Swordfish

A Swordfish is the size-3 basic Fish in Sudoku.

It follows one candidate digit across three base rows and three cover columns, or three base columns and three cover rows.

For a row-based Swordfish, choose three rows such that every candidate for the Fish digit in those rows lies inside the same three columns.

The three base rows each need one copy of the digit.

So the three required placements must occupy the three cover columns.

Candidate copies of the digit can therefore be removed from those cover columns everywhere outside the three base rows.

The central relationship is:

3 base sets require 3 placements, covered by 3 cover sets.

Swordfish is not a new kind of proof after X-Wing.

It is the same basic Fish counting logic at size 3.

Quick rule

For a row-based Swordfish:

1. Choose one candidate digit X.
2. Select three rows whose complete candidate-X positions are all contained in the same three columns.
3. Those rows are the base sets.
4. The three columns are the cover sets.
5. Remove X from the cover columns outside the three base rows.

A base row commonly contains two or three candidate positions for X.

The three base rows do not need identical position patterns.

Swordfish is not a 3×3 rectangle

X-Wing is often visually neat because two rows may use the exact same two columns.

Swordfish is usually less tidy.

Consider candidate 2:

r1 → c1/c8
r4 → c1/c5/c8
r9 → c5/c8

The union of source columns is:

{c1, c5, c8}

There are:

• 3 base rows;
• 3 distinct cover columns.

That can form a Swordfish.

Several intersections between the three rows and three columns contain no candidate 2 at all.

That does not break the Fish.

The proof depends on coverage, not on filling every intersection.

Why Swordfish works

Each base row must eventually contain one copy of the Fish digit.

Three base rows therefore require three placements.

All legal source positions for those placements are contained in only three cover columns.

A Sudoku column can contain the digit only once.

So the three placements must consume the three cover columns.

There is no capacity for another copy of that digit elsewhere in any cover column.

Therefore candidate X can be eliminated from:

• the three cover columns;
• outside the three base rows.

This is exactly the X-Wing proof with N = 3 instead of N = 2.

Every base and cover must genuinely participate

A useful Swordfish should involve three real base units and three real cover units.

If the union of candidate columns across three proposed rows is only two columns, you are not looking at a genuine size-3 Fish.

You may instead have:

• an X-Wing;
• a simpler restriction;
• or another deduction that should be solved first.

Likewise, if the union needs four columns, the proposed three rows do not form a basic Swordfish.

The clean test is:

3 selected base units → candidate-position union contained in exactly 3 cover units.

Step-by-step board example

Column-based Swordfish

Transpose the pattern.

Suppose three columns contain every candidate 6 in only three rows.

Then:

• columns = base sets;
• rows = cover sets.

The three base columns require three placements of 6.

Those placements must occupy the three cover rows.

So candidate 6 can be removed from the cover rows outside the three base columns.

A solver who understands the proof should be able to switch orientation without learning a separate pattern.

How many source candidates can a Swordfish contain?

A standard basic Swordfish is often built from base units containing:

• two candidate positions;
• three candidate positions.

For example, a 2/3/2 distribution is common.

What matters is not the total number of source candidates.

What matters is that:

• every source candidate in the selected bases lies inside the three covers;
• all three cover sets are involved.

This is why a Swordfish does not require nine candidate marks arranged in a full 3×3 grid.

Swordfish vs X-Wing

Both are Basic Fish.

X-Wing

2 base sets → 2 cover sets.

Swordfish

3 base sets → 3 cover sets.

The proof scales perfectly.

Recognition does not.

X-Wing often appears as two matching position pairs.

Swordfish may involve:

• different two-position pairs;
• one or more three-position bases;
• empty intersections;
• a visually irregular shape.

That is why Swordfish should be learned with candidate-position unions rather than picture matching.

Swordfish vs Naked Triple

Both contain a “three constrained by three” idea, but the objects are different.

Naked Triple

Three cells in one house reserve three candidate digits.

Swordfish

Three base houses require three placements of one Fish digit, all covered by three opposite houses.

The comparison is useful because both techniques reward the same general Sudoku habit:

identify a constrained set, count its available capacity, and eliminate candidates that would exceed that capacity.

Swordfish vs Jellyfish

Jellyfish is the size-4 basic Fish:

4 base sets → 4 cover sets.

The underlying proof is unchanged.

The search space becomes much larger.

That is why Jellyfish is best learned after the base/cover model feels automatic rather than as another geometric picture.

A dedicated Jellyfish Guide belongs to the expansion phase.

What about Finned or Sashimi Swordfish?

A basic Swordfish requires all selected source candidates to fit inside its three cover sets.

If a promising pattern contains an additional source candidate outside the covers, the basic proof fails.

Some such structures can form Finned or Sashimi Fish, but those techniques use extra logic.

Do not treat an almost-Swordfish as a basic Swordfish and eliminate candidates anyway.

This page intentionally stays with Basic Fish.

How to find Swordfish efficiently

Testing arbitrary triples of rows is inefficient.

Use candidate sparsity.

1. Filter one digit

Fish are single-digit patterns.

Choose a digit whose candidate positions are relatively sparse.

2. Record rows with two or three positions

For example:

r1 → c1/c8
r4 → c1/c5/c8
r9 → c5/c8

3. Compare promising groups of three rows

Focus on rows whose position sets overlap heavily.

4. Count the union of cover columns

Merge the three column sets.

If the union contains exactly three columns, continue.

If it contains four or more, that group is not a basic Swordfish.

5. Verify the complete source state

Do not omit an additional candidate X elsewhere in a selected base row.

All source candidates must fit inside the three covers.

6. Check the cover columns for outside candidates

Those candidates are the elimination targets.

7. Repeat with columns

If the row orientation yields nothing, transpose the search.

A practical Swordfish recognition shortcut

Instead of visually scanning every candidate mark, translate sparse base units into compact maps.

For one digit:

r1 → c1/c8
r4 → c1/c5/c8
r9 → c5/c8

Then calculate:

union = {c1,c5,c8}

Three rows.

Three cover columns.

That compact notation makes irregular Swordfish much easier to see than a mental 9×9 picture.

Productive vs nonproductive Swordfish

A Swordfish may be structurally valid but produce no immediate elimination.

If the three cover columns contain no additional candidate X outside the bases, the Fish is nonproductive.

For manual solving, prioritize patterns that actually remove at least one candidate.

The goal is not to label every Fish in the grid.

The goal is to make progress.

What Swordfish usually unlocks

Like X-Wing, Swordfish is normally an elimination technique.

A common chain of progress is:

Swordfish
↓
remove candidate X from a cover column
↓
Hidden Single appears
↓
placement updates peers
↓
Locked Candidates or subset appears

After the Fish elimination, return immediately to simpler logic.

Do not continue hunting Swordfish while the candidate state has changed.

Common mistakes

Requiring three candidates in every base row

Two or three source positions are common.

Requiring identical candidate columns in all three rows

Not required.

The union of the source cover positions must be contained in exactly three cover units.

Accepting four cover columns

Three base rows spread across four cover columns do not form a size-3 basic Fish.

Ignoring an extra source candidate

If a selected base row has candidate X outside the three proposed covers, the basic Swordfish proof fails.

Eliminating from the base rows

For a row-based Swordfish, eliminate from the cover columns outside the bases.

Removing source candidates

The Fish source candidates remain possible.

Mixing candidate digits

One Fish follows one digit.

Searching Swordfish before X-Wing and simpler techniques

Use cheaper deductions first. They may change the candidate map and remove the need for Swordfish.

Recognition drill

With one digit filtered, write:

r1 → c1/c8
r4 → c1/c5/c8
r9 → c5/c8

Then ask:

1. How many base rows am I using?
2. How many distinct cover columns appear in their complete source-position union?
3. Are there candidate eliminations in those cover columns outside the bases?

If the answers are:

• three;
• three;
• yes;

you have a productive row-based Swordfish.

FAQ

Does Swordfish require nine source candidates?

No. A Swordfish can use an irregular pattern with fewer source candidates.

Can one base row contain two candidates?

Yes. Two or three candidate positions in a base row are common in a basic Swordfish.

Can one base row contain only one candidate?

That row already has a Hidden Single for the Fish digit. Solve the simpler deduction first.

Must every intersection of the three base rows and three cover columns contain the Fish digit?

No. Empty intersections are normal.

Is Swordfish just a larger X-Wing?

It uses the same basic Fish proof at size 3, but it is harder to recognize because the source pattern need not be rectangular or uniform.

What if the three rows need four cover columns?

Then they do not form a basic Swordfish.

Should I learn Jellyfish immediately after Swordfish?

Not necessarily. Understanding the size progression is useful, but Wings, Links, and other pattern families may provide more practical variety before scaling Fish again.

What to learn next

Move to XY-Wing to switch from single-digit Fish to bivalue-cell relationships. Jellyfish and more advanced Fish remain natural expansion topics once the existing corpus is complete.