this step
Filled in: row 4. The other 72 cells are left blank: they are not needed for this step. Placed: R4C4 = 7.
Common mistakes
Counting a row with four places
Four places in one row means four different columns, so that row can always put its digit outside your three columns and nothing is proved. Two or three places is the limit for a Swordfish base row; four rows spread over four columns is a Jellyfish, a different and rarer pattern.
Waiting for three places in every row
Players who scan for nine candidates in a tidy 3×3 shape rarely find a Swordfish at all. Rows with only two places are perfectly good base rows — the example above is 2-3-2 — and the only test is that the three rows together use exactly three columns.
Scanning rows only
A digit can form a Swordfish on three base columns while no row-based one exists. If the row scan comes up empty, run the same steps on columns — list each column's places, keep those with two or three, look for three that share three rows — before you decide the digit has nothing to give.
Learn the move, not just the digit
In a real game, when a Swordfish is what opens the next cell, the hint in the app names it and shows the cell it unlocks — the same move as step 5 above.