

Finned XWing
This is a very subtle yet beautiful extension of logic. We're looking at formations that could potentially be XWings but have a corner that's not quite right. In an XWing we are looking for four cells in a rectangle which contain a candidate N that exists just twice in either the two rows that form the rectangle or the two columns. Our Finned version is still a rectangle but it has extra candidates of the number in question that prevent one of the two pairs we need from existing.
Let’s look at the distribution of 8 candidates on the board in Figure 1. We have a potential XWing marked with the green X. The two blue lines show the top pair of 8s and the potential pair of 8s on the bottom row, F. It’s not a real XWing because two cells have gotten in the way. These are the green +8s marked in F8 and F9. If these cells didn’t exist, we’d be able to eliminate 8s in columns 1 and 7 (marked with a green strikeout line).
These +8 cells are the “fin”. The “fin” or “fillet” rule goes as follows:
If you can form an XWing by ignoring the fin cells, then you can keep your elimination of any cell that shares the same unit as all the cells in the fin.

Finned XWing Example 
It's important to remember we can only have one fin at a time! In our example, the 8 is the only cell that shares a box with the +8 cells. It would have been eliminated anyway if the XWing were real. However, none of the other XWing eliminations are valid.
Turning to a real example, consider the potential XWing on 7 marked in yellow in Figure 2. We would dearly like to remove all the 7s marked with a green circle. However, the are extra 7s in box 9, marked in green. These are the fin cells. But the fin rule allows us to remove the 7 on H9 at least (red circle).

Finned XWing Example: Load Example or : From the Start 
Sashimi Finned XWings
Now there is more to the idea of Finned XWings as I demonstrate in this example.
It so happens, that when using the "fin" or “filleting” rule, it is permissible for the XWing to be missing a corner in the finned box. The logic can still be applied! It's going to be fun to explain how and why it works, but first lets look at the example on the right.
We are looking at candidate 4. The fin is again marked in green but the corner of the XWing missing. There is no 4 at D6  which so happens to be a clue, and therefore was never a candidate 4 there at any time! But it doesn't matter, we can remove the 4s from E6 and F6 because they are in the same box as the fin and the potential XWing eliminates in the columns in this example.
Where the Finned XWing is missing the candidate in the finned box, the type is called a Sashimi Finned XWing.

Sashimi Finned XWing: Load Example or : From the Start 
It is possible to consider this example in another way. Either there will be a 4 in D9 or there will be a 4 in one of the two cells {D4,D5}. If the later then the 4s in E6/F6 must go (same box situation) or the 4 in D9 forces a chain giving us 6 in H9 and 4 in H6  which also eliminates the 4s in E6/F6.


