What is a Siamese Fish?
A "fish" in Sudoku (X-Wing, Swordfish, Jellyfish) is a pattern for a single digit where candidates are restricted to a small number of rows and columns so you can eliminate that digit from other cells in the crossing columns or rows. A Siamese fish is simply two fish for the same digit that overlap or share cells. They "sit together" like Siamese twins: each fish is valid on its own but they share a row, column or box. That overlap tightens the net of eliminations and often makes the pattern easier to spot if you know what to look for.
When to look for it
- After basic eliminations and single-candidate moves, when candidate marks are fairly complete.
- When you notice multiple fish-like shapes for the same digit clustered near each other (same region or sharing a row/column).
- When a single fish doesn’t give a useful elimination but a nearby second fish might extend the effect.
Siamese fish are not an everyday tactic for beginners because they need reliable pencil marks and some pattern thinking, but they’re an excellent intermediate technique. If you routinely use X-Wings or Swordfish, adding siamese fish recognition is a natural next step.
How to spot one (step-by-step)
1. Pick a digit and pencil all candidates for it.
2. Look for a small fish (2-row X-Wing, 3-row Swordfish, 4-row Jellyfish) in one area of the grid. Mark its two/three/four columns (for row-based fish) or rows (for column-based fish).
3. Look nearby for another fish of the same digit that shares at least one row, column or box with the first fish. The shared line may contain more candidate spots than a single fish normally allows — that’s the clue.
4. Confirm both fish independently (each must satisfy the fish rule on its own). Then combine their elimination effects: remove that digit from any cell that lies in a restricted column (or row) of one fish and is not one of that fish’s anchor rows (or columns).
4a. Because the fish overlap, there will be columns/rows covered by the union of both fish that you can clear of the digit in many other units.
Practical tips
- Use a single-digit view: when you pencil, occasionally hide other digits and scan only for one digit at a time. Siamese fish are much easier to see that way.
- Look for a row or column with more candidate positions than expected. If row 5 shows candidates in four positions for the same digit, it may be acting as a shared row between two X-Wings (each using two of those positions).
- Don’t force the label "siamese" — if two fish overlap but you can already eliminate all candidates with one fish, treat them as separate. The benefit comes when the overlap creates extra eliminations.
- Practice with X-Wings first, then Swordfish. Overlapping X-Wings (Siamese X-wings) are conceptually easiest: one shared row can contain the union of both fish’s candidate columns.
Example explained (use the candidate grid below)
In the example candidate grid I’ve annotated one digit (7) only. Two X-wing patterns are present and they share row 5. Fish A uses rows 2 and 5 with candidate 7 only in columns 3 and 8 of those rows. Fish B uses rows 5 and 9 with candidate 7 only in columns 1 and 6 of those rows. Row 5 is part of both fish and therefore shows candidate 7 in columns 1, 3, 6 and 8 — four positions in a single row.
Each X-wing by itself eliminates 7 from other cells in its two columns. Fish A eliminates 7 from columns 3 and 8 except in rows 2 and 5; Fish B eliminates 7 from columns 1 and 6 except in rows 5 and 9. Taken together (the siamese configuration) you can eliminate 7 from any other cell that lies in columns {1,3,6,8} and is not protected by being in the anchor rows of the corresponding fish. In the diagram I highlight a few concrete candidate 7s that can be removed because they lie in those columns but outside the fish rows.
Why this helps
- Siamese fish let you use two nearby fish to clear a larger set of columns/rows than either alone.
- The shared row/column acts as a bridge: it shows you where the same digit clusters and hints at multiple fish using the same anchor line.
- If you’re stuck and see a crowded row or column for a single digit, try to partition its candidate positions into two fish — that’s the telltale sign of a siamese fish.
Practice suggestion
Pick a medium/harder puzzle, pencil all candidates, and scan each digit separately. Try to spot any rows or columns that look unusually busy for one digit. Then ask: can I partition those candidate positions into two separate valid fish? If yes, apply both eliminations and see the progress. Over time your eyes will learn to pick up the overlapping shape quickly.
Conclusion
The siamese fish sudoku technique is a useful extension of fish patterns. It’s not a new rule — just the simultaneous presence of two fish that share part of their structure — but recognizing it can unlock eliminations you might otherwise miss. Use full pencil marks, scan single digits, and pay attention to rows or columns with more candidate spots than you expect; those are often the seats of Siamese fish.