Finned X-Wing in Sudoku: How the Fin Works (With Diagram)

A finned X-Wing is an X-Wing with one or two extra candidates, called the fin, sitting in a single box next to one of its corners. Either the fin holds the digit or the X-Wing is real, so you can remove the digit from cells that the X-Wing would clear and that also share a box with the fin.

To spot one, look for two rows where a digit fits almost exactly into two columns: one row is a clean pair, the other has the same two columns plus a stray candidate in the box of one corner. The eliminations are few, often just one cell, but they come in puzzles where a plain X-Wing is missing by one candidate.

How the finned X-Wing works

In this position from a real library puzzle, the digit 3 has these spots:

• Row 7: R7C1 and R7C9. A clean pair.
• Row 1: R1C1 and R1C9, plus R1C8.

Without R1C8, rows 1 and 7 would be an X-Wing on columns 1 and 9, and every other 3 in those two columns would go. The fin spoils that, so split it into two cases:

• If R1C8 is not 3, the X-Wing is real. Column 9 gets its 3 from R1C9 or R7C9, and no other cell in column 9 can be 3.
• If R1C8 is 3, every cell in box 3 loses its 3.

A cell that is in column 9 and in box 3 loses its 3 in both cases. Outside the pattern, that is R2C9 (and R3C9, which is already a 1). R2C9 had 2 and 3 as candidates, so the elimination solves it: R2C9 is 2.

Column 1 gets nothing from the fin. Its targets would have to share a box with R1C8, and no cell in column 1 does.

Puzzle 202136 from the Sudoku Royale library. Givens (row by row, dots are blanks): ..............65..8..72.46...7.65.28.3.8.41..6......7..7.5.2...186.4.............. The candidates shown are what is left after singles, pointing and claiming, naked and hidden pairs, triples and quads, X-Wing and Swordfish, with nothing else applied.

How to spot a finned X-Wing

1. Look for near-miss X-Wings. Pick a digit and find a row where it has exactly two candidates. Then look for another row whose candidates cover the same two columns plus one or two extra cells.
2. Check the fin's box. All the extra cells must sit in one box, and that box must contain one of the X-Wing's corners in the finned row.
3. Find the overlap. The targets are the cells in the cover column through that corner, inside the fin's box, and outside the two base rows. That is at most two cells.
4. Try columns too. The same pattern works with columns as the base and the fin in a box above or below a corner.

Sashimi: when the corner is missing too

In the example the corner R1C9 is a candidate, next to the fin. If that corner were missing and only the fin remained in its box, the pattern would be called a sashimi X-Wing. The logic and the targets are the same. A sashimi X-Wing with a one-cell fin is exactly a skyscraper, so if you already find skyscrapers, you are finding sashimi X-Wings.

Fins work on bigger fish as well: a finned Swordfish or finned jellyfish follows the same two-case argument. For where this sits among the other techniques, see our list of sudoku techniques in learning order or the overview of advanced sudoku strategies. Other single-digit patterns worth knowing next are the 2-String Kite and the empty rectangle.