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 9, Two Intertwined ALS Produces Rank 0 Sets

This logic is made of a column ALS, 4r2378c256, an AALS, 14569r78c678, and a branching chain that interleaves through both. Although the overall rank is 2, linksets 4r7 and 8n5, highlighed black, are both rank 0 and can eliminate candidates without overlap. The rank of both sets is lowered by the presence of 2 linkset triplets each. All 3 triplets are in column set 4r5. The set logic notation is:

Rank 2(8+10), [5r7 4c256 7n89 8n7 1b8]x[4r3 149r7 4r8 78n5 4b2 56b9]

(TT)4r7 => r7c3<>4, r7c7<>4, (TT)8n5 => r8c5<>3, r8c5<>5