An Expert 6×6 Puzzle Solved with Forced Chain in 18 Steps
Play this board yourself →A
B
C
D
E
F
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2×
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4×
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6×
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This 6×6 board rates as expert (difficulty score 1159). Solving it from scratch takes 18 logical steps, using 7 techniques: Single cell, Row/column exclusion, Adjacency clear, Line confinement, Paired regions, Shape squeeze, Forced chain. Every step below is forced: nothing here is a guess.
- First, together, two regions have open cells only in columns E and F; with one marker each, those two markers have to fill exactly those two columns, so every other region's open cells there can be cleared.
- Next, every remaining candidate in this region touches B5, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- Then, marking A1 would force F2 (the last open cell in region 2), then D6 and E6 cleared (every open cell left in this region sits in row 6, so its marker has to land there), then E5 (the last open cell in region 4), and then column D would be left with no open cell for its marker. So A1 can't be the marker there.
- After that, if B1 were the marker, it would force F2 (the last open cell in region 2), then C4, D4, D5, and 1 more cleared (every open cell in row 3 belongs to the same region, so that region's marker has to be somewhere in this row), and column D would end up with no open cell for its marker, which can't happen. So it can't go there.
- Now, that one can't be the marker: at C1 it would force F2 (the last open cell in region 2), then D4 cleared (every open cell left in this region sits in row 4, so its marker has to land there), then D5 and D6 cleared (every open cell in row 3 belongs to the same region, so that region's marker has to be somewhere in this row), and column D would be left with no open cell for its marker.
- From there, that one can't be the marker: at F1 it would force C5, D5 and D6 cleared (together, two regions have open cells only in rows 5 and 6), then C4 and D4 cleared (every open cell left in this region sits in row 4, so its marker has to land there), then A2 and B2 cleared (every open cell in column D belongs to the same region, so that region's marker has to be somewhere in this column), and the chain continues, and row 4 would be left with no open cell for its marker.
- Following that, that one can't be the marker: at A2 it would force E1 (the last open cell in region 2), then D6 and F6 cleared (every open cell left in this region sits in row 6, so its marker has to land there), then C3 and C4 cleared (every open cell in column D belongs to the same region, so that region's marker has to be somewhere in this column), and the chain continues, and row 6 would be left with no open cell for its marker.
- First, every remaining candidate in this region touches C2, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- Next, if E1 were the marker, it would force B2 (the last open cell in row 2), then F3 (the last open cell in row 3), then C4 cleared (every open cell in column D belongs to the same region, so that region's marker has to be somewhere in this column), and the chain continues, and row 5 would end up with no open cell for its marker, which can't happen. So it can't go there.
- Then, place a marker at F2. Region has exactly one open cell left. Placing here clears the rest of row 2, column F, and its region.
- After that, place a marker at D1. Row 1 has exactly one open cell left. Placing here clears the rest of row 1, column D, and its region.
- Now, every open cell in row 3 belongs to the same region, so that region's marker has to be somewhere in this row; that clears every other open cell in the region.
- From there, every open cell in row 4 belongs to the same region, so that region's marker has to be somewhere in this row; that clears every other open cell in the region.
- Following that, every remaining candidate in this region touches B4, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- First, place a marker at A4. Region has exactly one open cell left. Placing here clears the rest of row 4, column A, and its region. Placing here also clears its 1 touching neighbour.
- Next, place a marker at C3. Region has exactly one open cell left. Placing here clears the rest of row 3, column C, and its region.
- Then, place a marker at B6. Region has exactly one open cell left. Placing here clears the rest of row 6, column B, and its region.
- Finally, place a marker at E5. Region has exactly one open cell left.
The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎