Fish & Wings
Finned X-Wing
A Finned X-Wing is an X-Wing with one flaw: in one of the two base rows the digit has an extra place or two, the fin, and the fin sits in the same box as one corner of the rectangle. Either the fin holds the digit or the X-Wing is real, so the digit leaves only the cells that lose it both ways: the cover-column cells inside the fin's box. It works the same with rows and columns swapped, and, like every fish, it never places a digit by itself.
What you need to see on the grid
Look for a Finned X-Wing when an X-Wing hunt falls just short: two rows share the same two columns for a digit, but one of them has a third place, or a fourth. Singles, locked candidates, subsets and the plain X-Wing should already have run dry. Four terms carry the method:
- Clean row and finned row
- The two base rows. The clean row has exactly two places for the digit, and they fix the two cover columns. The finned row has a place in both of those columns — its two corners — plus the fin. In the example, row 2 is clean (C1, C7) and row 5 is finned (C1, C7 and C8).
- The fin
- The extra place, or places, of the finned row. Every fin cell must lie in one box, and that box must also hold one of the finned row's corners. Here the fin is R5C8, in box 6 with the corner R5C7. A finned row that has lost its corner in the fin's box (a "Sashimi" X-Wing) is a different pattern; the app's hint does not use it, and this page does not cover it.
- Cover columns
- The two columns of the clean row's places, as in an X-Wing. The fin does not change which columns they are, only how much of them you may clear: just their cells inside the fin's box, outside the base rows.
- The column version
- Swap the roles: a clean column and a finned column whose places share the same two rows, with the fin in one box beside a corner. What it clears is then the cover-row cells inside the fin's box. 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 9, on a teaching position where the easy moves and the plain X-Wing have run out. 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 1Spot an X-Wing spoiled by an extra place
Start as you would for an X-Wing: pick a digit and list its places row by row. For 9, only rows 2 and 6 have exactly two places, C1 and C7 for row 2, C5 and C7 for row 6. They share only column 7, so there is no X-Wing on rows.
Now look for a near miss: a row holding the clean row's two columns plus something more. Row 5 lists 9 in C1, C7 and C8. Without R5C8, rows 2 and 5 would be a textbook X-Wing on columns 1 and 7. That extra place is your candidate fin. Rows 7 to 9 already hold their 9, at R7C3, R8C9 and R9C4, which is also why the cells above them in columns 3, 4 and 9 do not list 9.
Rows 1 to 6 in full, and the 9s already placed in rows 7 to 9. Row 2 keeps 9 in C1 and C7; row 5 has the same two columns plus C8. C1 C2 C3 C4 C5 C6 C7 C8 C9 R1 6 7 5 1 R2 7 5 8 1 3 R3 1 2 7 R4 7 1 R5 5 7 8 1 4 R6 6 1 7 5 R7 9 R8 9 R9 9 - Digit already on the grid
- Row 2 (two places) and row 5, which almost matches it
- A place for 9 in those rows
- Candidate 9, the digit studied
- Not needed for this step
Filled in: rows 1, 2, 3, 4, 5 and 6; cells R7C3, R8C9 and R9C4. 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 2Check that the fin shares a box with a corner
Split the finned row's places in two. R5C1 and R5C7 sit in the clean row's columns: they are corners, exactly as in an X-Wing. What is left, R5C8, is the fin. Now find its box: R5C8 is in box 6, and so is the corner R5C7. The pattern holds. Had row 5 a second extra place, it would have to be in box 6 as well.
A fin in a box with no corner, or fin cells spread over two boxes, gives you nothing: no cover-column cell outside the base rows could see the whole fin. While you are in box 6, note that apart from the corner and the fin, R6C7 is its only cell that lists 9. R4C7, R4C8 and R6C8 already hold digits, and the 9 at R8C9 rules out R4C9 and R6C9.
Rows 2 and 5, and box 6 shaded. The fin R5C8 shares box 6 with the corner R5C7; the 9 at R8C9 explains why R4C9 and R6C9 do not list 9. C1 C2 C3 C4 C5 C6 C7 C8 C9 R1 R2 7 5 8 1 3 R3 R4 7 1 R5 5 7 8 1 4 R6 5 R7 R8 9 R9 - Digit already on the grid
- Base rows: clean row 2, finned row 5
- Box 6, the fin's box
- A place for 9 in a base row (corner or fin)
- Candidate 9, the digit studied
- Not needed for this step
Filled in: rows 2 and 5; box 6; cell R8C9. The other 56 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 3Reason in two cases: the fin holds the digit, or the X-Wing is real
Row 5 must hold a 9 somewhere: in a corner or in the fin. Take each case in turn.
If the fin is not 9, row 5 puts its 9 in R5C1 or R5C7, and rows 2 and 5 form a real X-Wing. Columns 1 and 7 then get their 9 from those two rows, so 9 would leave R1C1, R3C1 and R4C1 in column 1 and R6C7 in column 7.
If the fin is 9, box 6 has its 9 at R5C8, and every other cell of box 6 loses it: the corner R5C7 and, below it, R6C7. Columns 1 and 7 are not settled in this case: row 2 can still take either corner.
You do not know which case is true, and you do not need to.
Base rows 2 and 5, the cover columns and the fin's box. The no-fin case would clear R1C1, R3C1, R4C1 and R6C7; the fin case would clear R5C7 and R6C7. Only R6C7 is on both lists. C1 C2 C3 C4 C5 C6 C7 C8 C9 R1 5 R2 7 5 8 1 3 R3 2 R4 7 1 R5 5 7 8 1 4 R6 6 5 R7 7 9 R8 5 1 9 R9 1 3 - Digit already on the grid
- Base rows: clean row 2, finned row 5
- Reach of one case: columns 1 and 7 if the fin is not 9, box 6 if it is
- A place for 9 in a base row (corner or fin)
- Candidate 9, the digit studied
- Not needed for this step
Filled in: rows 2 and 5; columns 1 and 7; box 6; cells R7C3 and R8C9. The other 43 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 only where both cases agree
A candidate may go only if it goes in both cases. The no-fin case clears four cells, the fin case two, and the one cell on both lists is R6C7: it lies in a cover column, outside the base rows, and inside the fin's box, so it sees the fin. Remove 9 from R6C7.
R1C1, R3C1 and R4C1 keep their 9. A plain X-Wing would clear them, but they lie outside box 6 and cannot see the fin: if R5C8 is the 9, any one of them can still be the 9 of column 1. To be sure you have every elimination, check each cover-column cell inside the fin's box.
Technique: Finned X-Wing
The base rows and the cover columns, every cell of them. Of the cover-column cells outside rows 2 and 5 that list 9, only R6C7 is in the fin's box: 9 leaves it, and nowhere else. C1 C2 C3 C4 C5 C6 C7 C8 C9 R1 5 R2 7 5 8 1 3 R3 2 R4 7 R5 5 7 8 1 4 R6 6 R7 7 9 R8 5 1 R9 1 3 - Digit already on the grid
- Base rows: clean row 2, finned row 5
- Cover columns
- A place for 9 in a base row (corner or fin)
- Candidate 9, the digit studied
- Candidate removed
- Not needed for this step
Filled in: rows 2 and 5; columns 1 and 7; cell R7C3. The other 48 cells are left blank: they are not needed for this step. Removed: 9 from R6C7.
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Step 5Collect what the elimination unlocks
Like an X-Wing, a Finned X-Wing places nothing by itself, so look at the cell it cleared. Row 6 had two places for 9, R6C5 and R6C7: the row that could not find a partner in step 1. With R6C7 gone, R6C5 is the only place left: a Hidden Single. The other cells of row 6 hold digits or are blocked by the 9s in columns 3, 4 and 9.
One elimination is typical: a fin costs you most of the X-Wing's reach. One cell is often enough, so check every row, column and box that lost a candidate before you move on.
Technique: Hidden Single
Row 6 after the Finned X-Wing, with the 9s of columns 3, 4 and 9. 9 now fits only R6C5. C1 C2 C3 C4 C5 C6 C7 C8 C9 R1 R2 R3 R4 R5 R6 6 1 9 7 5 R7 9 R8 9 R9 9 - Digit already on the grid
- Row 6: one place left for 9
- The cell that must be 9
- Candidate 9, the digit studied
- Digit placed
- Not needed for this step
Filled in: row 6; cells R7C3, R8C9 and R9C4. The other 69 cells are left blank: they are not needed for this step. Placed: R6C5 = 9.
Common mistakes
Clearing the cover columns as if there were no fin
A fin costs you range. In the example a plain X-Wing would also clear R1C1, R3C1 and R4C1, but those cells are safe only in the case where the fin is not 9. Erasing them assumes the fin is false, which the grid never told you: if R5C8 is the 9, any one of them can still be the 9 of column 1.
A fin that does not share a box with a corner
The fin only helps when its box also holds one of the finned row's corners, and every fin cell must be in that one box. Had row 5's extra place been in column 4, 5 or 6, its box 5 would hold no corner: no cover-column cell outside the base rows would see the fin, the two cases would share no cell, and there would be nothing to remove.
Clearing the whole fin's box
The same overreach the other way: the fin case clears all of box 6, but the no-fin case only clears the cover columns. A cell of the fin's box outside the cover columns — R4C9 or R6C9, had they listed 9 — survives the no-fin case and keeps its candidate. The base rows are never touched either: R5C7 is a corner, not a target.
Recent daily puzzles that needed this technique
Learn the move, not just the digit
In a real game, when a Finned X-Wing is what opens the next cell, the hint in the app shows that cell and names Finned X-Wing as the reason the other place is ruled out — the same move as step 5 above.