The basic Swordfish strategy is based on three Rows with constraints on three Columns, or vice-versa. In the Franken Swordfish strategy, we still use constraints on three regions. However the regions must not be all of the same kind; they can represent various combinations of Rows or Columns and one Square, leading to the different types of Franken Swordfishes.

CCBRRR Franken Swordfish

The CCBRRR Franken Swordfish is based on constraints between two Columns and one Square. It leads to potential eliminations in three Rows.

If a particular Candidate is present in three Cells in two Columns and if these Cells also belong to the same Rows,
if you can find a Square that does not overlap these Columns and where the Candidate is present in the same two Rows as in these Columns,
then these Cells form a pattern called a CCBRRR Franken Swordfish. Such a pattern allows eliminating the Candidate from all Cells in the Rows of the CCBRRR Franken Swordfish except from the Cells that are included in the CCBRRR Franken Swordfish itself.

The candidate must not be present in all Cells of the CCBRRR Franken Swordfish, as long as all allowed combinations of the candidate present in the pattern result in the candidate being the solution in each region (Columns and Square) of the pattern.

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

In the example above the CCBRRR Franken Swordfish is based on candidate 3 and it is made of Columns "2" and "5", and Square "3".
If candidate 3 is the solution in B5, then it is the solution in H2 and either in C7, or in C8.
If candidate 3 is the solution in H5, then it is the solution in C2 or either in C7, or in C8.
Whichever the solution for candidate 3 in Column "5", it can never be the solution in C3, C6 or H3.

RRRCCB Franken Swordfish

The RRRCCB Franken Swordfish is based on constraints between three Rows. It leads to potential eliminations in two Columns and one Square. It is the inverse of the CCBRRR Franken Swordfish.

Let us define a band as a group of three Squares that are aligned either horizontally, or vertically. E.g. Squares "1", "2" and "3" form a band; squares "1", "4" and "7" form another band.

If you can find a Row (called Row-1) where the Candidate is present in only two Cells (belonging to Column-1 and Column-2) in different Squares,
If you can find two other Rows

• that share a common band,
• that only contain the Candidate in Column-1 in the band including Column-1
• that only contain the Candidate in Column-2 in the band including Column-2
• that also contain the Candidate in the third Square (called Square-3)

then the Cells containing the Candidate form a pattern called a RRRCCB Franken Swordfish. Such a pattern allows eliminating the Candidate from all Cells in Column-1, in Column-2 and in Square-3, except in the Cells that are included in the RRRCCB Franken Swordfish itself.

The candidate must not be present in all Cells of the pattern as long as all allowed combinations of the candidate present in the pattern result in the candidate being the solution in each Row of the pattern.

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

In this example the RRRCCB Franken Swordfish is based on candidate 7 and it is made of Rows "F", "H" and "J".
If candidate 7 is the solution in F3, then it is the solution in H4 or H6, and in J9.
If candidate 7 is the solution in F9, then it is the solution in J5 or J6, and in H3.
Whichever the solution for candidate 7 in Row "F", it can never be the solution in D3, G6 or C9.

You can practice this strategy by installing the SudokuCoach application on your Android™ device.