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

This 9×9 board rates as expert (difficulty score 1151). Solving it from scratch takes 21 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 column F, so its marker has to land there; that clears every other open cell in the column.
2. Next, 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.
3. Then, together, two regions have open cells only in columns I 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.
4. After that, every open cell left in this region sits in column E, so its marker has to land there; that clears every other open cell in the column.
5. Now, every remaining candidate in this region touches D2, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
6. From there, every remaining candidate in this region touches H6 and H7, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
7. Following that, marking A1 would force E3 (the last open cell in region 2), then B6 (the last open cell in region 7), then G7 (the last open cell in region 8), and the chain continues, and then row 4 would be left with no open cell for its marker. So A1 can't be the marker there.
8. First, if B1 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.
9. Next, that one can't be the marker: place it at C1, and row 2 would be left with no open cell for its marker.
10. Then, marking D1 would force E3 (the last open cell in region 2), then B2 (the last open cell in row 2), then I5 cleared (every open cell in row 4 belongs to the same region, so that region's marker has to be somewhere in this row), and the chain continues, and then row 4 would be left with no open cell for its marker. So D1 can't be the marker there.
11. After that, place a marker at E1. Row 1 has exactly one open cell left. Placing here clears the rest of row 1, column E, and its region.
12. Now, marking B2 would force D3 (the last open cell in region 1), then I5 cleared (every open cell in row 4 belongs to the same region, so that region's marker has to be somewhere in this row), then H5 (the last open cell in row 5), and then row 4 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, 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 B6. Region has exactly one open cell left. Placing here clears the rest of row 6, column B, and its region. Placing here also clears its 2 touching neighbours.
16. Next, place a marker at G7. Region has exactly one open cell left. Placing here clears the rest of row 7, column G, and its region. Placing here also clears its 2 touching neighbours.
17. Then, 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.
18. After that, place a marker at I3. Row 3 has exactly one open cell left. Placing here clears the rest of row 3, column I, and its region.
19. Now, place a marker at H5. Region has exactly one open cell left. Placing here clears the rest of row 5, column H, and its region.
20. From there, place a marker at C4. Region has exactly one open cell left. Placing here clears the rest of row 4, column C, and its region.
21. Finally, place a marker at D8. Region has exactly one open cell left.

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