An Expert 9×9 Puzzle Solved with Forced Chain in 27 Steps

This 9×9 board rates as expert (difficulty score 1299). Solving it from scratch takes 27 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 column A, so its marker has to land there; that clears every other open cell in the column.
2. Next, together, two regions have open cells only in columns B and C; 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.
3. Then, 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.
4. After that, every remaining candidate in this region touches B7, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
5. Now, every remaining candidate in this region touches F7, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
6. From there, that one can't be the marker: at C1 it would force I2 (the last open cell in region 3), then E9, F3, F5, and 2 more cleared (together, two regions have open cells only in columns E and F), then A7 cleared (every remaining candidate in this region touches A7), and the chain continues, and region 9 would be left with no open cell for its marker.
7. Following that, if E1 were the marker, it would force I2 (the last open cell in region 3), then B5 (the last open cell in region 1), then F8 (the last open cell in region 9), and the chain continues, and column A would end up with no open cell for its marker, which can't happen. So it can't go there.
8. First, that one can't be the marker: at F1 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), and region 9 would be left with no open cell for its marker.
9. Next, 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.
10. Then, marking G1 would force F3, H3, H4, and 6 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), then H8 (the last open cell in column H), then D9 (the last open cell in row 9), and the chain continues, and then column A would be left with no open cell for its marker. So G1 can't be the marker there.
11. After that, if C2 were the marker, it would force E9, F3, F5, and 2 more cleared (together, two regions have open cells only in columns E and F), then A7 cleared (every remaining candidate in this region touches A7), then D6, E6, G6, and 8 more cleared (together, two regions have open cells only in rows 6 and 8), and the chain continues, and region 9 would end up with no open cell for its marker, which can't happen. So it can't go there.
12. Now, 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.
13. From there, if H1 were the marker, it would force B5 (the last open cell in region 1), then E3, E4 and F4 cleared (every open cell in row 2 belongs to the same region, so that region's marker has to be somewhere in this row), then G4, I4, I6, and 6 more cleared (every open cell in row 3 belongs to the same region, so that region's marker has to be somewhere in this row), and row 4 would end up with no open cell for its marker, which can't happen. So it can't go there.
14. Following that, every open cell left in this region sits in column I, so its marker has to land there; that clears every other open cell in the column.
15. First, that one can't be the marker: at I1 it would force B5 (the last open cell in region 1), then E3, E4 and F4 cleared (every open cell in row 2 belongs to the same region, so that region's marker has to be somewhere in this row), then G4, H4, H6, and 5 more cleared (every open cell in row 3 belongs to the same region, so that region's marker has to be somewhere in this row), and row 4 would be left with no open cell for its marker.
16. Next, place a marker at I2. Region has exactly one open cell left. Placing here clears the rest of row 2, column I, and its region. Placing here also clears its 1 touching neighbour.
17. Then, place a marker at B1. Row 1 has exactly one open cell left. Placing here clears the rest of row 1, column B, and its region.
18. After that, 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.
19. Now, every remaining candidate in this region touches H7, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
20. From there, if G3 were the marker, it would force H8 (the last open cell in region 6), and column F would end up with no open cell for its marker, which can't happen. So it can't go there.
21. Following that, place a marker at E3. Row 3 has exactly one open cell left. Placing here clears the rest of row 3, column E, and its region.
22. First, place a marker at F8. Region has exactly one open cell left. Placing here clears the rest of row 8, column F, and its region. Placing here also clears its 2 touching neighbours.
23. Next, 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. Placing here also clears its 1 touching neighbour.
24. Then, place a marker at A7. Region has exactly one open cell left. Placing here clears the rest of row 7, column A, and its region.
25. After that, place a marker at C5. Region has exactly one open cell left.
26. Now, place a marker at D9. Region has exactly one open cell left. Placing here clears the rest of row 9, column D, and its region.
27. Finally, place a marker at H4. Region has exactly one open cell left.

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