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 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. |