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 5, Multi-loops

This rank 1 logic works by the overlap of 2 linksets 5c7 and 5r5. The looped structure is made of 3 ALS and 1 cell set 5n5, which might be expressed as 5r5c4-als(5=46r78c4)-als(46=46r6c146)-(59=r568c1)-46r5c5. The set logic notation for the elimination is:

Rank 1(8+7), [46r6 59c4 78n7 5n8]x[59r5 456c7 6n49 8n4] 5c7*5r5 => r5c7<>5