A General Logic for Sudoku

Monster #224 from list 1465

This is part of a set-logic solution to monster puzzle #224 from the 1465 list. The original solution to the puzzle (by ttt) was presented here. The elimination logic has the form:

rank N(n sets+ m linksets), [ cover set list ]x[ cover linkset list ] reason for elimination => results

For more information on notation and set logic eliminations, see quick reference. For a full description of sets and Sudoku set logic, see the SudokuOne.com website. The entire set logic solution is here.

Elimination 12, 3D Multi-loop with Triple Overlap

This logic forms a rank 4 multiloop that has 3 short chain branches. All three branches converge to eliminate the candidate at 6r7c7, which assigns 5r7c7 triggering more eliminations. The rank of the 3 branch chains is augmented by two triplets A and B. The set logic notation for the elimination is:

Rank 4 = 14-10, [5r147 6c1 8c3 14c5 6c8 3n7 4b1], [6r2 48r3 6r7 5c15 6c7 1n13 2n3 4n8 7n57 8n5]

(TT)6r7*6c7*7n7 => r7c7<>6 5r7c7 => r7c57<>5 => 5r8c5 => r56c4<>5 r8c4<>39

=> 5r5c8 => r4c8<>5 r5c8<>9.