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

This 9×9 board rates as expert (difficulty score 1531). 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, marking A1 would force I2 (the last open cell in region 3), and then region 4 would be left with no open cell for its marker. So A1 can't be the marker there.
2. Next, if B1 were the marker, it would force I2 (the last open cell in region 3), and region 4 would end up with no open cell for its marker, which can't happen. So it can't go there.
3. Then, that one can't be the marker: at C1 it would force I2 (the last open cell in region 3), and region 4 would be left with no open cell for its marker.
4. After that, marking D1 would force I2 (the last open cell in region 3), and then region 4 would be left with no open cell for its marker. So D1 can't be the marker there.
5. 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.
6. From there, marking G1 would force A3, B3, C3, and 3 more cleared (every open cell left in this region sits in row 3, so its marker has to land there), then H4 (the last open cell in region 5), and then row 3 would be left with no open cell for its marker. So G1 can't be the marker there.
7. Following that, if H1 were the marker, it would force I3, I6, I7, and 2 more cleared (every open cell left in this region sits in column I, so its marker has to land there), then F2 (the last open cell in region 4), then 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), 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.
8. First, that one can't be the marker: at I1 it would force H3, H4, H7, and 2 more cleared (every open cell left in this region sits in column H, so its marker has to land there), then A2, B2, C2, and 2 more cleared (every open cell left in this region sits in row 2, so its marker has to land there), then E3 cleared (every remaining candidate in this region touches E3), and the chain continues, and row 8 would be left with no open cell for its marker.
9. Next, every remaining candidate in this region touches E2 and F2, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
10. Then, that one can't be the marker: at A2 it would force D3, E3, F3, and 1 more cleared (every open cell left in this region sits in row 3, so its marker has to land there), then F4, G4, H4, and 1 more cleared (every open cell left in this region sits in row 4, so its marker has to land there), then G5 (the last open cell in region 5), and region 7 would be left with no open cell for its marker.
11. After that, marking B2 would force D3, E3, F3, and 1 more cleared (every open cell left in this region sits in row 3, so its marker has to land there), then F4, G4, H4, and 1 more cleared (every open cell left in this region sits in row 4, so its marker has to land there), then G5 (the last open cell in region 5), and then region 7 would be left with no open cell for its marker. So B2 can't be the marker there.
12. Now, that one can't be the marker: at D2 it would force F1 (the last open cell in region 3), then A3, B3 and G3 cleared (every open cell left in this region sits in row 3, so its marker has to land there), then H4, H7, H8, and 5 more cleared (together, two regions have open cells only in columns H and I), and the chain continues, and row 8 would be left with no open cell for its marker.
13. From there, that one can't be the marker: at G2 it would force E1 (the last open cell in region 3), then H4 (the last open cell in region 5), and region 7 would be left with no open cell for its marker.
14. Following that, together, two regions have open cells only in columns H and I; 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.
15. First, every remaining candidate in this region touches F4, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
16. Next, if A3 were the marker, it would force H2 (the last open cell in region 4), then G4 and I4 cleared (every open cell left in this region sits in row 4, so its marker has to land there), then G5 (the last open cell in region 5), and column I 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 B3 it would force H2 (the last open cell in region 4), then G4 and I4 cleared (every open cell left in this region sits in row 4, so its marker has to land there), then G5 (the last open cell in region 5), and column I would be left with no open cell for its marker.
18. After that, marking C3 would force E4 (the last open cell in region 2), then F1 (the last open cell in region 3), then H2 (the last open cell in region 4), and the chain continues, and then column I would be left with no open cell for its marker. So C3 can't be the marker there.
19. Now, marking H2 would force D4, E4, G4, and 3 more cleared (together, two regions have open cells only in rows 4 and 5), then D3 (the last open cell in region 2), and then region 5 would be left with no open cell for its marker. So H2 can't be the marker there.
20. From there, 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.
21. Following that, 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.
22. First, every open cell left in this region sits in column G, so its marker has to land there; that clears every other open cell in the column.
23. 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.
24. Then, place a marker at A8. Row 8 has exactly one open cell left. Placing here clears the rest of row 8, column A, and its region. Placing here also clears its 1 touching neighbour.
25. After that, place a marker at F7. Row 7 has exactly one open cell left. Placing here clears the rest of row 7, column F, and its region.
26. Now, place a marker at E1. Region has exactly one open cell left. Placing here clears the rest of row 1, column E, and its region.
27. From there, place a marker at D9. Region has exactly one open cell left. Placing here clears the rest of row 9, column D, and its region.
28. Following that, place a marker at H6. Row 6 has exactly one open cell left. Placing here clears the rest of row 6, column H, and its region. Placing here also clears its 1 touching neighbour.
29. First, place a marker at I3. Region has exactly one open cell left.
30. Next, place a marker at G4. Region has exactly one open cell left. Placing here clears the rest of row 4, column G, and its region.
31. Finally, place a marker at B5. Region has exactly one open cell left.

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