The Quadruple Lock: Mastering the Sudoku Jellyfish Strategy

1. Introduction: The Deep Ocean of Logic

The Jellyfish is a legendary pattern in the world of Sudoku. It serves as the "Size 4" iteration of the Fish family, following the X-Wing (Size 2) and the Swordfish (Size 3). While rare in casual puzzles, the Jellyfish is a staple of "Diabolical" or "Extreme" tier solving.

Ideally, a solver should master X-Wings and Swordfish before attempting to spot a Jellyfish. The logic is identical, merely expanded: it relies on the principle that if N rows contain candidate k in only N columns, then those N columns claim candidate k for those rows exclusively.

2. Theoretical Framework

2.1 The General Theorem

Theorem: Let the candidate digit be d. If d appears in 4 Rows (R1, R2, R3, R4) and, within those rows, is restricted to only 4 Columns (C1, C2, C3, C4): Then d must be the solution in exactly one of the intersections for each base row.

Since the 4 Base Rows consume the availability of digit d in the 4 Cover Columns, no other row can place digit d in those columns.

3. Visual Analysis: Horizontal Jellyfish

In the grid below, we are analyzing Candidate 2.
Base Sets (Rows): 2, 4, 6, 8 (Highlighted Yellow)
Cover Sets (Cols): 2, 4, 6, 8 (Highlighted Blue/Green)

The Logic Trace:

• Constraints: Rows 2, 4, 6, and 8 have no 2s in the odd columns. The 2s are trapped in columns 2, 4, 6, 8.
• The Lock: We have 4 rows competing for 4 columns. This is a closed system.
• Elimination: Any 2 found in Column 2, 4, 6, or 8 that is not in a Base Row (shown in red background) would break the system.

4. Hierarchy of Fish

The Jellyfish sits near the top of the "Basic Fish" taxonomy.

5. Conclusion

The Jellyfish is a "pattern of exclusion." It does not tell you where the number is; it tells you where the number cannot be. By understanding the constraints of rows and columns as interconnected sets, the advanced solver can visualize these large-scale locks and reduce the puzzle to its solution state.