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 the candidate is also present in Cell(s) of this Row that belong to the same Square as one of the Cells of the three-by-three rectangular pattern (these extra-cells are called the "fin" and the related Cell in the three-by-three rectangular pattern is called the "finned" Cell), then the candidate can not be the solution for any Cell in the Column of the Square containing the "fin", except of course for the "finned" Cell.
Indeed, either the candidate is the solution for the "finned" Cell or 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 "finned" Cell, which eliminates it from all other Cells in that column.
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). Because of the "fin" it might even be absent from an unsolved "finned" Cell.
In the example above the swordfish is made of Cells B3, B4, B7, C3, C4, C7, G3, G4 and G7.
G8 is the "finned" Cell.
The "fin" comprises G8 only, as G9 is already solved.
If candidate 8 is the solution in C4, then it must be the solution either in B3 which implies it is the solution in G5 or in G6 which eliminates all candidates 8 in Square "9" (in particular in H7), or in B7 which eliminates all candidates 8 from Colum "7" (in particular in H7).
If it is the solution C7, then all candidates 8 can be eliminated in Column "7" (in particular in H7).
Whichever the solution for candidate 8 in Row "C", it can never be the solution in H7.
You can practice this strategy by installing the SudokuCoach application on your Android™ device.
