Finned X-Wing in Sudoku

Specialist S10 Fish

A Finned X-Wing is an X-Wing where one row has extra places for the digit, the fin, all in one box with a corner. Either the fin holds the digit or the X-Wing does, so cells in that box and in an X-Wing column lose the digit.

A candidate is a digit that can still go in an empty cell. Cells see each other when they share a row, column or 3×3 box. A strong link means a digit has exactly two possible cells in one such group: exactly one must contain it.

How to spot it

  • Find a row where a digit, say 3, has exactly two places. Their columns are the cover columns.
  • Find a second row where 3 sits in both cover columns and in one or two more cells. Those extra cells are the fin, and they must all be in one box that also holds one of this row's corners.
  • Look at that box. Its cells in a cover column, outside the two rows, are the targets.
  • The same works with columns and cover rows. With no fin at all, it is an ordinary X-Wing.

Why it works

Suppose no fin cell is 3. Then the second row has only its two corners left, and the two rows form an X-Wing: the cover columns lose 3 outside the two rows.

Suppose a fin cell is 3. Then the rest of the fin's box loses 3.

One of the two must be true. A target is in a cover column, outside the two rows, and in the fin's box, so it loses 3 either way.

A Finned X-Wing removes fewer candidates than an X-Wing. Only the cells covered by both cases lose the digit.

A real example from Sudokuno

The board below is a real Sudokuno puzzle, shown exactly as it stands just before Finned X-Wing applies. Everything up to this point was solved with ordinary techniques.
4
2 7 1
6
9
7
4
2 7
4 8
9 3
7 4
2 8 3
7 9
4
4
5 8 2 7
4 7
3 5 1
5
8 9 4
7 1
1
7 2 6 4

Click a candidate to cross it out; click it again to restore it. Remove the 2 candidates ruled out by this technique, then press Check. This exercise leaves your game unchanged.

Sudoku: SNC-01083 — Sudokuno

  • Candidate 1
  • Houses: row 2, row 6, column 3 and column 5
  • Pattern: R2C3, R2C5, R6C3 and R6C5
  • Removes 1 from R4C3 and R5C3
  • Step 19 of 57 in the solve

Key: pattern cells fin target cells

How the hint helps you

Sudokuno's hint reveals the structure in three steps, without giving away the digit straight away.

  1. Hint 1 The hint names Finned X-Wing. No cells or digits are shown yet.
  2. Hint 2 The two rows (or columns) are marked: one with exactly two places for the digit, one with the same two places and the fin.
  3. Hint 3 The cover columns appear, together with the fin and the box it shares with a corner.
  4. Hint 4 The corners and targets are marked. The targets are in the fin's box and a cover column, so they lose the digit either way.

You do not need to know whether the fin or the X-Wing holds the digit. The targets lose it in both cases.

Ready to try it yourself?

You will get a real Sudokuno puzzle at Specialist level S10, where Finned X-Wing is needed to finish it.

Practise Finned X-Wing

What Sudokuno covers

Sudokuno covers the standard Finned X-Wing with all fins in one box. Sashimi X-Wing, Finned Swordfish and larger finned fish are outside this form.

Where to go next

  • X-Wing An X-Wing appears when one candidate has exactly two possible cells in each of two different rows, and both pairs sit in the same two columns. The four cells form a rectangle. The candidate must then occupy two opposite corners, one per row, so it can be removed from every other cell in those two columns.
  • Swordfish Work on one digit. Find three rows with two or three possible cells each for it, all within the same three columns. Those columns must contain the digit in the selected rows, so remove it from their other cells. The same pattern works with rows and columns reversed.
  • Rectangle Elimination Rectangle Elimination tests whether a candidate would leave a box with no place for a digit. Assuming the target contains the digit forces another cell to contain it too. If together they rule out every place in the opposite box, remove the candidate from the target.

All Sudoku techniques