A Hard 9×9 Puzzle Solved with Forced Chain in 20 Steps

This 9×9 board rates as hard (difficulty score 1078). Solving it from scratch takes 20 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 7, 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 8, 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 row 9, so its marker has to land there; that clears every other open cell in the row.
4. After that, every open cell left in this region sits in row 6, so its marker has to land there; that clears every other open cell in the row.
5. Now, together, two regions have open cells only in columns E and F; 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.
6. From there, every remaining candidate in this region touches I2, 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 B5 and B7, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
8. First, place a marker at C7. Region has exactly one open cell left. Placing here clears the rest of row 7, column C, and its region. Placing here also clears its 1 touching neighbour.
9. Next, place a marker at A6. Region has exactly one open cell left. Placing here clears the rest of row 6, column A, and its region.
10. Then, marking D1 would immediately leave column B with no open cell for its marker, so it can't be the marker there.
11. After that, marking G1 would immediately leave row 2 with no open cell for its marker, so it can't be the marker there.
12. Now, if H1 were the marker, it would force D5 (the last open cell in region 1), and region 5 would end up with no open cell for its marker, which can't happen. So it can't go there.
13. From there, that one can't be the marker: at I1 it would force D5 (the last open cell in region 1), and region 5 would be left with no open cell for its marker.
14. Following that, place a marker at H2. Region has exactly one open cell left. Placing here clears the rest of row 2, column H, and its region. Placing here also clears its 2 touching neighbours.
15. First, place a marker at G8. Region has exactly one open cell left. Placing here clears the rest of row 8, column G, and its region. Placing here also clears its 1 touching neighbour.
16. Next, place a marker at E9. Region has exactly one open cell left. Placing here clears the rest of row 9, column E, and its region.
17. Then, place a marker at F5. Region has exactly one open cell left. Placing here clears the rest of row 5, column F, and its region.
18. After that, place a marker at B1. Region has exactly one open cell left. Placing here clears the rest of row 1, column B, and its region.
19. Now, 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.
20. Finally, place a marker at D3. Region has exactly one open cell left.

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