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 6, Multi-loops

This rank 2 group of multi-loops can eliminate candidates anywhere that 3 linksets overlap. Candidate 5r6c7 is therefore eliminated by the overlap of 5r6, 6n7, and 5b6. Candidate 5r7c8 is eliminated by the overlap of 2 linksets 5c8 and 7c8 augmented by a triplet at 5r4c8, which requires set 5c8 be a linkset thus the two eliminations use two different groups of cover sets for the same candidates. The set logic notation for the elimination is:

Rank 2(12+14), [8r1 46r6 6c1 5c3 3c7 356c8 23n4 6b2]x

[6r1 36r2 5r6 3r9 168c4 1n3 4n8 6n79 7n8 5b6]

5r6*6n7*5b6 => r6c7<>5, (L)5c8*7c8 => r7c8<>5