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

This 9×9 board rates as hard (difficulty score 1087). Solving it from scratch takes 21 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 2, so its marker has to land there; that clears every other open cell in the row.
3. Then, every open cell left in this region sits in column A, so its marker has to land there; that clears every other open cell in the column.
4. After that, every remaining candidate in this region touches H2 and I2, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
5. Now, every remaining candidate in this region touches F3, 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 E4, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
7. Following that, every remaining candidate in this region touches B8 and B9, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
8. First, marking E2 would force F4 (the last open cell in region 2), then G8 (the last open cell in region 7), then H5 (the last open cell in region 8), and the chain continues, and then region 5 would be left with no open cell for its marker. So E2 can't be the marker there.
9. Next, every remaining candidate in this region touches G3, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
10. Then, that one can't be the marker: at G2 it would force I1 (the last open cell in region 4), then H4, H5 and H7 cleared (every open cell left in this region sits in column H, so its marker has to land there), then F4, F7, F8, and 1 more cleared (every open cell left in this region sits in column F, so its marker has to land there), and the chain continues, and row 4 would be left with no open cell for its marker.
11. After that, 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 1 touching neighbour.
12. Now, place a marker at D3. Region has exactly one open cell left. Placing here clears the rest of row 3, column D, and its region. Placing here also clears its 1 touching neighbour.
13. From there, place a marker at C5. Region has exactly one open cell left. Placing here clears the rest of row 5, column C, and its region. Placing here also clears its 2 touching neighbours.
14. Following that, 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. Placing here also clears its 1 touching neighbour.
15. First, place a marker at A9. Region has exactly one open cell left. Placing here clears the rest of row 9, column A, and its region.
16. Next, every open cell in column E 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.
17. Then, marking G4 would immediately leave region 8 with no open cell for its marker, so it can't be the marker there.
18. After that, place a marker at G6. Column 7 has exactly one open cell left. Placing here clears the rest of row 6, column G, and its region.
19. Now, 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.
20. From there, place a marker at I4. Region has exactly one open cell left. Placing here clears the rest of row 4, column I, and its region.
21. Finally, place a marker at H1. Region has exactly one open cell left.

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