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 1134). 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 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.
- Next, every remaining candidate in this region touches F6, 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 D2 and E2 cleared (every open cell left in this region sits in row 2, so its marker has to land there), then F3, F4, F5, and 2 more cleared (together, two regions have open cells only in columns F and G), then E3 (the last open cell in region 5), and then region 4 would be left with no open cell for its marker. So A1 can't be the marker there.
- After that, every open cell in column A belongs to the same region, so that region's marker has to be somewhere in this column; that clears every other open cell in the region.
- Now, if B1 were the marker, it would force D2 and E2 cleared (every open cell left in this region sits in row 2, so its marker has to land there), then D5, E5, D6, and 3 more cleared (every open cell in column C belongs to the same region, so that region's marker has to be somewhere in this column), then E4, F4 and F5 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 column D would end up with no open cell for its marker, which can't happen. So it can't go there.
- From there, that one can't be the marker: at C1 it would force B6 (the last open cell in column B), then A2 and E2 cleared (every open cell left in this region sits in row 2, so its marker has to land there), then G5 cleared (every open cell in row 7 belongs to the same region, so that region's marker has to be somewhere in this row), and the chain continues, and column D would be left with no open cell for its marker.
- Following that, 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.
- First, marking D1 would force A2 (the last open cell in row 2), then C3 (the last open cell in region 1), then G4 (the last open cell in region 5), and then region 4 would be left with no open cell for its marker. So D1 can't be the marker there.
- Next, if E1 were the marker, it would force F4 and F5 cleared (together, two regions have open cells only in columns F and G), then D5, D6 and D7 cleared (every open cell left in this region sits in column D, so its marker has to land there), then A3, B3, C3, and 1 more cleared (together, two regions have open cells only in rows 3 and 4), and the chain continues, and column A would end up with no open cell for its marker, which can't happen. So it can't go there.
- Then, together, two regions have open cells only in columns F and G; 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.
- After that, 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.
- Now, every open cell left in this region sits in column D, so its marker has to land there; that clears every other open cell in the column.
- From there, together, two regions have open cells only in rows 2 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.
- Following that, place a marker at D4. Region has exactly one open cell left. Placing here clears the rest of row 4, column D, and its region. Placing here also clears its 3 touching neighbours.
- First, place a marker at E2. Region has exactly one open cell left. Placing here clears the rest of row 2, column E, and its region. Placing here also clears its 1 touching neighbour.
- Next, place a marker at G1. Region has exactly one open cell left. Placing here clears the rest of row 1, column G, and its region.
- 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 C6. Region has exactly one open cell left. Placing here clears the rest of row 6, column C, and its region.
- Now, place a marker at F7. Region has exactly one open cell left. Placing here clears the rest of row 7, column F, and its region.
- Finally, place a marker at A5. Region has exactly one open cell left.
The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎