A General Logic for Sudoku

Golden Nugget

 

 

 

Elimination 39

 

Elimination 39 has the following set logic interpretation. A, the logic is rank 1 with 6 sets and 7 linksets, which would need 2 overlap linksets for elimination. B, the linkset triplet at 4r2c7 raises the rank in the upper (digit 2) level to 0. C, the set triplet at 2r2c7 then lowers the rank back to 1 except along its minor branch, row set 2r2, which is still rank 0 (black highlight) and eliminates candidate 2r2c5 (orange).

 

 

Set Logic and Grid

 

E39a 15 Nodes, Rank 1:

     6 Sets = {2c378 4c3 2n7 4b6}

     7 Links = {2r126 4r25 4c7 4n8}

     --> (2r2) => r2c5<>2

 

  +--------------------------------------------------------------------+

  | 257    145    157(2) | 68     2467   678    | 14(2)  3      9      |

  | 89     89     7(24)  | 3      247    1      | (24)   6      5      |

  | 26     146    3      | 29     5      49     | 8      147    147    |

  +--------------------------------------------------------------------+

  | 235    345    8      | 15     9      357    | 1357(4 17(24) 6      |

  | 359    7      6(4)   | 1568   136    2      | 359(4) 189(4) 138(4) |

  | 1      3569   56(2)  | 4      367    35678  | 3579   789(2) 378    |

  +--------------------------------------------------------------------+

  | 367    136    9      | 126    8      346    | 1347   5      24     |

  | 3578   2      157    | 159    134    3459   | 6      14789  13478  |

  | 4      368    156    | 7      1236   3569   | 139    189    1238   |

  +--------------------------------------------------------------------+

 

Logic Diagram