Finned X-Wing

An X-Wing with one extra in-box candidate that narrows the cut.

A Finned X-Wing is a near-miss version of the classic X-Wing fish. In a perfect X-Wing a single digit occupies exactly the same two columns across two rows, forming a rectangle whose corners let you erase that digit from the rest of those columns. The finned x-wing sudoku technique handles the far more common case where one base line carries an extra candidate — the fin — that spoils the clean rectangle. Because the fin is trapped in one box, only eliminations that also see the fin still hold, which is why finned fish turn up much more often than perfect ones (and cut fewer cells).

Worked example

An X-Wing on 1 (rows 1-2, columns 2 & 5) with a fin at R2C3. The fin restricts the usual cut to cells sharing its box, so only R3C2 — which sees the fin — loses 1.121315171619
An X-Wing on 1 (rows 1-2, columns 2 & 5) with a fin at R2C3. The fin restricts the usual cut to cells sharing its box, so only R3C2 — which sees the fin — loses 1.

On digit 1, rows 1 and 2 almost form an X-Wing: the 1s sit in columns 2 and 5 at R1C2, R1C5, R2C2 and R2C5. Row 2 spoils it with one extra 1 at R2C3 — the fin — which shares box 1 with the cover cell R2C2. A clean X-Wing would remove 1 from the rest of columns 2 and 5, but the fin restricts that to cells which also see it. R3C2 lies in column 2 and shares box 1 with the fin, so it still loses its 1; cuts further down the columns that miss box 1 are spared.

When to use it

Reach for a finned X-Wing once basic fish stall — when you spot an almost-X-Wing: two rows (or two columns) where a digit occupies the same pair of lines except for one or two stray candidates confined to a single box. Trace what a perfect fish would eliminate, then keep only the cuts that also see every fin cell. In the example that filter leaves just R3C2. If nothing sees the fin, there is no elimination to make.

How to use it

  1. Spot the almost X-Wing. Find two rows (or columns) where a digit would form an X-Wing except that one of them has one or two extra spots — the fin — all inside a single box.
  2. Reason about the fin. If the fin is empty the X-Wing is real; if the fin holds the digit it sits in that one box. Either way the digit is committed near the fin’s box.
  3. Cut only where both apply. Remove the digit only from cells that the basic X-Wing would clear AND that also see every fin cell — in practice, the cover cell inside the fin’s box.
Practice on a real puzzle

Frequently asked questions

What is a Finned X-Wing in Sudoku?

A Finned X-Wing is an X-Wing that would be perfect except one base line carries an extra candidate — the fin — sitting in the same box as one of the cover cells. The clean fish's eliminations survive only for cells that also see that fin. On digit 1 in our example, R1C2, R1C5, R2C2 and R2C5 form the fish, R2C3 is the fin, and only R3C2 can be cut.

How do I spot a Finned X-Wing?

Hunt for an almost-X-Wing: two rows or columns where your digit sits in the same two lines apart from one or two extra candidates penned into a single box. Those strays are the fin. Work out what a real X-Wing would eliminate, then discard every cut that does not see the whole fin. In the example only R3C2 both lies in the fish's column 2 and shares box 1 with the fin at R2C3.

What is a sashimi X-Wing?

A sashimi X-Wing is a degenerate finned fish where the fin effectively replaces a corner of the base rectangle instead of sitting beside a complete one. The logic is identical to a finned X-Wing — eliminations survive only where they also see the fin — but one true corner is missing, so the fish leans entirely on the fin and its partner. Solvers normally treat sashimi and finned fish as the same technique.