Finned X-Wing in Sudoku: How the Fin Works

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Published April 17, 2026 · Updated October 14, 2026

Our Evil sudoku puzzle 245 opens with 27 givens. After 19 naked singles, 15 hidden singles and one pointing pair, 20 squares are open and nothing simple is left. Look at the 1s in columns 2 and 9. Column 2 has two places for a 1, in rows 2 and 7. Column 9 has the same two and a third, R1C9. Without that third 1 the four squares would be an X-Wing. With it they are a finned X-Wing, which still takes two 1s off the board, and after it the puzzle needs nothing but naked singles.

Our Sudoku Helper doesn’t look for finned X-Wings, so we gave our measuring solver a finder of its own and counted. Not one puzzle on our Easy to Expert levels needs it. Evil puzzles often use one, but it seldom does anything the helper’s own techniques couldn’t.

What is a finned X-Wing in sudoku?

Start from an X-Wing: two parallel lines, rows or columns, in which a digit has exactly two places left, in the same two cross lines. In a finned X-Wing, one or two extra squares on one of the two lines hold the digit too, all in the same box as one of that line’s corners. The extra squares are the fin.

A plain X-Wing removes the digit from both cross lines, everywhere except the corners. A finned X-Wing removes it only where those cross lines run through the fin’s box, which is usually one or two squares.

Here the fin, R1C9, shares box 3 with the corner R2C9. Rows 2 and 7 are the cover lines, and only row 2 passes through box 3, so the only squares that can lose the 1 are R2C7 and R2C8.

Watch the 1 in R7C7. It is on a cover line, so a plain X-Wing would remove it, but it is outside box 3, so this one can’t. Clearing it anyway is the usual finned X-Wing mistake. On this board it would do no harm, as R7C7 turns out to be a 3, but that is luck: of the 345 finned X-Wings our solver played on the first 500 Evil puzzles, 146 had a square like R7C7 that held the answer.

Why can only the fin’s box lose the digit?

The fin breaks the X-Wing’s argument: column 9 could put its 1 in R1C9 instead of a corner. So take the two cases one at a time. Either the fin is the 1 or it isn’t.

• The fin is the 1. Every 1 that R1C9 sees goes: R1C1 in its row, R2C9 and R7C9 in its column, and R2C7, R2C8 and R2C9 in its box.
• The fin is not the 1. Column 9 is left with R2C9 and R7C9, the four corners are a plain X-Wing, and rows 2 and 7 lose the 1 everywhere but the corners: R2C7, R2C8 and R7C7.

One case must be true, so whatever both cases remove can go, and that is R2C7 and R2C8. It is always the same kind of square. On a cover line, the fin sees only the corners and the squares in its own box, so the overlap is the cover-line squares in the fin’s box. A fin in a box that no cover line crosses leaves no overlap at all, which is why the fin has to share a box with a corner.

You never need to know which case holds. On puzzle 245 it was the X-Wing: the solution puts the 1s in R2C9 and R7C2. Across the first 500 Evil puzzles, the fin held the digit in 146 of the 345 finned X-Wings and the plain X-Wing stood in the other 199. That 146 is the same count as above, and not by chance: when the fin is the digit, the cover line it leaves short has to take its digit outside the fin’s box, in exactly the kind of square the rule protects.

How do you spot a finned X-Wing?

Search as for an X-Wing, but keep the near misses. One digit at a time:

1. Write down each line with exactly two places for the digit, as a pair of cross positions: column 2 → rows 2, 7.
2. Find a parallel line with the same pair and something extra. Column 9 holds the 1 in rows 2 and 7, and in row 1.
3. Check that all the extras share a box with one corner. Usually there is one: 300 of the 345 had a single fin and 45 had two.
4. Look for targets in that box. A cover-line square there that still holds the digit, off the base lines, loses it. If there is none, the pattern removes nothing; move on.
5. Turn the board. 217 of the 345 stood on rows, 128 on columns like the one on puzzle 245.

Expect a small payoff each time. 308 of the 345 removed one candidate and 37 removed two, and 75 made a single straight away.

How often do you need a finned X-Wing?

Our measuring solver uses the Sudoku Helper’s eighteen techniques plus five it lacks, and always takes the simplest move; we set it loose on puzzles from our own levels. The finned X-Wing goes straight after the plain fish (X-Wing, Swordfish and Jellyfish) and before any wing.

• Our classic levels: never. Across 800 puzzles, 200 from each of Easy, Medium, Hard and Expert, it was never the move. Our generator deals a board at those levels only if singles can finish it, letting in locked candidates at Hard and naked pairs at Expert. Finned X-Wings do turn up there, at 107 of the 277 Expert positions with the singles exhausted, but never as the simplest move on offer.
• Evil: about one puzzle in two. It was the simplest move on 256 of the first 500, 345 times in all, partly because it is tried before the wings and so takes moves a wing would otherwise have made. The plain X-Wing, as the helper plays it, is needed on 74.

So at each of those 345 moves we also asked what the helper’s eighteen would have played instead.

The first 500 puzzles of our Evil bank, which is stored in score order, so they are harder than the 5,000 as a whole. Each row counts the positions where our 23-technique solver played a finned X-Wing and the helper’s first technique, in its own order, would have been the one named. Basic fins only; measured October 2026.

Learn it for speed, then, not as a lifeline. It is cheap to check, and it turns up more often than the plain version: at the Evil positions with no single left, a finned X-Wing was there 31.1% of the time and a plain X-Wing 19.7%.

What is a sashimi X-Wing, and is a Skyscraper one?

Take away a corner. If the finned line holds the digit in one corner and the fin, and its other corner is filled or has lost the digit, the two-case argument still works as long as the fin shares a box with the missing corner. That is a sashimi X-Wing. Our solver’s finder leaves sashimi out, so every count on this page is for fins with both corners present.

You may know the one-fin sashimi X-Wing under another name. Its finned line holds the digit exactly twice, so both its lines are strong links with one end in the same cross line: a Skyscraper. On puzzle 245 that is the helper’s own move. Row 1 holds the 1 only in R1C1 and R1C9, row 9 only in R9C1 and R9C7, and the Skyscraper they make takes the 1 from R2C7 and R7C9. Read from each end, it is two sashimi X-Wings, and one of them uses the finned X-Wing’s fin, R1C9.

That holds in general, not just on this board. At every position of those 500 Evil solves, each of the 13,126 one-fin sashimi X-Wings was half of a Skyscraper, and each of the 5,457 Skyscrapers removed what its sashimi readings remove, give or take candidates that locked candidates clear anyway. (A pattern that stays on the board for several moves counts once per position.) A sashimi X-Wing with two fins is not a Skyscraper, because its finned line holds the digit three times.

The same fin works on bigger fish. A finned Swordfish is a Swordfish with a fin, and it was the simplest move on 104 of the first 500 Evil puzzles.

Stuck, and the Sudoku Helper finds nothing?

The helper won’t point you to a finned X-Wing; it isn’t among its eighteen techniques. Open puzzle 245’s position in the helper and press Next Hint to fill in the marks, then Next Hint again: it finds a pointing pair that takes a 6 from R2C8. Apply it and press Next Hint once more. It offers the Skyscraper, with Simple Colouring and an Almost Locked Set as the other choices on its menu, and no finned X-Wing. Our Sudoku Solver won’t name one either: it names no techniques, and its Step button fills the next square in reading order.

When the eighteen find nothing, the helper says No logical technique found and fills one square by trial and error. On the 168 of the first 500 Evil puzzles where that happened, a finned X-Wing was waiting at 54 of the stalls. So before you accept the trial-and-error square, look for one: on one digit, a three-place line beside a two-place line.

If there is none, the other extras that got past a stall of the eighteen in our measurement were the finned Swordfish and 3D Medusa. After those come chains. In chain terms a finned X-Wing is a short X-cycle in which the fin and the corner in its box act as one grouped end of a link. From there the road runs through XY-chains to a BUG check near the finish and, when nothing else is left, forcing chains. Our list of sudoku techniques has the whole ladder.

The Sudoku Trainer drills the plain X-Wing among its eighteen techniques but has no finned positions, so practise the plain one there and look for fins on Evil puzzles.