Finned RCBRCB Mutant Swordfish

In an RCBRCB Mutant Swordfish as defined here, the Candidate may only be present in Cells Cell-1 and Cell-2 outside of Square-3. If it is also present in one or several additional Cells (these additional Cells are called fin Cells), this would still lead to potential eliminations. However, these eliminations would only take place in the Cells of Row-1 and Column-2 that "see" all fin Cells, except in the Cells of the Finned RCBRCB Mutant Swordfish itself.

An RCBRCB Mutant Swordfish with a fin Cell is called a Finned RCBRCB Mutant Swordfish.

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

In this example the Finned RCBRCB Mutant Swordfish is based on candidate 1 and it is made of Row "D", Column "9" and Square "7".
B9 is the fin Cell.
If candidate 1 is the solution in D2, this eliminates candidate 1 in Column "2" (in particular in B2).
If candidate 1 is the solution in D7 or in D8, then it is the solution either in B9, or in G9. If it is the solution in B9, this eliminates candidate 1 in Row "B" (in particular in B2); if it is the soution in G9, then it is the solution in H2, which eliminates it in Column 2 (in particular in B2).
Whichever the solution for candidate 1 in Row "D", it can never be the solution in B2.

In this second example the Finned RCBRCB Mutant Swordfish is based on candidate 3 and it is made of Row "J", Column "9" and Square "2".
B9 is the fin Cell.
If candidate 3 is the solution in J8, this eliminates candidate 3 in Column "8" (in particular in A8).
If candidate 3 is the solution in J5, then it is the solution in A4, which eliminates candidate 3 in Row "A" (in particular in A8).
Whichever the solution for candidate 3 in Row "J", it can never be the solution in A8.

Finned RCCRRB Mutant Swordfish

If one can find a Column that contains a particular Candidate in only two Cells (in Rows we call "Row-1" and "Row-2") and another Column with the same Candidate also present in "Row-1" and "Row-2",

if in this second Column the Candidate is also present in maximum two Cells of a Square that shares no Cells with "Row-1" and "Row-2" (we call this Square "Square-3"),

if a Row

• shares Cells with "Square-3" where the Candidate is present
• intersects the second Column above in a Cell where the Candidate is not present
• contains the Candidate in only one Cell outside of "Square-3" (we call that Cell the fin Cell)

then these Cells form a pattern called a Finned RCCRRB Mutant Swordfish. Such a pattern allows eliminating the Candidate from all Cells in "Row-1" and "Row-2" that "see" the fin Cell.

In this example the Finned RCCRRB Mutant Swordfish is based on candidate 5 and it is made of Row "D" and Columns "2" and "9".
D1 is the fin Cell.
If candidate 5 is the solution in A9, this eliminates candidate 5 in Row "A" (in particular in A1). This implies it is the solution in G2, which eliminates it in Row "G" (in particular in G1).
If candidate 5 is the solution in F9, then it is the solution in D1 which eliminates it in Column "1" (in particular in A1 and G1).
If candidate 5 is the solution in G9, this eliminates candidate 5 in Row "G" (in particular in G1). This implies it is the solution in A2, which eliminates it in Row "A" (in particular in A1).
Whichever the solution for candidate 5 in Column "9", it can never be the solution in A1 or in G1.

Finned RCCRBB Mutant Swordfish

In an RCCRBB Mutant Swordfish as defined here, the Cells at the intersection of Row-3 with Column-1 or Column-2 do not contain the Candidate.

If one of these Cells did contain the Candidate (this Cell is then called a fin Cell), this would still lead to potential eliminations. However, these eliminations would only take place in the Square containing the fin Cell, except in the Cells that are included in the Finned RCCRBB Mutant Swordfish itself.

Again, the candidate must not be present in all Cells of Row-3, as long as it is present at least once in each of the portions of Row-3 inside Square-1 and Square-2.

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

The above example is in fact a Finned RCCRBB Mutant Swordfish where "Column" has been by "Row" and "Row" by "Column". It is based on candidate 2 and it is made of Rows "D" and "J", and Column "6".
D6 is the fin Cell.
If candidate 2 is the solution in J4 or in J5, then it is the solution either in D6, or either in E6, or F6, and in D9.
If candidate 2 is the solution in J9, then it is the solution either in D6, or either in D4, or D5, and in H6.
Whichever the solution for candidate 2 in Row "J", it can never be the solution in F5.

Finned CCBRRB Mutant Swordfish

If it is possible to find a first Column where a particular Candidate is present in only two Cells (that we call Cell-1 in Row-1 and Cell-2 in Row-2) in different Squares,

if it is possible to find a second Column where this particular Candidate

• is not present in the Square that shares Cells with Row-2
• is present in Row-1 and only once in the Square that contains that Cell
• is present in Cells of the Square that does not share any Cell with Row-2 (we call that Square Square-3)

which means that if the Candidate is the solution in Cell-1, it must be the solution in Square-3,

if the Square that shares Cells with Row-2 and the second Column contains the particular Candidate in Row-2 plus Cell(s) in only one Column (we call these extra-Cells the fin Cells and they form what we call the fin), so that if the Candidate is the solution in Cell-2 it must be the solution in the fin,

then these Cells form a pattern called a Finned CCBRRB Mutant Swordfish. Such a pattern allows eliminating the Candidate from all Cells in Row-1 and Square-3 that "see" the fin.

Now, if the particular Candidate is also present in one Cell of the third Square in the first Column, then this Cell is also a fin Cell. It allows to eliminate the Candidate in the Cell in Square-3 that "sees" all the fin Cells.

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

In this example the Finned CCBRRB Mutant Swordfish is based on candidate 2 and it is made of Columns "6" and "9", and Square "8".
B8 is the fin Cell.
If candidate 2 is the solution in A9, then it is the solution in D4, which eliminates it in Row "D" (in particular in D4).
If candidate 2 is the solution in G9, then it is the solution in J4, which eliminates it in Column "4" (in particular in D4).
Whichever the solution for candidate 2 in Column "9", it can never be the solution in D4.

Finned RRBCCB Mutant Swordfish

If it is possible to find a Square where a particular Candidate is present in one Column (that we call Column-1 and in another Cell (that we call the fin Cell),

if it is possible to find a first Row

• that shares no Cell with the above Square
• where this particular Candidate is present in only two Cells (that we call Cell-1 and Cell-2) belonging to different Squares
• where Cell-1 belongs to Column-1

which means that if the Candidate is the solution in Cell-1, it must be the solution in the fin Cell,

if it is possible to find a second Row

• that shares no Cell with the above Square
• where the particular Candidate is present in the Square that shares Cells with Column-1 (we call that Square Square-3)
• where the particular Candidate is present in Column-2 (this is the Column to which Cell-2 belongs)
• and nowhere else in that second Row

which means that if the Candidate is the solution in Cell-2, it must be the solution in Square-3,

then these Cells form a pattern called a Finned RRBCCB Mutant Swordfish. Such a pattern allows eliminating the Candidate from all Cells in Column-2 and Square-3 that "see" the fin Cell.

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

In this example the Finned RRBCCB Mutant Swordfish is based on candidate 3 and it is made of Rows "D" and "J", and Square "2".
B6 is the fin Cell.
If candidate 3 is the solution in J2, then it is the solution either in D4, or in D5, or in D6, which eliminates it in Square "5" (in particular in E6).
If candidate 3 is the solution in J5, then it is the solution in B6, which eliminates it in Column "6" (in particular in E6).
Whichever the solution for candidate 3 in Row "J", it can never be the solution in E6.

Finned RCCBBB Mutant Swordfish

If it is possible to find a Row where a particular Candidate is present in only two Squares (that we call Square-1 and Square-2), in no more than two Cells in each of these Squares,

if it is possible to find a first Column that shares Cells with Square-1 and where this particular Candidate

• is present in maximum two Cells in Square-1,
• is not present in the Cell at the intersection of the Column and the above Row in Square-1,
• is present in only one Cell outside of Square-1 (we call that Cell the fin Cell),

which means that if the Candidate is the solution in one of the Cells of the above Row in Square-1, it must be the solution in the fin Cell,

if it is possible to find a second Column that shares Cells with Square-2 and where this particular Candidate

• is present in maximum two Cells in Square-2,
• is not present in the Cell at the intersection of the Column and the above Row in Square-2,
• is present in Cells of the Square that "sees" the fin Cell (we call that Square Square-3),

which means that if the Candidate is the solution in one of the Cells of the above Row in Square-2, it must be the solution in Square-3,

then these Cells form a pattern called a Finned RCCBBB Mutant Swordfish. Such a pattern allows eliminating the Candidate from all Cells in Square-3 that "see" the fin Cell.

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

In this example the Finned RCCBBB Mutant Swordfish is based on candidate 7 and it is made of Row "E" and Columns "8" and "2",
A8 is the fin Cell.
If candidate 7 is the solution in A8, then it eliminates all candidates 7 in Row "A" (in particular in A3).
If candidate 7 is the solution in D8, then it is the solution either in E3, or in E1, which implies it is the solution either in A2, or in C2 which eliminates it in Square "1" (in particular in A3).
Whichever the solution for candidate 7 in Column "8", it can never be the solution in A3.

Finned BBBRCC Mutant Swordfish

If it is possible to find a Row (that we call Row-1) where a particular Candidate is present in two Squares,

if in the first Square this particular Candidate

• is present in one or more Cells outside of Row-1 that belong to only one Column (that we call Column-1),
• is present in at least one Cell in Row-1 outside of Column-1,

if in the second Square this particular Candidate

• is present in one or more Cells outside of Row-1 that belong to only one Column (that we call Column-2),
• is present in at least one Cell in Row-1 outside of Column-2,

if it is possible to find a third Square that shares Cells with Column-2 and where this particular Candidate

• is present in Cells in Column-2,
• is present in one or more Cells outside of Column-2 that belong to only one Row (we call these Cells fin Cells and they form what we call the fin),

then these Cells form a pattern called a Finned BBBRCC Mutant Swordfish. Such a pattern allows eliminating the Candidate from the Cell in Column-1 that "sees" the fin.

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

In this example the Finned BBBRCC Mutant Swordfish is based on candidate 9 and it is made of Squares "6", "5" and "2",
the fin comprises C4 and C5.
If candidate 9 is the solution in D7, then it eliminates all candidates 9 in Column "7" (in particular in C7).
If candidate 9 is the solution in F9, then it is the solution in D6, which implies it is the solution either in C4, or in C5, which eliminates it in Row "C" (in particular in C7).
Whichever the solution for candidate 9 in Square "6", it can never be the solution in C7.

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