An Expert 9×9 Puzzle Solved with Forced Chain in 31 Steps

This 9×9 board rates as expert (difficulty score 1395). Solving it from scratch takes 31 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.

1. First, every open cell left in this region sits in row 1, so its marker has to land there; that clears every other open cell in the row.
2. Next, every open cell left in this region sits in row 9, so its marker has to land there; that clears every other open cell in the row.
3. Then, every open cell left in this region sits in row 8, so its marker has to land there; that clears every other open cell in the row.
4. After 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.
5. Now, every remaining candidate in this region touches H6, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
6. From there, every remaining candidate in this region touches A8 and B8, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
7. Following that, that one can't be the marker: at A2 it would force B9 (the last open cell in region 9), then E7, F7, G7, and 2 more cleared (every open cell left in this region sits in row 7, so its marker has to land there), then G6 (the last open cell in region 7), and the chain continues, and row 7 would be left with no open cell for its marker.
8. First, every remaining candidate in this region touches C3, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
9. Next, marking B2 would force A9 (the last open cell in region 9), then E7, F7, G7, and 2 more cleared (every open cell left in this region sits in row 7, so its marker has to land there), then G6 (the last open cell in region 7), and the chain continues, and then row 4 would be left with no open cell for its marker. So B2 can't be the marker there.
10. Then, that one can't be the marker: at D2 it would force F3, G3, H3, and 4 more cleared (every open cell in column E belongs to the same region, so that region's marker has to be somewhere in this column), then G4, H4, I4, and 4 more cleared (every open cell in column F belongs to the same region, so that region's marker has to be somewhere in this column), then E6 and G6 cleared (every remaining candidate in this region touches E6 and G6), and the chain continues, and row 9 would be left with no open cell for its marker.
11. After that, marking E2 would force B5, B6, B7, and 1 more cleared (every open cell left in this region sits in column B, so its marker has to land there), then A9 (the last open cell in region 9), then F7, G7, H7, and 1 more cleared (every open cell left in this region sits in row 7, so its marker has to land there), and the chain continues, and then row 8 would be left with no open cell for its marker. So E2 can't be the marker there.
12. Now, if F2 were the marker, it would force B5, B6, B7, and 1 more cleared (every open cell left in this region sits in column B, so its marker has to land there), then A9 (the last open cell in region 9), then E7, G7, H7, and 1 more cleared (every open cell left in this region sits in row 7, so its marker has to land there), and the chain continues, and row 8 would end up with no open cell for its marker, which can't happen. So it can't go there.
13. From there, that one can't be the marker: at G2 it would force I1 (the last open cell in region 3), then H7 (the last open cell in region 7), then B5, B6 and B9 cleared (every open cell left in this region sits in column B, so its marker has to land there), and the chain continues, and region 4 would be left with no open cell for its marker.
14. Following that, if I2 were the marker, it would force G1 (the last open cell in region 3), then H7 (the last open cell in region 7), then B5, B6 and B9 cleared (every open cell left in this region sits in column B, so its marker has to land there), and the chain continues, and region 4 would end up with no open cell for its marker, which can't happen. So it can't go there.
15. First, place a marker at C2. Row 2 has exactly one open cell left. Placing here clears the rest of row 2, column C, and its region. Placing here also clears its 1 touching neighbour.
16. Next, if A3 were the marker, it would force D4 (the last open cell in region 2), then H8 (the last open cell in region 8), then G6 (the last open cell in region 7), and column F would end up with no open cell for its marker, which can't happen. So it can't go there.
17. Then, that one can't be the marker: at E3 it would force G4, H4, I4, and 4 more cleared (every open cell in column F belongs to the same region, so that region's marker has to be somewhere in this column), then A4 (the last open cell in row 4), then B9 (the last open cell in region 9), and the chain continues, and row 7 would be left with no open cell for its marker.
18. After that, every open cell in column E 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.
19. Now, place a marker at I3. Row 3 has exactly one open cell left. Placing here clears the rest of row 3, column I, and its region. Placing here also clears its 1 touching neighbour.
20. From there, every open cell in column F 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.
21. Following that, together, two regions have open cells only in columns G 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.
22. First, place a marker at D8. Region has exactly one open cell left. Placing here clears the rest of row 8, column D, and its region. Placing here also clears its 1 touching neighbour.
23. Next, every remaining candidate in this region touches F5, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
24. Then, 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.
25. After that, place a marker at B9. Column 2 has exactly one open cell left. Placing here clears the rest of row 9, column B, and its region.
26. Now, every remaining candidate in this region touches G6 and G7, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
27. From there, 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.
28. Following that, place a marker at G1. Region has exactly one open cell left.
29. First, place a marker at F6. Region has exactly one open cell left. Placing here also clears its 1 touching neighbour.
30. Next, place a marker at E4. Region has exactly one open cell left. Placing here clears the rest of row 4, column E, and its region.
31. 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. ∎