Fish & Wings
X-Wing
An X-Wing removes one digit from two columns at once. It appears when, in two rows, the digit has exactly two possible cells each and those four cells sit in the same two columns, at the corners of a rectangle: the digit must fill one of the rectangle's two diagonals, so each column gets it from those rows and it can be removed from every other cell in them. It is the smallest fish, the pattern that Swordfish and Jellyfish grow from, and it works the same way with rows and columns swapped.
What you need to see on the grid
Hunt an X-Wing one digit at a time, once singles, locked candidates and subsets have stopped producing moves. It is the first fish worth looking for, because rows where a digit has exactly two places are quick to spot. Four terms carry the whole method:
- Base rows
- The two rows you build on. In each one the digit must have exactly two candidate cells: one place is a Hidden Single you should simply play, and three places can never fit into two columns. The rows need not be neighbours or share a band of boxes.
- Cover columns
- The two columns that hold every candidate of the digit from the base rows. Eliminations happen only in these columns, and only outside the base rows.
- The rectangle and its diagonals
- The four cells where the base rows cross the cover columns. Each base row puts the digit in one of its two corners, and the two rows cannot pick the same column, so the digit ends up on one diagonal or the other. You never need to know which: both diagonals use both columns. The pattern takes its name from that X.
- The column version
- Swap the roles: two base columns in which the digit has exactly two places, on the same two rows, clear the digit from the rest of those two 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 4, late in an expert puzzle from the app, at the exact point where its hint needs an X-Wing. 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. A digit missing from a drawn cell is already placed in its row, column or box, drawn or not.
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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 3 leaves 4 just two places, R3C6 and R3C8. Write it down as "R3: C6, C8".
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 adds a place that does not exist; one you erased by mistake hides a place that does, and a row with three places then passes for a row with two.
Only row 3 matters here. 4 is a candidate in exactly two of its cells: R3C6 and R3C8. C1 C2 C3 C4 C5 C6 C7 C8 C9 R1 R2 R3 6 9 3 7 1 2 5 R4 R5 R6 R7 R8 R9 - Digit already on the grid
- Row being read
- A place for 4
- Candidate 4, the digit studied
- Not needed for this step
Filled in: row 3. 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 exactly two places
Sort the rows by how many places the digit has left. Only a row with exactly two places can serve as an X-Wing base row. Three are already too many: three cells of one row sit in three different columns, and two columns cannot hold them all.
Rows 2, 7 and 8 already have their 4, at R2C2, R7C7 and R8C3, so they are out of the count. Rows 3 and 5 have exactly two places each: these two rows stay on the list. Row 9 has three places, row 1 four, row 4 five and row 6 six, so they drop out.
Rows 1, 3, 4, 5, 6 and 9 in full, and the 4s already placed in rows 2, 7 and 8. Kept rows 3 and 5 have two places for 4 each; rows 9, 1, 4 and 6 have three, four, five and six. C1 C2 C3 C4 C5 C6 C7 C8 C9 R1 8 7 5 6 R2 4 R3 6 9 3 7 1 2 5 R4 8 6 R5 5 2 8 9 3 R6 3 8 R7 4 R8 4 R9 7 5 8 6 1 9 - Digit already on the grid
- Kept: exactly two places for 4
- A place for 4 in a kept row
- Candidate 4, the digit studied
- Not needed for this step
Filled in: rows 1, 3, 4, 5, 6 and 9; cells R2C2, R7C7 and R8C3. The other 24 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 two rows whose places share the same two columns
Compare the kept rows two at a time, looking for a pair whose places sit in exactly the same two columns. Rows 3 and 5 match: both have 4 only in columns 6 and 8. These are the base rows; columns 6 and 8 are the cover columns. The four places, R3C6, R3C8, R5C6 and R5C8, are the corners of a rectangle.
One matching column is not enough; both must match. Had row 5 kept a place in column 4 instead of column 6, the pair would spread over three columns and prove nothing. The two rows do not need to be close, either: rows 3 and 5 sit in different bands of boxes.
Technique: X-Wing
Base rows 3 and 5 keep 4 inside columns 6 and 8: the four corners of a rectangle. Both columns are shown top to bottom, because the next step clears them. C1 C2 C3 C4 C5 C6 C7 C8 C9 R1 R2 9 R3 6 9 3 7 1 2 5 R4 6 R5 5 2 8 9 3 R6 R7 2 R8 1 3 R9 1 - Digit already on the grid
- Base rows
- Cover columns
- A corner: a place for 4 in a base row
- Candidate 4, the digit studied
- Not needed for this step
Filled in: rows 3 and 5; columns 6 and 8. The other 49 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 two columns
Row 3 must contain a 4, in R3C6 or R3C8, and so must row 5, in R5C6 or R5C8. The two rows cannot both use the same column, because a column holds 4 only once. That leaves exactly two ways to fill the rectangle, its two diagonals: R3C6 with R5C8, or R3C8 with R5C6. We do not know yet which one is right, but either way columns 6 and 8 each get their 4 from the base rows.
Every other cell of those two columns therefore loses 4: R1C6, R6C6 and R9C6 in column 6, R1C8, R4C8 and R6C8 in column 8. Check all nine cells of each cover column, not only the rows you happened to look at. The four corners keep their candidates: the two 4s are still on one of the diagonals.
Technique: X-Wing
The base rows and the cover columns, every cell of them. 4 leaves the six cover-column cells outside the base rows that still list it. C1 C2 C3 C4 C5 C6 C7 C8 C9 R1 R2 9 R3 6 9 3 7 1 2 5 R4 6 R5 5 2 8 9 3 R6 R7 2 R8 1 3 R9 1 - Digit already on the grid
- Base rows
- Cover columns
- A corner: a place for 4 in a base row
- Candidate 4, the digit studied
- Candidate removed
- Not needed for this step
Filled in: rows 3 and 5; columns 6 and 8. The other 49 cells are left blank: they are not needed for this step. Removed: 4 from R1C6, R1C8, R4C8, R6C6, R6C8 and R9C6.
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Step 5Collect what the elimination unlocks
An X-Wing never places a digit by itself, so look at the cells it just cleared. R1C8 had two candidates, 4 and 9. With 4 gone, only 9 is left: a Naked Single, and the app's next hint in this puzzle.
Check every row, column and box that lost a candidate before you move on — that is where an X-Wing pays you back.
Technique: Naked Single
Row 1 after the X-Wing. R1C8 has only 9 left. C1 C2 C3 C4 C5 C6 C7 C8 C9 R1 8 7 5 6 9 R2 R3 R4 R5 R6 R7 R8 R9 - Digit already on the grid
- The cell that must be 9
- Candidate 9, the digit studied
- Digit placed
- Not needed for this step
Filled in: row 1. The other 72 cells are left blank: they are not needed for this step. Placed: R1C8 = 9.
Common mistakes
Counting a row with three places
Three places in one row means three different columns, so that row can always put its digit outside your two columns and nothing is proved. Row 9 in the example, with three places, is out. An X-Wing base row has exactly two places; three rows that share three columns between them make a Swordfish, the next fish up.
Clearing the base rows instead of the columns
The base rows have nothing to give: by definition the digit has no place in them outside the four corners. What an X-Wing on rows clears is the rest of the two columns. If you catch yourself erasing the digit along a row, stop and check which lines have exactly two places. When it is two columns, you are looking at the column version, and it clears the two rows instead.
Scanning rows only
A digit can form an X-Wing on two 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 exactly two, look for two that share the same two rows — before you decide the digit has nothing to give.
Recent daily puzzles that needed this technique
Learn the move, not just the digit
In a real game, when an X-Wing 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.