A Hard 6×6 Puzzle Solved with Forced Chain in 16 Steps
Play this board yourself →A
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This 6×6 board rates as hard (difficulty score 1102). Solving it from scratch takes 16 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, every open cell in row 1 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.
- Next, together, two regions have open cells only in columns F and E; 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.
- Then, together, two regions have open cells only in rows 5 and 6; with one marker each, those two markers have to fill exactly those two rows, so every other region's open cells there can be cleared.
- After that, every remaining candidate in this region touches B3, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- Now, marking A1 would force B4 (the last open cell in region 2), then C2 (the last open cell in region 3), then F3 (the last open cell in region 4), and the chain continues, and then row 5 would be left with no open cell for its marker. So A1 can't be the marker there.
- From there, 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.
- Following that, if B1 were the marker, it would force F2 (the last open cell in row 2), then E6 (the last open cell in region 6), and column D would end up with no open cell for its marker, which can't happen. So it can't go there.
- First, that one can't be the marker: place it at C1, and region 3 would be left with no open cell for its marker.
- Next, place a marker at D1. Region has exactly one open cell left. Placing here clears the rest of row 1, column D, and its region.
- Then, that one can't be the marker: at A2 it would force B6 (the last open cell in column B), then F5 (the last open cell in region 6), and column E would be left with no open cell for its marker.
- After that, if F2 were the marker, it would force E6 (the last open cell in region 6), then C5 (the last open cell in region 5), and column B would end up with no open cell for its marker, which can't happen. So it can't go there.
- Now, place a marker at B2. Row 2 has exactly one open cell left. Placing here clears the rest of row 2, column B, and its region. Placing here also clears its 1 touching neighbour.
- From there, 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.
- Following that, place a marker at F3. Region has exactly one open cell left. Placing here clears the rest of row 3, column F, and its region.
- First, place a marker at E6. Region has exactly one open cell left. Placing here clears the rest of row 6, column E, and its region.
- Finally, place a marker at C5. Region has exactly one open cell left.
The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎