A General Logic for Sudoku

Rank 0 and 1 Double Loops, with Triplets

Points. Set triplets can lower rank while linkset triplets can raise rank. Examples of both cases are shown with multiple loops.

Rank 0 Double Loop, Set Triplet Raises Rank

This double loop example has 5 sets, 5 linksets, and a rank of 0. When the set triplet at 2r4c4 is occupied, there are only 4 true nodes in the logic and the effective rank is 1 however, the minor branch of the triplet along linkset c42 will be occupied and thus has a rank of 0 (highlighted black). Since c42 is always occupied, it eliminates candidate 2r1c4. In short, a set triplet can raise the rank of a structure by 1 except along its minor branch.

Rank 1 Double Loop, with Linkset Triplet Lowers Rank

This logic in the second example is almost the opposite. The rank 1 double loop has a linkset triplet at 9r5c3 that makes linksets along its minor branch rank 0. The only linkset along its minor branch is cell set n51, which is rank 0 (black highlight) eliminating candidate 8r5c1.