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

This 9×9 board rates as hard (difficulty score 1049). 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 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 G2 and H2, 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 B3, 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 A2, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
5. Now, if H1 were the marker, it would force A3, C3, D3, and 2 more cleared (every open cell left in this region sits in row 3, so its marker has to land there), then B2 (the last open cell in region 5), then C4 (the last open cell in region 1), and the chain continues, and row 5 would end up with no open cell for its marker, which can't happen. So it can't go there.
6. From there, place a marker at G1. Region has exactly one open cell left. Placing here clears the rest of row 1, column G, and its region. Placing here also clears its 1 touching neighbour.
7. Following that, 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.
8. First, marking B2 would force C4 (the last open cell in region 1), then E3 and F3 cleared (every open cell left in this region sits in row 3, so its marker has to land there), then D6 (the last open cell in region 2), and the chain continues, and then region 8 would be left with no open cell for its marker. So B2 can't be the marker there.
9. Next, 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. Placing here also clears its 1 touching neighbour.
10. Then, every open cell left in this region sits in column C, so its marker has to land there; that clears every other open cell in the column.
11. After that, every open cell left in this region sits in column B, so its marker has to land there; that clears every other open cell in the column.
12. Now, together, two regions have open cells only in rows 2 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.
13. From there, every open cell left in this region sits in column D, so its marker has to land there; that clears every other open cell in the column.
14. Following that, together, two regions have open cells only in rows 5 and 6; 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.
15. First, 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 2 touching neighbours.
16. Next, 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. Placing here also clears its 1 touching neighbour.
17. Then, place a marker at C2. Region has exactly one open cell left. Placing here clears the rest of row 2, column C, and its region.
18. After that, 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.
19. Now, place a marker at I6. Region has exactly one open cell left.
20. From there, 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.
21. Finally, place a marker at B8. Region has exactly one open cell left.

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