A Hard 9×9 Puzzle Solved with Forced Chain in 19 Steps

This 9×9 board rates as hard (difficulty score 1002). Solving it from scratch takes 19 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 7, 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, 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 3 touching neighbours.
5. Now, place a marker at C3. Region has exactly one open cell left. Placing here clears the rest of row 3, column C, and its region. Placing here also clears its 2 touching neighbours.
6. From there, 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.
7. Following that, 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.
8. First, every open cell in row 4 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, place a marker at I4. Column 9 has exactly one open cell left. Placing here clears the rest of row 4, column I, and its region. Placing here also clears its 1 touching neighbour.
10. Then, every open cell in row 5 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.
11. After that, 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.
12. Now, that one can't be the marker: at F1 it would force H2 (the last open cell in region 2), then G8 (the last open cell in region 6), then E6 (the last open cell in region 7), and row 5 would be left with no open cell for its marker.
13. From there, every remaining candidate in this region touches H2, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
14. Following that, if H1 were the marker, it would force E6 (the last open cell in row 6), and column D would end up with no open cell for its marker, which can't happen. So it can't go there.
15. First, 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.
16. Next, place a marker at E2. Region has exactly one open cell left. Placing here clears the rest of row 2, column E, and its region.
17. Then, place a marker at D8. Region has exactly one open cell left. Placing here clears the rest of row 8, column D, and its region.
18. After that, place a marker at F5. Region has exactly one open cell left.
19. Finally, place a marker at H6. Region has exactly one open cell left.

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