An Expert 9×9 Puzzle Solved with Forced Chain in 20 Steps

This 9×9 board rates as expert (difficulty score 1125). Solving it from scratch takes 20 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 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 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.
3. 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. Placing here also clears its 3 touching neighbours.
4. 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 2 touching neighbours.
5. Now, marking G1 would force C2 and C3 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 I9 and H9 cleared (together, two regions have open cells only in columns I and H), and then row 9 would be left with no open cell for its marker. So G1 can't be the marker there.
6. From there, if H1 were the marker, it would force I7 (the last open cell in region 6), then G3 (the last open cell in region 4), and row 9 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 D1. Region has exactly one open cell left. Placing here clears the rest of row 1, column D, and its region. Placing here also clears its 1 touching neighbour.
8. First, marking B2 would force G4 (the last open cell in region 2), then I3 (the last open cell in row 3), then H7 (the last open cell in region 6), and then row 9 would be left with no open cell for its marker. So B2 can't be the marker there.
9. Next, that one can't be the marker: at G2 it would force C3 (the last open cell in region 2), and region 1 would be left with no open cell for its marker.
10. Then, marking H2 would force I7 (the last open cell in region 6), then G9 (the last open cell in region 9), then C3 (the last open cell in region 2), and then region 1 would be left with no open cell for its marker. So H2 can't be the marker there.
11. After that, if I2 were the marker, it would force H9 cleared (every open cell left in this region sits in column H, so its marker has to land there), then G9 (the last open cell in region 9), then C3 (the last open cell in region 2), and region 1 would end up with no open cell for its marker, which can't happen. So it can't go there.
12. Now, 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.
13. From there, 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.
14. Following that, place a marker at C3. Column 3 has exactly one open cell left. Placing here clears the rest of row 3, column C, and its region.
15. First, place a marker at G9. Column 7 has exactly one open cell left. Placing here clears the rest of row 9, column G, and its region.
16. 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.
17. Then, every remaining candidate in this region touches H4 and H5, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
18. After that, 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.
19. Now, place a marker at B5. Region has exactly one open cell left. Placing here clears the rest of row 5, column B, and its region.
20. Finally, place a marker at I4. Region has exactly one open cell left.

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