If you have the X-Wing, you already hold most of the Swordfish. It is the same reasoning, with three rows and three columns instead of two.
That single step from two to three changes everything in practice. The X-Wing draws a rectangle the eye eventually catches on its own. The Swordfish draws no recognisable shape at all, and that is exactly why it needs a method.
The Swordfish principle, why no row needs three locations, the column-based search method, and the mistake that makes people see a Swordfish where there is none.
🎬 The Domino33 video on the Swordfish
Tutorial 16-1 covers the theory and then three detailed examples.
▶ English audio track and English subtitles: pick either from the ⚙️ icon.
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▶ Subscribe for freePart 1
The X-Wing, one size up
X-Wing reminder: a digit has only two possible locations on two rows, and those locations fall in the same two columns. You then eliminate that digit from the rest of those two columns.
The Swordfish applies exactly the same logic one notch higher:
If, across three rows, every possible location of a digit fits inside the same three columns, then that digit is eliminated from the rest of those three columns.
The reasoning is mechanical. Each of those three rows has to place the digit somewhere, and that somewhere is necessarily within those three columns. Three digits to fit into three columns: each column takes exactly one. So there is no room left anywhere else in those columns.
A row does not need three possible locations. Two will do. What matters is that the union of the three rows' locations does not exceed three columns. It is exactly the same flexibility as the naked triple.
A worked example
Here is a grid showing only the possible locations of the 4. Look at rows R2, R5 and R8:
R2: the 4 in C1 and C4 · R5: in C4 and C7 · R8: in C1 and C7
None of those three rows has three locations, each has two. But pooled together, those locations occupy exactly three columns: C1, C4 and C7. The Swordfish is complete.
The three 4s of R2, R5 and R8 will therefore spread across C1, C4 and C7, one per column. Consequence: no other row can hold a 4 in those three columns.
The 4 disappears from R1C4, R3C1, R4C7, R6C4 and R9C7
Five candidates eliminated in one move, without a single digit being placed. On a level 8 or 9 grid, this is very often the elimination that restarts the whole solve.
Part 2
Rows or columns, both directions
Like the X-Wing, the Swordfish works both ways, and both have to be searched:
- Row direction: you read 3 rows, you eliminate in 3 columns
- Column direction: you read 3 columns, you eliminate in 3 rows
Many solvers look in one direction only and mechanically miss half the configurations.
Always check that the pooled locations fit inside exactly three columns. If there are four, it is not a Swordfish and no elimination is allowed. Counting the distinct columns before acting prevents almost every false positive.
Part 3
The search method
Step 1, Pick one digit and only one
The Swordfish concerns a single digit at a time. Finish it before moving to the next. Jumping between digits is the surest way to see nothing.
Step 2, Map that digit out
For each row, write down the columns where the digit is still a candidate. Note them in the margin, one line per row. It is the only slightly tedious step, and it does all the work.
Step 3, Keep only rows with 2 or 3 locations
A row where the digit has four locations or more cannot be part of a Swordfish. Cross it out. You are usually left with a handful.
Step 4, Look for three rows fitting into three columns
Among the rows left, test the combinations of three. Pool their columns and count the distinct ones. Exactly three: it is a Swordfish. Four: move to the next combination.
Start from the row with the fewest locations, then look for two companions that reuse its columns. A row sharing none of its columns is ruled out immediately, which shrinks the number of combinations enormously.
What comes next?
The family continues. With four rows and four columns, the pattern is called a Jellyfish. The principle is rigorously the same, but it is far rarer and far harder to spot by eye.
🎬 See the method in action
In the video the theory is followed by three examples worked through on real grids. It is the fastest way to grasp the mechanism.
Exercise
Your turn
Here is a new map of the possible locations of the 6. It contains a Swordfish, but not the one from the earlier example: neither the same rows nor the same columns.
First find the three rows whose 6s fit into three columns. Then click the cells to eliminate, and check.
Part 4
Practice quiz
Four questions to check what you have learned. Good luck!
❓ Frequently asked questions
A Swordfish happens when, across three rows, every possible location of a digit fits inside the same three columns. Those three rows will therefore place their digit within those three columns, one per column, which lets you eliminate that digit from the rest of those three columns.
No, and that is the most widespread mistake. A row may have only two locations. All that counts is the union of the three rows' locations, which must not exceed three distinct columns.
It is the same logic at a different scale. The X-Wing uses two rows and two columns, the Swordfish three rows and three columns. With four rows and four columns the pattern is called a Jellyfish.
Pool the columns where the digit is a candidate on the three chosen rows, then count the distinct columns. Exactly three and it is a Swordfish. Four and it is not, so no elimination is allowed.
📋 Summary
Swordfish essentials
- Setup: a digit whose locations across 3 rows fit inside 3 columns
- Action: eliminate that digit from the rest of those 3 columns
- Remember: a row may have only 2 locations, only the union counts
- The test: count the distinct columns, three and not four
- Both directions: 3 rows onto 3 columns, and 3 columns onto 3 rows
- Related techniques: X-Wing at two, Sashimi X-Wing, Jellyfish at four
The Swordfish belongs to the elaborate techniques, alongside the W-Wing, the XYZ-Wing and the Sashimi X-Wing. It extends the X-Wing directly and assumes rigorous candidate bookkeeping, the kind the six basic techniques give you.
📘 Go further with the Domino33 books
The Swordfish and every other technique on this site are covered step by step in the Domino33 memento, available in English.
