An Expert 7×7 Puzzle Solved with Forced Chain in 20 Steps
Play this board yourself →A
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This 7×7 board rates as expert (difficulty score 1139). Solving it from scratch takes 20 logical steps, using 8 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Line 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 column A, so its marker has to land there; that clears every other open cell in the column.
- Next, every open cell left in this region sits in column B, so its marker has to land there; that clears every other open cell in the column.
- Then, every open cell in row 7 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.
- After that, 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.
- Now, every remaining candidate in this region touches A3 and C3 and C4, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
- From there, together, two regions have open cells only in rows 1 and 2; 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.
- Following that, together, two regions have open cells only in rows 3 and 4; 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.
- First, that one can't be the marker: at C1 it would force A2 (the last open cell in region 1), then B4 (the last open cell in region 4), then D7 cleared (every open cell left in this region sits in column D, so its marker has to land there), and the chain continues, and row 7 would be left with no open cell for its marker.
- Next, marking D1 would force A2 (the last open cell in region 1), then B4 (the last open cell in region 4), and then region 6 would be left with no open cell for its marker. So D1 can't be the marker there.
- Then, if E1 were the marker, it would force A2 (the last open cell in region 1), then B4 (the last open cell in region 4), then F5 (the last open cell in region 5), and the chain continues, and row 7 would end up with no open cell for its marker, which can't happen. So it can't go there.
- After that, that one can't be the marker: at F1 it would force A2 (the last open cell in region 1), then B4 (the last open cell in region 4), then G3 (the last open cell in region 3), and the chain continues, and row 6 would be left with no open cell for its marker.
- Now, place a marker at A1. Row 1 has exactly one open cell left. Placing here clears the rest of row 1, column A, and its region.
- From there, together, two regions have open cells only in columns C and D; 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.
- Following that, if C2 were the marker, it would force B4 (the last open cell in region 4), then E5 and E6 cleared (every remaining candidate in this region touches E5 and E6), then F5 (the last open cell in region 5), and the chain continues, and row 7 would end up with no open cell for its marker, which can't happen. So it can't go there.
- First, place a marker at D2. Region has exactly one open cell left. Placing here clears the rest of row 2, column D, and its region.
- Next, place a marker at C5. Region has exactly one open cell left. Placing here clears the rest of row 5, column C, and its region. Placing here also clears its 1 touching neighbour.
- Then, place a marker at B3. Region has exactly one open cell left. Placing here clears the rest of row 3, column B, and its region.
- After that, 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. Placing here also clears its 1 touching neighbour.
- Now, place a marker at G7. Region has exactly one open cell left. Placing here clears the rest of row 7, column G, and its region.
- Finally, place a marker at F4. Region has exactly one open cell left.
The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎