... by: Norman Powell
Opening the Same as AS, some variations, then Bowman's Bingo finds the solution.Hidden Pair: 5 7 in D4, E5
X-Cycles: 4 in 8B
Almost Locked Sets
Set 1 C9 F9 G9 J9 with candidates 12459
Set 2 B9 B1 B4 B7 B8 with candidates 134679
With restricted Common Value 4
Rule 1: Eliminate All possibilities that can see non-Restricted Common in both ALSs
Eliminate Value 1 from Cell A9 - This is Found by AS's Forcing Network. I have ALS before FN in my chain of techniques.
Forcing Network 1st Pass:
Value 1 in Row 1 Column 7 cannot be ON so eliminate
Contradiction: More than one Value 1 ON in Row 4
Value 1 in Row 3 Column 7 cannot be ON so eliminate
Contradiction: More than one Value 1 ON in Column 9
Value 1 in Row 3 Column 9 cannot be ON so eliminate
Contradiction: More than one Value 1 ON in Box 6
This is where AS's Solver Stops, my Forcing Networks continues with:
Value 5 in Row 3 Column 9 cannot be ON so eliminate
Contradiction: More than one Value ON in Row 8 Column 5
Value 2 in Row 7 Column 7 cannot be ON so eliminate
Contradiction: No possibilities left for Row 4 Column 2
Forcing Networks 2nd Pass
Value 2 in Row 8 Column 3 cannot be ON so eliminate
Contradiction: More than one Value ON in Row 4 Column 1
Value 2 in Row 8 Column A1cannot be ON so eliminate
Contradiction: More than one Value ON in Row 4 Column 1
Bowman's Bingo
Level 0: Cell D2 is first with min poss: Try Value 3 ON and look for contradictions
Level 1: Cell A6 is first with min possibilities: Try Value 1 ON and look for contradictions
Level 2: Cell A2 is first with min possibilities: Try Value 2 ON and look for contradictions
Level 3: Cell A7 is first with min possibilities: Try Value 3 ON and look for contradictions
Switch OFF Value 3 in Cell A7 for Level 2
Contradiction: More than one Value 7 ON in Column 8
Level 3: Cell A7 is first with min possibilities: Try Value 8 ON and look for contradictions
Switch OFF Value 8 in Cell A7 for Level 2
Contradiction: No possibilities left for Row 3 Column 9
Switch OFF Value 2 in Cell A2 for Level 1
Contradiction: No possibilities left for Row 1 Column 7
Level 2: Cell A2 is first with min possibilities: Try Value 3 ON and look for contradictions
Level 3: Cell A3 is first with min possibilities: Try Value 2 ON and look for contradictions
Switch OFF Value 2 in Cell A3 for Level 2
Contradiction: No possibilities left for Row 8 Column 1
Level 3: Cell A8 is first with min poss: Try Value 2 ON and look for contradictions
Solution Found - Eliminate all Trial OFFs