Finned X-Wing

A Finned X-Wing is an X-Wing that almost works. One of the two base lines carries an extra candidate or two — the fin — and as long as every fin cell sits in a single box, you can still eliminate, just from fewer cells than a clean X-Wing would give you.

What the pattern is

Start with the usual shape: one digit, two base rows, and two cover columns holding the digit in both rows. In a clean X-Wing every candidate in those two rows lies in the two cover columns, and the digit leaves both columns everywhere else.

Now allow one base row to have extra positions outside the cover columns. Those extras are the fin. The reasoning splits in two:

• If no fin cell holds the digit, the shape is a real X-Wing and its eliminations apply.
• If a fin cell holds the digit, everything the fin sees loses the digit instead.

Only the eliminations that are true in both cases survive. That means a target cell must lie on a cover column and see every fin cell — in practice, the cover-column cells inside the fin's box. This is why the fin has to be confined to one box: spread the fin over two boxes and nothing sees all of it.

When to look for it

Look whenever an X-Wing search fails by one or two candidates. If you keep noticing "this would be an X-Wing except for that cell", check whether the offending cells share a box with one of the four corners. That is a Finned X-Wing.

How to apply it, step by step

1. Pick a digit and a base row with exactly two positions.
2. Find a second base row that shares those two columns and has one or two extra positions.
3. Check that all the extra positions sit inside one box, and that the box also contains one of the four corners.
4. Take the cover column running through that box.
5. Remove the digit from the cells of that column which lie inside the fin's box, leaving the pattern cells alone.

A worked example

digit 3

r2:  c4      c7          clean base line
r5:  c4  c5  c7          c5 is the fin

cover columns: c4 and c7
fin cell r5c5 sits in box 5 (rows 4-6, columns 4-6)
box 5 also holds the corner r5c4

=> 3 leaves r4c4 and r6c4

Test both branches. If r5c5 is not 3, rows 2 and 5 form a plain X-Wing on columns 4 and 7, so 3 leaves both columns outside those rows — including r4c4 and r6c4. If r5c5 is 3, then r4c4 and r6c4 are in the same box as a placed 3 and lose the candidate anyway. Either way, both cells give up their 3. Note that r4c7 and r6c7 are not eliminated: they do not see the fin.

Sashimi is the same pattern with a hole. Suppose r5 held 3 only in c5 and c7 — the corner r5c4 is missing entirely. If r5c7 is 3, then r2c7 is not, so r2c4 is, and column 4 clears out. If r5c5 is 3, box 5 clears out. Same two eliminations, from a pattern that no longer looks like a rectangle at all.

Common mistakes

• A fin spread across two boxes. Then no cell sees all of it and the technique yields nothing.
• Eliminating from the far cover column. Only the column passing through the fin's box is in play.
• Removing candidates from the fin cells or the corners. They are part of the pattern.
• Forgetting to try columns as base lines. Every fish runs in both directions.
• Treating three or more fin cells in different rows as a fin. Keep it to the cells of one base line inside one box.

Where you meet it

The Finned X-Wing is an extreme-tier pattern. It first becomes necessary in Master puzzles, where clean fish have usually been mined out and the near-misses are all that remain. On Hard and Expert grids, look for the unfinned version first.