# Franken X-Wing

The basic X-Wing strategy is based on two Rows with constraints on two Columns, or vice-versa. In the *Franken X-Wing* strategy, we use a Column and a Square with constraints on two Rows (or a Row and a Square with constraints on two Columns).

## CBRR Franken X-Wing

If a particular Candidate is present in **only Two** Cells in a Column,

if you can find a Square that **does not overlap** this Column and where the Candidate is present in the same **two** Rows as in this Column,

then these Cells form a pattern called an *CBRR Franken X-Wing* (derived from the
*BB/CC Franken X-Wing*).
Such a pattern allows eliminating the Candidate from all Cells in the Rows of the *CBRR Franken X-Wing* except from the Cells that are included in the *CBRR Franken X-Wing* itself.

If the Candidate is the solution in the first Cell of the Column, then it must be the solution in the second Row of the Square; if it is the solution in the second Cell of the Column, then it must be the solution in the first Row of the Square. Hence, whichever the solution for the Candidate in the Column, it can not be the solution in any Cell of the involved Rows outside of the *CBRR Franken X-Wing*.

The candidate must not be present in all Cells of the Square of the *CBRR Franken X-Wing*, as long as it is present in at leat one Cell of the involved Rows.

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

. / . | . . . | . . . |

. / . | . . . | . . . |

. / . | . . . | . . . |

* X * | * * * | X X X |

. / . | . . . | / / / |

* X * | * * * | X X X |

. / . | . . . | . . . |

. / . | . . . | . . . |

. / . | . . . | . . . |

"X" indicates a Cell where the Candidate is present.

"/" indicates a Cell where the Candidate is not present.

"*" indicates a Cell in which the Candidate can be eliminated.

This strategy is implemented in the **SudokuCoach** application.