Sudoku strategies explained with graphics

Strategies


Overview Singles Naked Pairs Naked Triples Hidden Pairs Hidden Triples Naked Quads Hidden Quads Pointing Pair Pointing Triple Box Reduction X-Wing Finned X-Wing Sashimi Finned X-Wing Franken X-Wing Finned Mutant X-Wing Skyscraper Chute Remote Pairs Simple Coloring Y-Wing W-Wing Swordfish Finned Swordfish Sashimi Finned Swordfish Franken Swordfish Mutant Swordfish Finned Mutant Swordfish Sashimi Finned Mutant Swordfish Sue De Coq XYZ-Wing X-Cycle Bi-Value Universal Grave XY-Chain 3D Medusa Jellyfish Jellyfish Jellyfish Avoidable Rectangle Unique Rectangle Hidden Unique Rectangle WXYZ-Wing Firework Subset Exclusion Empty Rectangle Sue De Coq Extended SK Loop Exocet Almost Locked Sets Alternating Inference Chain Digit Forcing Chains Nishio Forcing Chains Cell Forcing Chains Unit Forcing Chains Almost Locked Sets Forcing Chain Death Blossom Pattern Overlay Bowman Bingo



Sashimi Finned Swordfish


If a particular candidate is present in only three Cells in three Rows and if these Cells belong to the same Columns forming a three-by-three rectangular pattern, except for one Row where one of the Cells, called the "sashimi" Cell, in the three-by-three rectangular pattern is solved (either by an initial value, or by an induced value) and where the candidate is also present in Cell(s) of that Row that belong to the same Square as the "sashimi" Cell (these extra-cells are called the "fin"), then the candidate can not be the solution for any Cell in the Column of the Square containing the "fin".

Indeed, either the candidate is the solution for a Cell in the "fin" which eliminates it from all other Cells in the same Square, or it is the solution for one of the Cells in the three-by-three rectangular pattern in the same Column as the "sashimi" Cell.

The reasoning is also applicable when you replace "Row" by "Column" and "Column" by "Row".

The candidate must not be present in all Cells of the pattern, as long as the Cells where it is not present are "solved" Cells (i.e. either contain an initial value, or an induced value).


Sashimi Finned Swordfish

In the example above, the three-by-three rectangular pattern is comprised of Cells B1, B7, B8, F1, F7, F8, J1, J7 and J8.
The "sashimi" cell is B8. The "fin" comprises B9.
If candidate 1 is the solution in F7, then it must be the solution either in J1 which implies it is the solution in B7 or B9 which eliminates it from all Cells in Square "3" (in particular A8), or in J8 which eliminates all candidate 1 in Column "8" (in particular A8).
If candidate 1 is the solution in F8, then all candidates 1 are eliminated in Column "8" (in particular A8).
Whichever the solution for candidate 1 in Row "F", it can never be the solution in A8.



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