Sashimi X-Wing in Sudoku: when a stray candidate becomes useful

You go looking for an X-Wing, you think you have one, and one candidate too many spoils it. The rectangle is not clean, so you move on.

That is a mistake. That stray candidate does not destroy the pattern, it shrinks it. That is the whole point of the Sashimi X-Wing, the second X-Wing variant.

🎯 What you will learn

What a fin is, the difference between Finned and Sashimi, why the eliminations are confined to the fin's box, and how to spot these patterns almost nobody looks for.

🎬 The Domino33 video on the Sashimi X-Wing

Tutorial 29 covers the theory and the practice through worked examples.

▶ English audio track and English subtitles: pick either from the ⚙️ icon.

Did this video help? Over 120 free Sudoku tutorials are waiting for you on the channel.

▶ Subscribe for free

Part 1
The imperfect X-Wing

X-Wing reminder: a digit has only two possible locations on two rows, and those locations fall in the same two columns. Four cells, a perfect rectangle, and you eliminate down both columns.

In a real grid that rectangle is often spoiled by an extra candidate. That surplus candidate is called the fin.

Finned X-Wing: the rectangle is complete, plus a fin sitting in the same box as one of the corners
Sashimi X-Wing: the same, except one of the four corners is missing. The rectangle is incomplete, hence the image of a fish reduced to a single slice

The decisive condition is the same in both cases: the fin must sit in the same box as the corner concerned. Without that, there is nothing to conclude.

A worked example

Here is a grid showing only the possible locations of the 3:

The base 3s on R1 and R4 The fin, inside box 4 The 3s eliminated

R1: the 3 in C2 and C8 · R4: the 3 in C8, not in C2, but in C1 and C3 inside box 4

On row 1, the 3 has only two locations, C2 and C8: a perfect base row.

On row 4, the 3 sits in C8 but not in C2. The corner is missing, which is what makes the pattern "sashimi". On the other hand the 3 appears in C1 and C3, two cells inside box 4, the very box holding the absent corner.

Part 2
The two-branch reasoning

On row 4 the 3 has to go somewhere. It has only two options.

Either the 3 of R4 is in C8. Column 8 then has its 3, so R1 can no longer take it in C8: the 3 of R1 is in C2. Column 2 has its 3 right at the top.
Or the 3 of R4 is in the fin, at C1 or C3. Box 4 then has its 3.

Now let us find the cells penalised in both cases. They must be in column 2 and in box 4 at once.

Those are R5C2 and R6C2. In the first branch, column 2 already has its 3. In the second, box 4 already has its own. They lose the 3 whatever happens.

The 3 is eliminated from R5C2 and R6C2, at the intersection of column 2 and the fin's box

💡 The rule to remember

The fin restricts the eliminations instead of cancelling them. A clean X-Wing clears the whole column. With a fin, you only clear the intersection of that column and the fin's box. Fewer cells, but cells won where you would otherwise have seen nothing.

Finned or Sashimi, two names for one logic

The difference is purely descriptive and changes nothing about the method:

Finned: all four corners are present, the fin is added on top
Sashimi: one corner is missing, the fin replaces it

In both cases the two-branch reasoning is identical, and the eliminations land in the same place. There is no need to tell them apart while solving.

Part 3
The search method

Step 1, Start from a failed X-Wing

The best starting point is a pattern you have already dismissed. One clean row with two locations, a second row almost right, with one or two candidates too many. Stop throwing it away.

Step 2, Look at where the extra candidates sit

If they are all inside one box, and that box holds one of the pattern's corners, you have a fin. If they are scattered across two boxes, there is nothing to be done.

Step 3, Work out the elimination zone

Take the column of the corner concerned and cross it with the fin's box. The cells in that intersection, outside the two base rows, are your targets.

Step 4, Check before eliminating

Run both branches mentally. If both reach the same conclusion for a cell, the elimination is valid. Otherwise, touch nothing.

⚠️ The condition never to forget

The fin must be entirely contained within a single box, the one holding the corner concerned. A fin spilling across two boxes allows no elimination at all, and that is where most errors on this technique happen.

🎬 See the method in action

In the video the theory is followed by examples worked through on real grids.

▶ Watch the video ↗ The whole Domino33 channel

Exercise
Your turn

Here is a map of the possible locations of the 8. The X-Wing is not perfect, but it still yields something.

Click the cells where the 8 becomes impossible.

One clean base row, a second missing a corner, and a fin inside a single box.

Part 4
Practice quiz

Four questions to check what you have learned. Good luck!

Question 1: what is a fin?

Question 2: where must the fin sit?

Question 3: what is the difference between Finned and Sashimi?

Question 4: where do you eliminate with a Sashimi X-Wing?

📘 View the book ▶ Subscribe

❓ Frequently asked questions

What is a Sashimi X-Wing in Sudoku?

It is an X-Wing variant where the rectangle is not perfect. One base row is clean, the other carries extra candidates called the fin, and one of the four corners is missing. If the fin fits entirely inside the box of the absent corner, you can eliminate the digit at the intersection of the column concerned and that box.

What is a fin?

It is the extra candidate or candidates preventing the pattern from being a perfect X-Wing. They must all sit inside one box, the one holding the corner concerned. A fin spread across two boxes allows no elimination.

What is the difference between Finned and Sashimi?

In a Finned X-Wing, all four corners of the rectangle are present and the fin is added on top. In a Sashimi X-Wing, one of the four corners is missing and the fin replaces it. The reasoning and the elimination zone are identical in both cases.

Why are the eliminations more limited than with an X-Wing?

Because the fin opens a second possibility. Either the pattern behaves like a classic X-Wing, or the digit lands in the fin. Only the cells penalised in both cases can be cleaned, meaning those sitting in the column and in the fin's box at once.

📋 Summary

Sashimi X-Wing essentials

Starting point: an almost valid X-Wing spoiled by extra candidates
The fin: those extra candidates, which must fit inside a single box
Sashimi: one of the four corners is missing as well
Action: eliminate at the intersection of the column and the fin's box
The principle: the fin restricts the eliminations, it does not cancel them
Related techniques: X-Wing, Swordfish, Finned Swordfish

The Sashimi X-Wing completes the elaborate techniques, with the W-Wing, the XYZ-Wing and the Swordfish. It is the technique that teaches you to stop abandoning an imperfect pattern, a reflex that then serves on every finned variant.

← Back to Domino33 home