Finned X-Wing
A Finned X-Wing is an X-Wing that almost works: a digit has candidates in two rows that line up in two columns, except for one or more extra cells, the fins, in one of the two rows. All fins must lie in the same box. Either a fin holds the digit, or no fin does and the plain X-Wing applies; in both cases the digit cannot sit in the cells of the two cover columns that lie in the fin's box, outside the base rows, so it is removed from them. Rows and columns can be swapped. It is an Expert technique in Bare Sudoku.
When to use it
When an X-Wing almost appears: two rows with the digit lined up in two columns plus a stray candidate or two in a single box. Finned X-Wings are among the most common Expert patterns in Bare Sudoku, and they need complete notes for the digit you examine.
How to spot it
Pick a digit and look for rows in which it has two or three candidate cells. Take two such rows and find two columns that cover all of their candidates except one or two cells; those cells are the fins, and they must sit in one box. Then look at the cells of the two columns inside the fin's box, outside the two rows: any that contain the digit lose it. Repeat with columns as the base. In the game, tap the digit key: a near rectangle of highlighted notes with an extra note beside it is the sign.
Example
| c1 | c2 | c3 | c4 | c5 | c6 | c7 | c8 | c9 | |
|---|---|---|---|---|---|---|---|---|---|
| r1 | 3567 | 1 | 356 | 4 | 35 | 27 | 25 | 8 | 9 |
| r2 | 2 | 37 | 358 | 1 | 9 | 78 | 45 | 6 | 345 |
| r3 | 358 | 9 | 4 | 6 | 35 | 28 | 7 | 1 | 23 |
| r4 | 46 | 8 | 9 | 3 | 2 | 5 | 46 | 7 | 1 |
| r5 | 4567 | 247 | 256 | 9 | 1 | 46 | 4568 | 3 | 4568 |
| r6 | 1 | 34 | 356 | 7 | 8 | 46 | 9 | 2 | 456 |
| r7 | 48 | 24 | 7 | 5 | 6 | 1 | 3 | 9 | 28 |
| r8 | 38 | 6 | 1238 | 28 | 4 | 9 | 128 | 5 | 7 |
| r9 | 9 | 5 | 128 | 28 | 7 | 3 | 1268 | 4 | 268 |
Bold digits are given, blue digits were placed while solving, small digits are candidates. Highlighted cells form the pattern, crossed-out candidates are removed, and a circled candidate is the digit to place.
- Digit 5 has candidates in rows 2 and 6 only in columns 3 and 9, apart from one extra cell, r2c7, in box 3. Without r2c7 the pattern would be an X-Wing.
- If r2c7 is not 5, the X-Wing holds: rows 2 and 6 place their 5 in columns 3 and 9, and no other cell of those columns can be 5.
- If r2c7 is 5, no other cell of box 3 can be 5.
- A cell of column 3 or 9 that lies in box 3, outside rows 2 and 6, is ruled out either way. Remove 5 from r3c9.
Common mistakes
- Removing the digit from the whole of the two columns, as in a plain X-Wing. With a fin, only the cover cells inside the fin's box can be cleared.
- Using fins in two different boxes. The eliminated cells must see every fin, and cells in one box cannot see fins in two.
- Taking a candidate outside the base rows for a fin. Fins lie in the base rows; an extra candidate in a cover column outside them is a cell the X-Wing would eliminate.
In Bare Sudoku
Needed from level: Expert
In the game, the hint says: Finned X-Wing
Frequently asked questions
What is a Finned X-Wing in Sudoku?
An X-Wing with extra candidates, called fins, in one of its two base rows, all inside one box. Either a fin is the digit, or the X-Wing is valid; both cases rule out the digit in the cells of the cover columns that lie in the fin's box, so it is removed from them.
What is a fin?
A candidate cell in a base row of a fish that lies outside the cover columns. A fish with fins eliminates only in cells that see every fin, which is why all fins of a Finned X-Wing must lie in one box.
What is a Sashimi X-Wing?
A Finned X-Wing in which a base row keeps only one candidate in the cover columns once the fins are set aside. The reasoning is the same: either a fin holds the digit, or the rows force it into the cover columns. Bare Sudoku reports both as a Finned X-Wing.
How is a Finned X-Wing different from a Skyscraper?
Both use a digit in two rows. A Skyscraper needs exactly two candidates per row, aligned in one column, and eliminates in the cells that see both free ends. A Finned X-Wing needs the candidates aligned in two columns with the extra cells confined to one box, and eliminates only inside that box. Every Skyscraper can also be read as a fish with a fin; Bare Sudoku tries the Skyscraper first because it is easier to see.
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