Finned Swordfish

In sudoku, a Finned Swordfish is a Swordfish that almost works. Three rows would lock a digit into three columns, except one row carries one extra candidate for that digit. That extra candidate is the fin, and it does not kill the pattern, it only shrinks the list of cells you can clear.

What the pattern is

A clean Swordfish on digit d uses three base lines (three rows, say). In each base line every d sits in the same three columns, the cover lines. Because the three rows need three different columns between them, d is used up in those columns and can be removed from them everywhere else.

A Finned Swordfish breaks that neatness in one place. One base row has an additional d outside the cover columns, and that extra candidate sits in a box that also holds one of the pattern cells of the same row. Now there are two possibilities:

• The fin is false. The Swordfish is real, and all its normal eliminations hold.
• The fin is true. Then that cell is d, so d leaves the rest of its box.

Anything both cases agree on is safe to remove. That means only cover-line cells inside the fin's box.

When to look for it

Look after a plain fish search fails. If you find three rows where d is nearly confined to three columns and only one stray candidate spoils it, check whether that stray shares a box with a pattern cell in its own row. If it does, you have a Finned Swordfish. When the pattern cell in the fin's box carries no d at all, the shape is called sashimi and the same conclusion still holds.

How to apply it, step by step

1. Pick a digit and list, row by row, the columns where it can still go.
2. Find three rows whose candidates fall into three columns plus at most one intruder.
3. Check the intruder: it must lie in a box that also contains one of that row's pattern cells.
4. Take the cover columns and keep only the cells inside the fin's box.
5. Remove the digit from those cells, ignoring cells in the base rows.
6. Repeat with columns as base lines and rows as covers.

A worked example

Digit 7, base rows B, F and H. Row B holds 7 in B1 and B9, row H in H1, H2 and H9, row F in F2, F7 and F9. Every one of these lies in columns 1, 2 and 9 except F7, the fin, which shares box 6 with the pattern cell F9.

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1. Easier techniques are used up. Look at the 7s in rows B, F and H.

2. 1

   Row B can hold its 7 in B1 or B9, row H in H1, H2 or H9, and row F in F2, F7 or F9.

3. 2

   Every one of these 7s lies in columns 1, 2 and 9, except F7.

4. 3

   F7 is the fin. It shares box 6 with the pattern cell F9.

5. 4

   Case 1: F7 is not 7. Then the three rows are a plain Swordfish, and columns 1, 2 and 9 lose 7 everywhere else: A1, E1, A2, D2, E2, J2, D9 and J9.

6. 5

   Case 2: F7 is 7. Then the rest of box 6 loses 7: D8, D9, E7, E8 and F9.

7. 6

   7 removed from D9: it is the only cell that loses 7 in both cases, being in column 9 and in box 6.

Easier techniques are used up. Look at the 7s in rows B, F and H.

Two cases:

• F7 is not 7: a plain Swordfish, so columns 1, 2 and 9 lose 7 in A1, E1, A2, D2, E2, J2, D9 and J9.
• F7 is 7: box 6 loses 7 in D8, D9, E7, E8 and F9.

Only D9 is in both lists (column 9 and box 6), so 7 is removed from D9. The other cover-column cells do not see the fin and stay.

A sashimi Swordfish works the same way when the pattern cell in the fin's box has no candidate at all.

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Step 0 of 4

1. Easier techniques are used up. Look at the 1s in columns 5, 6 and 8.

2. 1

   Column 5 can hold its 1 in A5 or D5, column 6 in D6 or J6, and column 8 in B8 or J8.

3. 2

   All of them lie in rows A, D and J except B8. The corner A8 is a given 3, so B8 is a sashimi fin in box 3.

4. 3

   If B8 is not 1, the three columns are a Swordfish on rows A, D and J, and row A loses its other 1s.

   If B8 is 1, box 3 loses its other 1s. A9 is in row A and in box 3, so it cannot be 1 either way.

5. 4

   1 removed from A9 because row A and box 3 both rule it out.

Easier techniques are used up. Look at the 1s in columns 5, 6 and 8.

Here the digit is 1 and the base lines are columns 5, 6 and 8, with cover rows A, D and J. The corner A8 is a given 3, so B8 is a sashimi fin in box 3. If B8 is not 1, the columns form a Swordfish and row A loses its other 1s. If B8 is 1, box 3 loses its other 1s. A9 is in row A and box 3, so it loses its 1 either way.

Common mistakes

• Taking the full Swordfish eliminations anyway. Without the fin restriction the deduction is simply wrong.
• Accepting a fin that sits in a box with no pattern cell from its own row. Then the two cases share no conclusion.
• Allowing two stray candidates in different boxes. One box only.
• Forgetting the transposed search. Half of all finned fish appear only when you use columns as base lines.

Where you meet it

Finned Swordfish belongs to the extreme tier. You will rarely need it before Master, and it shows up regularly in Master puzzles where a clean fish is one candidate short of working. Learn the finless Swordfish first; the fin is a small extra rule on top of a pattern you already know.