An Expert 9×9 Puzzle Solved with Forced Chain in 33 Steps

This 9×9 board rates as expert (difficulty score 1607). Solving it from scratch takes 33 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 remaining candidate in this region touches G5, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
2. Next, that one can't be the marker: at F1 it would force H3, I3, G4, and 2 more cleared (every open cell in row 2 belongs to the same region, so that region's marker has to be somewhere in this row), then H5, H6, H9, and 2 more cleared (together, two regions have open cells only in columns H and I), then G6 (the last open cell in region 6), and the chain continues, and region 5 would be left with no open cell for its marker.
3. Then, marking G1 would force H7, H8 and H9 cleared (every open cell left in this region sits in column H, 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 1 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 then row 9 would be left with no open cell for its marker. So G1 can't be the marker there.
4. After that, if H1 were the marker, it would force G6 (the last open cell in region 6), 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 1 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 3 would end up with no open cell for its marker, which can't happen. So it can't go there.
5. Now, that one can't be the marker: at I1 it would force H5, H6 and H9 cleared (every open cell left in this region sits in column H, so its marker has to land there), then G6 (the last open cell in region 6), then H8 (the last open cell in region 7), and the chain continues, and column B would be left with no open cell for its marker.
6. From there, 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.
7. Following that, that one can't be the marker: at G2 it would force H4, H7, H8, and 1 more cleared (every open cell left in this region sits in column H, so its marker has to land there), then 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 A3 (the last open cell in row 3), and the chain continues, and region 5 would be left with no open cell for its marker.
8. First, if E1 were the marker, it would force H3, I3, F4, and 4 more cleared (every open cell in row 2 belongs to the same region, so that region's marker has to be somewhere in this row), then H5, H6, H9, and 2 more cleared (together, two regions have open cells only in columns H and I), then G6 (the last open cell in region 6), and the chain continues, 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, if I2 were the marker, it would force H5, H6 and H9 cleared (every open cell left in this region sits in column H, so its marker has to land there), then G6 (the last open cell in region 6), then H8 (the last open cell in region 7), 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.
10. Then, that one can't be the marker: at B3 it would force H2 (the last open cell in row 2), and row 4 would be left with no open cell for its marker.
11. After that, that one can't be the marker: at E3 it would force H2 (the last open cell in row 2), then G6 (the last open cell in region 6), then F8 (the last open cell in region 5), and the chain continues, and region 7 would be left with no open cell for its marker.
12. Now, marking F3 would force H2 (the last open cell in row 2), then G6 (the last open cell in region 6), then A4 (the last open cell in row 4), and the chain continues, and then region 5 would be left with no open cell for its marker. So F3 can't be the marker there.
13. From there, if G3 were the marker, row 2 would end up with no open cell for its marker, which can't happen. So it can't go there.
14. Following that, marking A1 would force H2, F4, G4, and 3 more cleared (every open cell in row 3 belongs to the same region, so that region's marker has to be somewhere in this row), then F2 (the last open cell in row 2), and then row 4 would be left with no open cell for its marker. So A1 can't be the marker there.
15. First, that one can't be the marker: at H3 it would force G6 (the last open cell in region 6), then F2 (the last open cell in row 2), then A4 (the last open cell in row 4), and the chain continues, and region 5 would be left with no open cell for its marker.
16. Next, marking I3 would force F2 (the last open cell in row 2), then A4 (the last open cell in row 4), then H5, H6 and H9 cleared (every open cell left in this region sits in column H, so its marker has to land there), and the chain continues, and then row 5 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. Placing here also clears its 1 touching neighbour.
18. After that, that one can't be the marker: at C1 it would force D9 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 F2 and E4 cleared (every open cell in column D belongs to the same region, so that region's marker has to be somewhere in this column), then H2 (the last open cell in row 2), and the chain continues, and column F would be left with no open cell for its marker.
19. Now, marking D1 would force C6, C7, C8, and 1 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 C4 (the last open cell in column C), then H2 (the last open cell in row 2), and the chain continues, and then column F would be left with no open cell for its marker. So D1 can't be the marker there.
20. From there, place a marker at B1. Region has exactly one open cell left. Placing here clears the rest of row 1, column B, and its region.
21. Following that, if F2 were the marker, it would force D9 (the last open cell in column D), and column C would end up with no open cell for its marker, which can't happen. So it can't go there.
22. First, place a marker at H2. Row 2 has exactly one open cell left. Placing here clears the rest of row 2, column H, and its region.
23. Next, place a marker at G6. Region has exactly one open cell left. Placing here clears the rest of row 6, column G, and its region. Placing here also clears its 1 touching neighbour.
24. Then, 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.
25. After that, 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.
26. Now, 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.
27. From there, 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.
28. Following that, place a marker at D4. Column 4 has exactly one open cell left. Placing here clears the rest of row 4, column D, and its region. Placing here also clears its 1 touching neighbour.
29. First, 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.
30. Next, every remaining candidate in this region touches E8 and F8, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
31. Then, place a marker at E7. Region has exactly one open cell left. Placing here clears the rest of row 7, column E, and its region.
32. After that, place a marker at C8. Region has exactly one open cell left.
33. Finally, place a marker at F9. Region has exactly one open cell left.

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