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

This 9×9 board rates as hard (difficulty score 1059). 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, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
3. Then, every remaining candidate in this region touches C5, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
4. After that, that one can't be the marker: at A2 it would force E6, E7, E8, and 1 more cleared (every open cell left in this region sits in column E, so its marker has to land there), then E3, F3, G3, and 2 more cleared (every open cell left in this region sits in row 3, so its marker has to land there), then H4, H5, H6, and 7 more cleared (every open cell in column I belongs to the same region, so that region's marker has to be somewhere in this column), and the chain continues, and column G would be left with no open cell for its marker.
5. Now, every remaining candidate in this region touches B4, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
6. From there, marking B2 would force E6, E7, E8, and 1 more cleared (every open cell left in this region sits in column E, so its marker has to land there), then A6, A7, A8, and 1 more cleared (every open cell left in this region sits in column A, so its marker has to land there), then C4, C8 and C9 cleared (every open cell left in this region sits in column C, so its marker has to land there), and the chain continues, and then region 9 would be left with no open cell for its marker. So B2 can't be the marker there.
7. Following that, together, two regions have open cells only in columns C and D; 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, 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.
9. Next, 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 2 touching neighbours.
10. Then, place a marker at F2. Region has exactly one open cell left. Placing here clears the rest of row 2, column F, and its region. Placing here also clears its 2 touching neighbours.
11. After that, place a marker at H1. Region has exactly one open cell left. Placing here clears the rest of row 1, column H, and its region.
12. Now, every open cell left in this region sits in row 3, so its marker has to land there; that clears every other open cell in the row.
13. From there, 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.
14. Following that, together, two regions have open cells only in rows 4 and 5; 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 G6. Region has exactly one open cell left. Placing here clears the rest of row 6, column G, and its region.
16. Next, every remaining candidate in this region touches C4 and D4, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
17. Then, 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.
18. After that, place a marker at C3. Region has exactly one open cell left.
19. Now, place a marker at A4. Region has exactly one open cell left. Placing here clears the rest of row 4, column A, and its region.
20. From there, place a marker at B7. Region has exactly one open cell left. Placing here clears the rest of row 7, column B, and its region.
21. Finally, place a marker at I9. Region has exactly one open cell left.

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