The X-Wing and Swordfish

Advanced Sudoku techniques, explained without the jargon

At some point every improving solver hits a wall: the singles are gone, the pairs are cleaned up, and the grid still won't budge. That's usually the puzzle asking for a fish — the family of techniques that starts with the X-Wing and grows into the Swordfish. Both look intimidating and both are actually one simple idea applied twice.

Before you start: keep honest pencil marks

Fish techniques live entirely in your candidates. If your pencil marks are stale or incomplete, you will not see the pattern — or worse, you'll "see" one that isn't there. Before hunting fish, sweep the grid and make sure every empty cell shows its true candidates. (New to notes? Start with our beginner's guide, then come back.)

The X-Wing

Here is the whole technique in one sentence: if a digit can only appear in the same two columns across two different rows, that digit is locked into opposite corners of the rectangle those cells form — so it can be removed from those two columns everywhere else.

Let's slow that down with an example. Suppose you're tracking the digit 7, and your pencil marks show:

Draw those four cells in your head — (R2,C3), (R2,C8), (R6,C3), (R6,C8). They form a rectangle. Now reason it out:

1. Row 2 must contain a 7, and it has only those two options.
2. Row 6 must contain a 7, and it has only the same two options.
3. If R2's 7 goes in column 3, then R6's 7 cannot also be in column 3 (two 7s in one column is illegal) — so it must be in column 8. And vice versa.
4. Either way, columns 3 and 8 each get exactly one 7, and it comes from row 2 or row 6.

That's the payoff: no other cell in column 3 or column 8 can be a 7. Erase the candidate 7 from every other cell in those two columns. Often one of those erasures collapses a cell to a single candidate, and the puzzle cracks open.

Spotting X-Wings faster

• Hunt one digit at a time. Pick a digit that's placed five or six times already — fewer remaining spots means cleaner patterns.
• Look for rows with exactly two candidates for that digit. Find two such rows; if the columns match, you have an X-Wing.
• Don't forget the mirror version. Everything above works with rows and columns swapped: two columns whose candidate cells share the same two rows let you erase along those rows.

The Swordfish

A Swordfish is an X-Wing that outgrew its rectangle. Instead of two rows and two columns, it uses three rows and three columns.

The condition: find three rows where a digit's candidates are confined to the same set of three columns. The rows don't each need all three columns — two of the three is fine — as long as no candidate in those rows falls outside the shared columns. For example, tracking 4s:

Three rows, and every candidate sits inside the column set {2, 5, 9}. Each of those three rows must place its 4 in one of those three columns, and no column can take two — so the three 4s occupy exactly those three columns, one each, coming only from rows 1, 5, and 8. Every other cell in columns 2, 5, and 9 can have its 4 erased.

Exactly like the X-Wing, the logic flips for columns: three columns confined to three shared rows clear those rows instead.

A realistic expectation

Swordfish are rare guests. Most hard puzzles fall to scanning, singles, pairs, pointing pairs, and the occasional X-Wing — techniques covered in our strategy guide. But when a genuinely tough grid freezes and nothing else moves, a digit-by-digit fish hunt is very often the key that was designed into the puzzle.

A practice routine that works

1. Fill complete, honest pencil marks.
2. For each digit 1–9, note the rows where it has exactly two or three candidate cells.
3. Compare those rows' columns. Matching pair of rows → X-Wing. Matching trio inside three columns → Swordfish.
4. Make the eliminations, then immediately re-scan for naked singles — fish eliminations love to create them.

The later stretches of Cosmic Sudoku's 777-level journey — from the outer planets onward — are built to demand this kind of thinking. The daily puzzle is also a great low-stakes place to drill the hunt.

Frequently asked questions

Do I ever need more than a Swordfish?

The pattern extends to four rows and columns (the Jellyfish), but well-made puzzles for humans almost never require it. Cosmic Sudoku's levels are all solvable with logic up to this tier — never guessing.

What's the difference between an X-Wing and a naked pair?

A naked pair locks two digits into two cells of one group. An X-Wing locks one digit into a rectangle spanning two rows and two columns. They feel similar because both are "locking" arguments — the fish just works across the whole grid instead of inside one group.

Is it faster to just guess on hard puzzles?

Guessing trades a solvable logic chain for coin-flip bookkeeping, and one wrong branch can poison ten minutes of work. Every Cosmic Sudoku level has a single unique solution reachable by logic — if you're stuck, there's always a deduction waiting. Slow down, pick a digit, and go fishing.

Put it into practice

Reading about fish is one thing; catching one mid-solve is the real thrill. Fire up a harder level and try the routine above.

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