A Severe 10×10 Puzzle Solved with Forced Chain in 41 Steps

This 10×10 board rates as severe (difficulty score 2011). Solving it from scratch takes 41 logical steps, using 6 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Paired regions, Forced chain. Every step below is forced: nothing here is a guess.

1. First, marking A1 would force J6 (the last open cell in region 6), then E7 (the last open cell in column E), then F10 (the last open cell in column F), and the chain continues, and then column D would be left with no open cell for its marker. So A1 can't be the marker there.
2. Next, marking G1 would force A8 (the last open cell in region 8), then D7 (the last open cell in region 7), then J6 (the last open cell in region 6), and the chain continues, and then row 3 would be left with no open cell for its marker. So G1 can't be the marker there.
3. Then, if H1 were the marker, it would force A8 (the last open cell in region 8), then D7 (the last open cell in region 7), then J6 (the last open cell in region 6), and the chain continues, and row 9 would end up with no open cell for its marker, which can't happen. So it can't go there.
4. After that, if F2 were the marker, region 6 would end up with no open cell for its marker, which can't happen. So it can't go there.
5. Now, marking H2 would force A8 (the last open cell in region 8), then D7 (the last open cell in region 7), then J6 (the last open cell in region 6), and then row 3 would be left with no open cell for its marker. So H2 can't be the marker there.
6. From there, marking F3 would force H4 (the last open cell in region 4), then J5 (the last open cell in row 5), and then row 6 would be left with no open cell for its marker. So F3 can't be the marker there.
7. Following that, marking A4 would force J6 (the last open cell in region 6), then F10 (the last open cell in region 10), and then row 8 would be left with no open cell for its marker. So A4 can't be the marker there.
8. First, that one can't be the marker: at A5 it would force J6 (the last open cell in region 6), then I4 (the last open cell in region 5), then F1 (the last open cell in region 2), and the chain continues, and row 8 would be left with no open cell for its marker.
9. Next, that one can't be the marker: at G5 it would force H3 (the last open cell in region 4), then F10 (the last open cell in region 10), and region 9 would be left with no open cell for its marker.
10. Then, marking H5 would force A8 (the last open cell in region 8), then D7 (the last open cell in region 7), then J6 (the last open cell in region 6), and the chain continues, and then row 9 would be left with no open cell for its marker. So H5 can't be the marker there.
11. After that, that one can't be the marker: at A2 it would force J6 (the last open cell in region 6), then I4 (the last open cell in region 5), then F1 (the last open cell in region 2), and the chain continues, and row 8 would be left with no open cell for its marker.
12. Now, if A3 were the marker, it would force J6 (the last open cell in region 6), then I4 (the last open cell in region 5), then F1 (the last open cell in region 2), and region 4 would end up with no open cell for its marker, which can't happen. So it can't go there.
13. From there, if I2 were the marker, it would force G3 (the last open cell in row 3), then F10 (the last open cell in region 10), and region 9 would end up with no open cell for its marker, which can't happen. So it can't go there.
14. Following that, marking C3 would force G2 (the last open cell in row 2), then J6 (the last open cell in row 6), then I1 (the last open cell in region 2), and then row 4 would be left with no open cell for its marker. So C3 can't be the marker there.
15. First, if B4 were the marker, it would force G2 (the last open cell in row 2), then J3 (the last open cell in row 3), then I1 (the last open cell in region 2), and the chain continues, and row 6 would end up with no open cell for its marker, which can't happen. So it can't go there.
16. Next, if A6 were the marker, region 7 would end up with no open cell for its marker, which can't happen. So it can't go there.
17. Then, marking F6 would force H7 (the last open cell in region 6), then A8 (the last open cell in region 8), and then region 7 would be left with no open cell for its marker. So F6 can't be the marker there.
18. After that, if G6 were the marker, it would force A8 (the last open cell in region 8), then D7 (the last open cell in region 7), and region 6 would end up with no open cell for its marker, which can't happen. So it can't go there.
19. Now, that one can't be the marker: at I1 it would force A8 (the last open cell in region 8), then D7 (the last open cell in region 7), then J6 (the last open cell in region 6), and column H would be left with no open cell for its marker.
20. From there, marking J1 would force A8 (the last open cell in region 8), then D7 (the last open cell in region 7), and then region 6 would be left with no open cell for its marker. So J1 can't be the marker there.
21. Following that, that one can't be the marker: at D2 it would force F1 (the last open cell in row 1), then A8 (the last open cell in region 8), and region 7 would be left with no open cell for its marker.
22. First, marking E2 would immediately leave row 1 with no open cell for its marker, so it can't be the marker there.
23. Next, that one can't be the marker: at G2 it would force I3 (the last open cell in region 2), then D4 (the last open cell in row 4), then J5 (the last open cell in row 5), and row 6 would be left with no open cell for its marker.
24. Then, if B1 were the marker, it would force J2 (the last open cell in row 2), then G3 (the last open cell in region 4), then F10 (the last open cell in region 10), and region 9 would end up with no open cell for its marker, which can't happen. So it can't go there.
25. After that, that one can't be the marker: at C1 it would force J2 (the last open cell in row 2), then G3 (the last open cell in region 4), then F10 (the last open cell in region 10), and region 9 would be left with no open cell for its marker.
26. Now, that one can't be the marker: at J2 it would force G3 (the last open cell in region 4), then F10 (the last open cell in region 10), and region 9 would be left with no open cell for its marker.
27. From there, marking D1 would force I3 (the last open cell in region 2), then B2 (the last open cell in row 2), then J5 (the last open cell in row 5), and then row 6 would be left with no open cell for its marker. So D1 can't be the marker there.
28. Following that, if E1 were the marker, it would force I3 (the last open cell in region 2), then B2 (the last open cell in row 2), then J5 (the last open cell in row 5), and row 6 would end up with no open cell for its marker, which can't happen. So it can't go there.
29. First, place a marker at F1. Row 1 has exactly one open cell left. Placing here clears the rest of row 1, column F, and its region.
30. Next, together, two regions have open cells only in columns G and H; 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.
31. Then, every open cell left in this region sits in column E, so its marker has to land there; that clears every other open cell in the column.
32. After that, together, two regions have open cells only in rows 9 and 10; 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.
33. Now, place a marker at A8. Region has exactly one open cell left. Placing here clears the rest of row 8, column A, and its region. Placing here also clears its 1 touching neighbour.
34. From there, place a marker at D7. Region has exactly one open cell left. Placing here clears the rest of row 7, column D, and its region. Placing here also clears its 1 touching neighbour.
35. Following that, place a marker at J6. Region has exactly one open cell left. Placing here clears the rest of row 6, column J, and its region. Placing here also clears its 1 touching neighbour.
36. First, 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. Placing here also clears its 1 touching neighbour.
37. Next, place a marker at G3. Region has exactly one open cell left. Placing here clears the rest of row 3, column G, and its region.
38. Then, place a marker at C2. Region has exactly one open cell left. Placing here clears the rest of row 2, column C, and its region.
39. After that, place a marker at B5. Region has exactly one open cell left.
40. Now, place a marker at H9. Region has exactly one open cell left. Placing here clears the rest of row 9, column H, and its region.
41. Finally, place a marker at E10. Region has exactly one open cell left.

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