An Expert 9×9 Puzzle Solved with Forced Chain in 24 Steps
Play this board yourself →A
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This 9×9 board rates as expert (difficulty score 1203). Solving it from scratch takes 24 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 B, so its marker has to land there; that clears every other open cell in the column.
- Next, every remaining candidate in this region touches A6 and C6 and A7 and C7, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
- Then, together, two regions have open cells only in rows 8 and 9; 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 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.
- Now, together, two regions have open cells only in columns A and C; 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, together, two regions have open cells only in rows 6 and 7; 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 E5. Region has exactly one open cell left. Placing here clears the rest of row 5, column E, and its region. Placing here also clears its 2 touching neighbours.
- First, place a marker at D7. Region has exactly one open cell left. Placing here clears the rest of row 7, column D, and its region.
- Next, place a marker at B6. Region has exactly one open cell left.
- Then, every remaining candidate in this region touches G3, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- After that, marking A1 would force I2 (the last open cell in region 2), and then region 4 would be left with no open cell for its marker. So A1 can't be the marker there.
- Now, 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.
- From there, that one can't be the marker: at F1 it would force A8 (the last open cell in row 8), then C2 (the last open cell in region 1), then H3 (the last open cell in region 4), and row 4 would be left with no open cell for its marker.
- Following that, every remaining candidate in this region touches H2, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- First, marking G1 would force H3 (the last open cell in region 4), and then column I would be left with no open cell for its marker. So G1 can't be the marker there.
- Next, if H1 were the marker, it would force F2 (the last open cell in region 4), then G9 (the last open cell in region 9), and column C would end up with no open cell for its marker, which can't happen. So it can't go there.
- Then, place a marker at I1. Region has exactly one open cell left. Placing here clears the rest of row 1, column I, and its region.
- After that, that one can't be the marker: at A2 it would force H3 (the last open cell in region 4), and row 4 would be left with no open cell for its marker.
- Now, if C2 were the marker, it would force H3 (the last open cell in region 4), and row 4 would end up with no open cell for its marker, which can't happen. So it can't go there.
- From there, place a marker at C9. Column 3 has exactly one open cell left. Placing here clears the rest of row 9, column C, and its region.
- Following that, place a marker at F8. Region has exactly one open cell left. Placing here clears the rest of row 8, column F, and its region.
- First, place a marker at G2. Row 2 has exactly one open cell left. Placing here clears the rest of row 2, column G, and its region.
- Next, place a marker at H4. Region has exactly one open cell left. Placing here clears the rest of row 4, column H, and its region.
- Finally, place a marker at A3. Region has exactly one open cell left.
The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎