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

This 9×9 board rates as expert (difficulty score 1372). Solving it from scratch takes 29 logical steps, using 7 techniques: Single cell, Row/column exclusion, Adjacency clear, Region 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 remaining candidate in this region touches H2 and I2, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
3. Then, every remaining candidate in this region touches H8, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
4. After that, every remaining candidate in this region touches E8, 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 B8, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
6. From there, if H1 were the marker, it would force I7, I8 and I9 cleared (every open cell left in this region sits in column I, so its marker has to land there), then G9 (the last open cell in region 8), then A8 (the last open cell in region 9), and the chain continues, and region 7 would end up with no open cell for its marker, which can't happen. So it can't go there.
7. Following that, place a marker at I1. Region has exactly one open cell left. Placing here clears the rest of row 1, column I, and its region.
8. First, 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.
9. Next, that one can't be the marker: at A2 it would force G9 (the last open cell in column G), and region 9 would be left with no open cell for its marker.
10. Then, marking B2 would force G9 (the last open cell in column G), then A8 (the last open cell in region 9), then C7 (the last open cell in region 6), and then region 7 would be left with no open cell for its marker. So B2 can't be the marker there.
11. After that, if C2 were the marker, it would force G9 (the last open cell in column G), then A8 (the last open cell in region 9), and region 6 would end up with no open cell for its marker, which can't happen. So it can't go there.
12. Now, 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.
13. From there, every remaining candidate in this region touches A4 and B4, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
14. Following that, that one can't be the marker: at D2 it would force G9 (the last open cell in column G), then F7 (the last open cell in region 7), then E4 (the last open cell in region 4), and the chain continues, and column C would be left with no open cell for its marker.
15. First, marking E2 would force G9 (the last open cell in column G), then A8 (the last open cell in region 9), then B3 (the last open cell in region 1), and the chain continues, and then region 7 would be left with no open cell for its marker. So E2 can't be the marker there.
16. Next, if F2 were the marker, it would force G9 (the last open cell in column G), then A8 (the last open cell in region 9), then B3 (the last open cell in region 1), and the chain continues, and region 7 would end up with no open cell for its marker, which can't happen. So it can't go there.
17. Then, place a marker at G2. Row 2 has exactly one open cell left. Placing here clears the rest of row 2, column G, and its region.
18. After that, every open cell left in this region sits in row 4, so its marker has to land there; that clears every other open cell in the row.
19. Now, every remaining candidate in this region touches E5 and F5, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
20. From there, if A3 were the marker, it would force D9, E9, F9, and 1 more cleared (every open cell left in this region sits in row 9, so its marker has to land there), then H7 (the last open cell in region 8), then C8 (the last open cell in region 6), and row 9 would end up with no open cell for its marker, which can't happen. So it can't go there.
21. Following that, place a marker at B3. Region has exactly one open cell left. Placing here clears the rest of row 3, column B, and its region.
22. First, together, two regions have open cells only in columns A and C; 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.
23. Next, that one can't be the marker: at D5 it would force F4 (the last open cell in region 4), then E9 (the last open cell in region 7), then H7 (the last open cell in region 8), and the chain continues, and row 6 would be left with no open cell for its marker.
24. Then, place a marker at A5. Row 5 has exactly one open cell left. Placing here clears the rest of row 5, column A, and its region.
25. After that, place a marker at C9. Region has exactly one open cell left. Placing here clears the rest of row 9, column C, and its region. Placing here also clears its 1 touching neighbour.
26. Now, 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.
27. From there, place a marker at F8. Region has exactly one open cell left. Placing here clears the rest of row 8, column F, and its region.
28. Following that, 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.
29. Finally, place a marker at D6. Region has exactly one open cell left.

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