A Severe 6×6 Puzzle Solved with Forced Chain in 24 Steps
Play this board yourself →A
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This 6×6 board rates as severe (difficulty score 1118). Solving it from scratch takes 24 logical steps, using 7 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Paired regions, Shape squeeze, Forced chain. Every step below is forced: nothing here is a guess.
- First, every open cell left in this region sits in row 2, so its marker has to land there; that clears every other open cell in the row.
- Next, together, two regions have open cells only in rows 1 and 3; 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.
- Then, every remaining candidate in this region touches B2, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- After that, every remaining candidate in this region touches C1 and D1 and D3, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
- Now, 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.
- From there, if B1 were the marker, it would force D2 (the last open cell in region 3), and row 3 would end up with no open cell for its marker, which can't happen. So it can't go there.
- Following that, every open cell left in this region sits in column A, so its marker has to land there; that clears every other open cell in the column.
- First, every remaining candidate in this region touches C5, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- Next, that one can't be the marker: at F1 it would force A3 (the last open cell in region 1), then E4 (the last open cell in region 4), then B6 (the last open cell in region 5), and row 5 would be left with no open cell for its marker.
- Then, every open cell left in this region sits in column E, so its marker has to land there; that clears every other open cell in the column.
- After that, every remaining candidate in this region touches D2, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- Now, place a marker at C2. Region has exactly one open cell left. Placing here clears the rest of row 2, column C, and its region.
- From there, marking D4 would immediately leave row 6 with no open cell for its marker, so it can't be the marker there.
- Following that, marking B5 would immediately leave row 6 with no open cell for its marker, so it can't be the marker there.
- First, place a marker at D6. Region has exactly one open cell left. Placing here clears the rest of row 6, column D, and its region.
- Next, place a marker at B4. Region has exactly one open cell left. Placing here clears the rest of row 4, column B, and its region. Placing here also clears its 1 touching neighbour.
- Then, place a marker at A1. Region has exactly one open cell left. Placing here clears the rest of row 1, column A, and its region.
- After that, place a marker at E3. Region has exactly one open cell left.
- Finally, place a marker at F5. Region has exactly one open cell left.
The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎