An Expert 9×9 Puzzle Solved with Forced Chain in 29 Steps

This 9×9 board rates as expert (difficulty score 1515). Solving it from scratch takes 29 logical steps, using 6 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Line confinement, Forced chain. Every step below is forced: nothing here is a guess.

1. First, marking A1 would force C7, D7, C8, and 4 more cleared (every open cell in column B belongs to the same region, so that region's marker has to be somewhere in this column), then C2 (the last open cell in column C), then D6 (the last open cell in column D), and then column E 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 C7, D7, C8, and 4 more cleared (every open cell in column A belongs to the same region, so that region's marker has to be somewhere in this column), and column C would end up with no open cell for its marker, which can't happen. So it can't go there.
3. Then, if H1 were the marker, it would force I3, I4, I8, and 1 more cleared (every open cell left in this region sits in column I, so its marker has to land there), then A9, B9, C9, and 2 more cleared (every open cell left in this region sits in row 9, so its marker has to land there), then G9, F4, F7, and 2 more cleared (together, two regions have open cells only in columns G and F), and row 9 would end up with no open cell for its marker, which can't happen. So it can't go there.
4. After that, that one can't be the marker: at I1 it would force H6 (the last open cell in region 6), then G8 (the last open cell in region 8), and region 9 would be left with no open cell for its marker.
5. Now, that one can't be the marker: at A2 it would force C7, D7, C8, and 4 more cleared (every open cell in column B belongs to the same region, so that region's marker has to be somewhere in this column), then C1 (the last open cell in column C), then D6 (the last open cell in column D), and column E would be left with no open cell for its marker.
6. From there, marking B2 would force C7, D7, C8, and 4 more cleared (every open cell in column A belongs to the same region, so that region's marker has to be somewhere in this column), and then column C would be left with no open cell for its marker. So B2 can't be the marker there.
7. Following that, marking H2 would force I4, I8 and I9 cleared (every open cell left in this region sits in column I, so its marker has to land there), then A9, B9, C9, and 2 more cleared (every open cell left in this region sits in row 9, so its marker has to land there), then D3, E3, D4, and 1 more cleared (every open cell in row 1 belongs to the same region, so that region's marker has to be somewhere in this row), and the chain continues, and then row 9 would be left with no open cell for its marker. So H2 can't be the marker there.
8. First, if I2 were the marker, it would force H6 (the last open cell in region 6), then G8 (the last open cell in region 8), and region 9 would end up with no open cell for its marker, which can't happen. So it can't go there.
9. Next, that one can't be the marker: at B3 it would force C7, D7, C8, and 4 more cleared (every open cell in column A belongs to the same region, so that region's marker has to be somewhere in this column), then C1 (the last open cell in column C), then D6 (the last open cell in column D), and column E would be left with no open cell for its marker.
10. Then, marking C3 would force B7, D7, B8, and 4 more cleared (every open cell in column A belongs to the same region, so that region's marker has to be somewhere in this column), and then column B would be left with no open cell for its marker. So C3 can't be the marker there.
11. After that, if D3 were the marker, it would force F2 and G2 cleared (every open cell in row 1 belongs to the same region, so that region's marker has to be somewhere in this row), and row 2 would end up with no open cell for its marker, which can't happen. So it can't go there.
12. Now, that one can't be the marker: at E3 it would force G2 (the last open cell in row 2), and row 1 would be left with no open cell for its marker.
13. From there, marking F3 would force C2, D2, D4, and 1 more cleared (every open cell in row 1 belongs to the same region, so that region's marker has to be somewhere in this row), and then row 2 would be left with no open cell for its marker. So F3 can't be the marker there.
14. Following that, if G3 were the marker, it would force C2, D2, E2, and 2 more cleared (every open cell in row 1 belongs to the same region, so that region's marker has to be somewhere in this row), and row 2 would end up with no open cell for its marker, which can't happen. So it can't go there.
15. First, that one can't be the marker: at H3 it would force A5, B5, C5, and 3 more cleared (every open cell left in this region sits in row 5, so its marker has to land there), then I8 and I9 cleared (every open cell left in this region sits in column I, so its marker has to land there), then A9, B9, C9, and 2 more cleared (every open cell left in this region sits in row 9, so its marker has to land there), and the chain continues, and row 2 would be left with no open cell for its marker.
16. Next, marking I3 would force H6 (the last open cell in region 6), then G8 (the last open cell in region 8), and then region 9 would be left with no open cell for its marker. So I3 can't be the marker there.
17. Then, place a marker at A3. Row 3 has exactly one open cell left. Placing here clears the rest of row 3, column A, and its region.
18. After that, every open cell in column B 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, every open cell in column C 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.
20. From there, place a marker at D6. Column 4 has exactly one open cell left. Placing here clears the rest of row 6, column D, and its region.
21. Following that, place a marker at E1. Column 5 has exactly one open cell left. Placing here clears the rest of row 1, column E, and its region.
22. First, place a marker at C2. Region has exactly one open cell left.
23. 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.
24. Then, every open cell in row 4 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.
25. After that, place a marker at I5. Row 5 has exactly one open cell left. Placing here clears the rest of row 5, column I, and its region. Placing here also clears its 1 touching neighbour.
26. Now, 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.
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 F9. Region has exactly one open cell left. Placing here clears the rest of row 9, column F, and its region.
29. Finally, place a marker at B8. Region has exactly one open cell left.

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