A Hard 9×9 Puzzle Solved with Forced Chain in 21 Steps

This 9×9 board rates as hard (difficulty score 1091). Solving it from scratch takes 21 logical steps, using 7 techniques: Single cell, Row/column exclusion, Adjacency clear, Line confinement, Paired regions, Shape squeeze, Forced chain. Every step below is forced: nothing here is a guess.

1. First, together, two regions have open cells only in rows 1 and 2; with one marker each, those two markers have to fill exactly those two rows, so every other region's open cells there can be cleared.
2. Next, together, two regions have open cells only in columns H and I; 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.
3. Then, together, two regions have open cells only in rows 3 and 4; with one marker each, those two markers have to fill exactly those two rows, so every other region's open cells there can be cleared.
4. After that, together, two regions have open cells only in columns A and B; 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.
5. Now, place a marker at I2. Row 2 has exactly one open cell left. Placing here clears the rest of row 2, column I, and its region. Placing here also clears its 1 touching neighbour.
6. From there, place a marker at H4. Region has exactly one open cell left. Placing here clears the rest of row 4, column H, and its region. Placing here also clears its 1 touching neighbour.
7. Following that, place a marker at A3. Region has exactly one open cell left. Placing here clears the rest of row 3, column A, and its region.
8. First, every open cell in row 9 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.
9. Next, every remaining candidate in this region touches E5, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
10. Then, every remaining candidate in this region touches C7 and C8, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
11. After that, marking D1 would force E6 (the last open cell in region 2), then G8 (the last open cell in region 6), and then column F would be left with no open cell for its marker. So D1 can't be the marker there.
12. Now, if E1 were the marker, it would force D7, D8 and D9 cleared (every open cell left in this region sits in column D, so its marker has to land there), then B7 (the last open cell in row 7), then C5 (the last open cell in region 8), and column D would end up with no open cell for its marker, which can't happen. So it can't go there.
13. From there, place a marker at C1. Region has exactly one open cell left. Placing here clears the rest of row 1, column C, and its region.
14. Following that, together, two regions have open cells only in columns D and E; 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.
15. First, together, two regions have open cells only in rows 7 and 8; with one marker each, those two markers have to fill exactly those two rows, so every other region's open cells there can be cleared.
16. Next, if F5 were the marker, it would force D6 (the last open cell in region 2), and column E 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 D5. Row 5 has exactly one open cell left. Placing here clears the rest of row 5, column D, and its region.
18. After that, 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. Placing here also clears its 1 touching neighbour.
19. Now, 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.
20. From there, place a marker at B8. Region has exactly one open cell left.
21. 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. ∎