An Expert 9×9 Puzzle Solved with Forced Chain in 21 Steps

This 9×9 board rates as expert (difficulty score 1264). Solving it from scratch takes 21 logical steps, using 6 techniques: Single cell, Row/column exclusion, Adjacency clear, Line confinement, Shape squeeze, Forced chain. Every step below is forced: nothing here is a guess.

1. First, every open cell in column I 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.
2. Next, 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.
3. Then, marking A1 would force B9 (the last open cell in region 8), then C7 (the last open cell in region 9), then E8 (the last open cell in region 6), and then column H would be left with no open cell for its marker. So A1 can't be the marker there.
4. After that, if B1 were the marker, it would force H8 (the last open cell in column H), then C6 cleared (every open cell left in this region sits in column C, so its marker has to land there), then A7 and A9 cleared (every open cell left in this region sits in column A, so its marker has to land there), and region 8 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 C1 it would force B7 (the last open cell in region 9), then A9 (the last open cell in region 8), and region 1 would be left with no open cell for its marker.
6. From there, marking D1 would force H8 (the last open cell in column H), then A9, B9 and C9 cleared (every open cell left in this region sits in row 9, so its marker has to land there), then A7 (the last open cell in region 8), and then region 9 would be left with no open cell for its marker. So D1 can't be the marker there.
7. Following that, if E1 were the marker, it would force H8 (the last open cell in column H), then F3, F4 and F5 cleared (every open cell in column G belongs to the same region, so that region's marker has to be somewhere in this column), then F9 (the last open cell in column F), 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.
8. First, that one can't be the marker: at F1 it would force H8 (the last open cell in column H), then D7, D9 and E9 cleared (together, two regions have open cells only in rows 7 and 9), then D6 (the last open cell in region 6), and the chain continues, and column B would be left with no open cell for its marker.
9. Next, marking G1 would force H8 (the last open cell in column H), then F9 cleared (every open cell left in this region sits in column F, so its marker has to land there), then D7, D9 and E9 cleared (together, two regions have open cells only in rows 7 and 9), and the chain continues, and then column F would be left with no open cell for its marker. So G1 can't be the marker there.
10. Then, that one can't be the marker: at I1 it would force H8 (the last open cell in column H), then D7, D9, E9, and 1 more cleared (together, two regions have open cells only in rows 7 and 9), then D6 (the last open cell in region 6), and the chain continues, and column B would be left with no open cell for its marker.
11. After that, place a marker at H1. Row 1 has exactly one open cell left. Placing here clears the rest of row 1, column H, and its region. Placing here also clears its 1 touching neighbour.
12. Now, marking B2 would force C6 cleared (every open cell left in this region sits in column C, so its marker has to land there), then A7, A8 and A9 cleared (every open cell left in this region sits in column A, so its marker has to land there), and then region 8 would be left with no open cell for its marker. So B2 can't be the marker there.
13. From there, if C2 were the marker, it would force B7 (the last open cell in region 9), then A9 (the last open cell in region 8), and region 1 would end up with no open cell for its marker, which can't happen. So it can't go there.
14. Following that, place a marker at A2. Row 2 has exactly one open cell left. Placing here clears the rest of row 2, column A, and its region. Placing here also clears its 1 touching neighbour.
15. First, place a marker at B9. Region has exactly one open cell left. Placing here clears the rest of row 9, column B, and its region. Placing here also clears its 1 touching neighbour.
16. Next, place a marker at C7. Region has exactly one open cell left. Placing here clears the rest of row 7, column C, and its region. Placing here also clears its 2 touching neighbours.
17. Then, place a marker at E8. Region has exactly one open cell left. Placing here clears the rest of row 8, column E, and its region.
18. After that, place a marker at F6. Region has exactly one open cell left. Placing here clears the rest of row 6, column F, and its region. Placing here also clears its 1 touching neighbour.
19. 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.
20. From there, place a marker at D5. Region has exactly one open cell left. Placing here clears the rest of row 5, column D, and its region.
21. Finally, place a marker at I3. Region has exactly one open cell left.

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