An Expert 9×9 Puzzle Solved with Forced Chain in 36 Steps

This 9×9 board rates as expert (difficulty score 1720). Solving it from scratch takes 36 logical steps, using 7 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Line confinement, Shape squeeze, Forced chain. Every step below is forced: nothing here is a guess.

1. 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.
2. Next, every open cell left in this region sits in column I, so its marker has to land there; that clears every other open cell in the column.
3. Then, place a marker at H7. Region has exactly one open cell left. Placing here clears the rest of row 7, column H, and its region. Placing here also clears its 2 touching neighbours.
4. After that, every remaining candidate in this region touches B1 and B2, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
5. Now, that one can't be the marker: at C1 it would force A2 (the last open cell in region 1), then I3 (the last open cell in region 3), then B4 (the last open cell in region 4), and the chain continues, and row 6 would be left with no open cell for its marker.
6. From there, if C2 were the marker, it would force A1 (the last open cell in region 1), then I3 (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.
7. Following that, that one can't be the marker: at D2 it would force A1 (the last open cell in region 1), then F3 (the last open cell in region 2), and column I would be left with no open cell for its marker.
8. First, marking E2 would force G1 (the last open cell in region 2), and then column A would be left with no open cell for its marker. So E2 can't be the marker there.
9. Next, that one can't be the marker: at G2 it would force A1 (the last open cell in region 1), then E3 (the last open cell in region 2), and column I would be left with no open cell for its marker.
10. Then, that one can't be the marker: at B3 it would force A1 (the last open cell in region 1), then F2 (the last open cell in region 2), and column I would be left with no open cell for its marker.
11. After that, marking C3 would force D5, E5, F5, and 1 more cleared (every open cell in row 4 belongs to the same region, so that region's marker has to be somewhere in this row), then I1 and I2 cleared (together, two regions have open cells only in rows 1 and 2), and then column I would be left with no open cell for its marker. So C3 can't be the marker there.
12. Now, every remaining candidate in this region touches B5, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
13. From there, if D3 were the marker, it would force B6 (the last open cell in region 7), and row 4 would end up with no open cell for its marker, which can't happen. So it can't go there.
14. Following that, if G3 were the marker, it would force F9 (the last open cell in region 8), then C5 (the last open cell in row 5), and row 4 would end up with no open cell for its marker, which can't happen. So it can't go there.
15. First, if B4 were the marker, it would force D8 (the last open cell in region 7), then C6 (the last open cell in column C), and region 9 would end up with no open cell for its marker, which can't happen. So it can't go there.
16. Next, every open cell left in this region sits in column C, so its marker has to land there; that clears every other open cell in the column.
17. Then, every remaining candidate in this region touches D4 and D5, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
18. After that, marking G1 would force A2 (the last open cell in region 1), then I3 (the last open cell in region 3), then F9 (the last open cell in region 8), and the chain continues, and then column B would be left with no open cell for its marker. So G1 can't be the marker there.
19. Now, if E4 were the marker, it would force C5 (the last open cell in region 4), then D8 (the last open cell in region 7), then I3 (the last open cell in row 3), and the chain continues, and column B would end up with no open cell for its marker, which can't happen. So it can't go there.
20. From there, that one can't be the marker: at F4 it would force C5 (the last open cell in region 4), then D8 (the last open cell in region 7), then E1 (the last open cell in region 2), and row 6 would be left with no open cell for its marker.
21. Following that, marking G4 would force C5 (the last open cell in region 4), then D8 (the last open cell in region 7), then F9 (the last open cell in region 8), and then column B would be left with no open cell for its marker. So G4 can't be the marker there.
22. First, place a marker at C4. Row 4 has exactly one open cell left. Placing here clears the rest of row 4, column C, and its region.
23. Next, every open cell in column G 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.
24. Then, every remaining candidate in this region touches E6, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
25. After that, marking E5 would force G9 (the last open cell in region 8), then B8 (the last open cell in region 9), and then row 6 would be left with no open cell for its marker. So E5 can't be the marker there.
26. Now, that one can't be the marker: at F1 it would force A2 (the last open cell in region 1), then I3 (the last open cell in region 3), then D6 (the last open cell in region 5), and region 7 would be left with no open cell for its marker.
27. From there, if F2 were the marker, it would force A1 (the last open cell in region 1), then I3 (the last open cell in region 3), then D6 (the last open cell in region 5), and region 7 would end up with no open cell for its marker, which can't happen. So it can't go there.
28. Following that, marking F3 would force D6 (the last open cell in region 5), and then region 7 would be left with no open cell for its marker. So F3 can't be the marker there.
29. First, that one can't be the marker: at G5 it would force D6 (the last open cell in region 5), and region 7 would be left with no open cell for its marker.
30. Next, place a marker at G9. Region has exactly one open cell left. Placing here clears the rest of row 9, column G, and its region. Placing here also clears its 1 touching neighbour.
31. Then, place a marker at F5. Row 5 has exactly one open cell left. Placing here clears the rest of row 5, column F, and its region.
32. After that, place a marker at B6. Row 6 has exactly one open cell left. Placing here clears the rest of row 6, column B, and its region.
33. Now, place a marker at E8. Region has exactly one open cell left. Placing here clears the rest of row 8, column E, and its region.
34. From there, place a marker at D1. Region has exactly one open cell left. Placing here clears the rest of row 1, column D, and its region.
35. Following that, place a marker at A2. Region has exactly one open cell left. Placing here clears the rest of row 2, column A, and its region.
36. Finally, place a marker at I3. Region has exactly one open cell left.

The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎