Finned Mutant X-Wing
Finned RCCB Mutant X-Wing
If it is possible to find a Row where a particular candidate is present in
- maximum two Cells in a Square (that we call Square-1)
- and in only one Cell (that we call Cell-1) outside of Square-1
If it is possible to find a Column that shares Cells with Square-1 where this particular candidate
- is present in maximum two Cells in Square-1
- and in only one Cell (that we call the fin Cell) outside of Square-1,
- is not present in the Cell at the intersection of the above Row with this Column
then these Cells form a pattern called a Finned RCCB Mutant X-Wing. Such a pattern allows eliminating the Candidate from the Cell that "sees" the fin Cell and Cell-1.
In the example above the Finned RCCB Mutant X-Wing is based on candidate 1 and it is made of Row "B" and Column "3".
If candidate 1 is the solution in B2, then it must be the solution in E3 which implies that it can not be the solution in any other cell in Row "E" (in particular in E6).
Conversely, if it is the solution in B6, then it can not be the solution in any other cell in Column "6" (in particular in E6).
Whichever the solution for candidate 1 in Row "B", it can never be the solution in E6.
Finned CBRC Mutant X-Wing
If it is possible to find a Column where a particular candidate is present in only two Cells (that we call Cell-1 and Cell-2) in different Squares.
If it is possible to find a Square
- that does not share Cells with the above Column
- where this particular candidate is present in the same Row as Cell-1 (we call it Row-1),
- and in one or more Cells that belong to only one Column (that we call Column-2)
- and where the candidate is present at least once in Column-2 and at least once in Row-1 outside of the Cell at the intersection of Column-2 and Row-1 (we call these Cells fin Cells and they form what we call the fin),
then these Cells form a pattern called a Finned CBRC Mutant X-Wing. Such a pattern allows eliminating the Candidate from the Cell in Column-2 that "sees" Cell-2.
In the example above the Finned CBRC Mutant X-Wing is based on candidate 2 and it is made of Column "3" and Square "5".
D6 is the fin.
If candidate 2 is the solution in A3, then it can not be the solution in any other cell in Row "A" (in particular in A6).
Conversely, if it is the solution in E3, then it must be the solution in D6 which implies that it can not be the solution in any other cell in Column "6" (in particular in A6).
Whichever the solution for candidate 2 in Column "3", it can never be the solution in A6.
Finned CCRB Mutant X-Wing
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 it is possible to find a first Column where a particular candidate is present in only two Cells (that we call Cell-1 and Cell-2) in different Squares.
If it is possible to find a second Column belonging to a different band than the first Column
- where this particular candidate is present in only two Squares (that we call Square-1 and Square-2),
- where this particular candidate is present only once in Square-1 in the same Row as Cell-1,
- and where Square-2 belongs to the same band as Cell-2,
then these Cells form a pattern called a Finned CCRB Mutant X-Wing. Such a pattern allows eliminating the Candidate from the Cells in Square-2 that "see" Cell-2.
The reasoning is also applicable when you replace "Column" by "Row" and "Row" by "Column".
In the example above the Finned CCRB Mutant X-Wing is based on candidate 2 and it is made of Rows "C" and "H".
H4 and H5 are the fin cells.
If candidate 2 is the solution in C6, then it can not be the solution in any other cell in Column "6" (in particular in J6).
Conversely, if it is the solution in C3, then it must be the solution in H4 or in H5 which implies that it can not be the solution in any other cell in Square "8" (in particular in J6).
Whichever the solution for candidate 2 in Row "C", it can never be the solution in J6.
Finned RBCC Mutant X-Wing
If it is possible to find a Row where a particular candidate is present in only two Cells (that we call Cell-1 and Cell-2 belonging respectively to Column-1 and Column-2) in different Squares.
If it is possible to find a Square
- that does not share Cells with the above Row
- where this particular candidate is present in Column-1,
- and in one or more Cells that belong to only one Row (that we call Row-2),
- and where the candidate is present at least once in Row-2 outside of the Cell at the intersection of Column-1 and Row-2 (we call these Cells fin Cells and they form what we call the fin),
then these Cells form a pattern called a Finned RBCC Mutant X-Wing. Such a pattern allows eliminating the Candidate from the Cell in Column-2 that "sees" the fin.
The reasoning is also applicable when you replace "Column" by "Row" and "Row" by "Column".
In the example above the Finned RBCC Mutant X-Wing is based on candidate 5 and it is made of Row "H" and Square "4".
E3 is the fin.
If candidate 5 is the solution in H9, then it can not be the solution in any other cell in Column "9" (in particular in E9).
Conversely, if it is the solution in H1, then it must be the solution in E3 which implies that it can not be the solution in any other cell in Row "E" (in particular in E9).
Whichever the solution for candidate 5 in Row "H", it can never be the solution in E9.
You can practice this strategy by installing the SudokuCoach application on your Android™ device.
