An Expert 9×9 Puzzle Solved with Forced Chain in 29 Steps
Play this board yourself →A
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This 9×9 board rates as expert (difficulty score 1492). Solving it from scratch takes 29 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, together, two regions have open cells only in columns I and H; 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 open cell in row 9 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.
- Then, every remaining candidate in this region touches F7, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- After that, if E1 were the marker, it would force G6, G7, G8, and 1 more cleared (every open cell left in this region sits in column G, so its marker has to land there), then F6 (the last open cell in region 9), then D7 (the last open cell in row 7), and row 8 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 F1 it would force G6, G7, G8, and 1 more cleared (every open cell left in this region sits in column G, so its marker has to land there), then E6 (the last open cell in region 9), and row 7 would be left with no open cell for its marker.
- From there, marking G1 would force D8 (the last open cell in row 8), and then row 7 would be left with no open cell for its marker. So G1 can't be the marker there.
- Following that, every remaining candidate in this region touches F3, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- First, that one can't be the marker: at A2 it would force G5, G6, G7, and 2 more cleared (every open cell left in this region sits in column G, so its marker has to land there), then D8 (the last open cell in row 8), and row 7 would be left with no open cell for its marker.
- Next, marking B2 would force G5, G6, G7, and 2 more cleared (every open cell left in this region sits in column G, so its marker has to land there), then D8 (the last open cell in row 8), and then row 7 would be left with no open cell for its marker. So B2 can't be the marker there.
- Then, if C2 were the marker, it would force I1 (the last open cell in row 1), then H5 (the last open cell in region 7), then G3 (the last open cell in region 3), and region 2 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 I1 it would force H5 (the last open cell in region 7), then E3, G3, E4, and 1 more cleared (together, two regions have open cells only in rows 3 and 4), then F2 and G2 cleared (every open cell left in this region sits in row 2, so its marker has to land there), and region 3 would be left with no open cell for its marker.
- Now, that one can't be the marker: at D2 it would force G8 (the last open cell in row 8), and column F would be left with no open cell for its marker.
- From there, marking E2 would force G6, G7, G8, and 1 more cleared (every open cell left in this region sits in column G, so its marker has to land there), then F6 (the last open cell in region 9), then D7 (the last open cell in row 7), and then row 8 would be left with no open cell for its marker. So E2 can't be the marker there.
- Following that, that one can't be the marker: at G2 it would force I3 (the last open cell in region 4), then H5 (the last open cell in region 7), then D8 (the last open cell in row 8), and row 7 would be left with no open cell for its marker.
- First, if I2 were the marker, it would force H5 (the last open cell in region 7), then G3 (the last open cell in region 3), then D1 (the last open cell in region 2), and row 8 would end up with no open cell for its marker, which can't happen. So it can't go there.
- Next, place a marker at F2. Row 2 has exactly one open cell left. Placing here clears the rest of row 2, column F, and its region. Placing here also clears its 1 touching neighbour.
- Then, every open cell left in this region sits in row 3, so its marker has to land there; that clears every other open cell in the row.
- After that, every remaining candidate in this region touches I4, 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 G5 (the last open cell in region 2), then B4 (the last open cell in region 5), then I6 (the last open cell in region 7), and then region 9 would be left with no open cell for its marker. So A1 can't be the marker there.
- From there, if B1 were the marker, it would force G5 (the last open cell in region 2), then A4 (the last open cell in region 5), then I6 (the last open cell in region 7), and region 9 would end up with no open cell for its marker, which can't happen. So it can't go there.
- Following that, that one can't be the marker: at C1 it would force G5 (the last open cell in region 2), then I6 (the last open cell in region 7), and region 9 would be left with no open cell for its marker.
- First, 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.
- Next, place a marker at C4. Region has exactly one open cell left. Placing here clears the rest of row 4, column C, and its region. Placing here also clears its 1 touching neighbour.
- Then, place a marker at A5. Region has exactly one open cell left. Placing here clears the rest of row 5, column A, and its region. Placing here also clears its 1 touching neighbour.
- After that, place a marker at I6. Region has exactly one open cell left. Placing here clears the rest of row 6, column I, and its region.
- Now, place a marker at H3. Region has exactly one open cell left.
- From there, place a marker at E7. Region has exactly one open cell left. Placing here clears the rest of row 7, column E, and its region.
- Following that, place a marker at G8. Region has exactly one open cell left. Placing here clears the rest of row 8, column G, and its region.
- Finally, place a marker at B9. Region has exactly one open cell left.
The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎