An Expert 11×11 Puzzle Solved with Forced Chain in 41 Steps

This 11×11 board rates as expert (difficulty score 1854). Solving it from scratch takes 41 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 1, so its marker has to land there; that clears every other open cell in the row.
2. Next, every remaining candidate in this region touches J2 and K2, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
3. Then, every remaining candidate in this region touches G8, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
4. After that, that one can't be the marker: at G2 it would force H4, H5, H6, and 3 more cleared (every open cell left in this region sits in column H, so its marker has to land there), then J4 cleared (every remaining candidate in this region touches J4), then I8 and I9 cleared (every remaining candidate in this region touches I8 and I9), and the chain continues, and region 5 would be left with no open cell for its marker.
5. Now, if I2 were the marker, it would force K1 (the last open cell in region 4), then J8 (the last open cell in region 8), then A9, B9, C9, and 3 more cleared (every open cell left in this region sits in row 9, so its marker has to land there), and the chain continues, and column F would end up with no open cell for its marker, which can't happen. So it can't go there.
6. From there, if G3 were the marker, it would force A5, B5, D5, and 2 more cleared (every open cell left in this region sits in row 5, so its marker has to land there), then H5, H6, H7, and 2 more cleared (every open cell left in this region sits in column H, so its marker has to land there), then I5 (the last open cell in region 3), and the chain continues, and region 8 would end up with no open cell for its marker, which can't happen. So it can't go there.
7. Following that, marking I3 would force J5, J6, J7, and 8 more cleared (together, two regions have open cells only in columns J and K), then G4, G5, G7, and 4 more cleared (together, two regions have open cells only in columns G and H), then F2, F4, F5, and 4 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 then region 7 would be left with no open cell for its marker. So I3 can't be the marker there.
8. First, if J3 were the marker, it would force K1 (the last open cell in region 4), then I6, I7, I10, and 1 more cleared (every open cell left in this region sits in column I, so its marker has to land there), then G4, G5, G7, and 5 more cleared (together, two regions have open cells only in columns G and H), and the chain continues, and column F would end up with no open cell for its marker, which can't happen. So it can't go there.
9. Next, that one can't be the marker: at K3 it would force J1 (the last open cell in region 4), then I4, I6, I7, and 2 more cleared (every open cell left in this region sits in column I, so its marker has to land there), then G4, G5, G7, and 5 more cleared (together, two regions have open cells only in columns G and H), and the chain continues, and column F would be left with no open cell for its marker.
10. Then, every remaining candidate in this region touches I4, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
11. After that, marking H2 would force I5 (the last open cell in region 3), then G9 (the last open cell in region 10), then A4, B4, A6, and 2 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 the chain continues, and then region 8 would be left with no open cell for its marker. So H2 can't be the marker there.
12. Now, that one can't be the marker: at C4 it would force A3, A5, A6, and 1 more 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 H3 (the last open cell in row 3), then G9 (the last open cell in region 10), and the chain continues, and region 7 would be left with no open cell for its marker.
13. From there, marking D4 would force A3, B3, A5, and 4 more 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 H3 (the last open cell in row 3), then G9 (the last open cell in region 10), and the chain continues, and then column E would be left with no open cell for its marker. So D4 can't be the marker there.
14. Following that, if E4 were the marker, it would force A3, B3, A5, and 4 more 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 H3 (the last open cell in row 3), then G9 (the last open cell in region 10), and the chain continues, and region 7 would end up with no open cell for its marker, which can't happen. So it can't go there.
15. First, marking G4 would force I5 (the last open cell in region 3), then H7, H10 and H11 cleared (every open cell left in this region sits in column H, so its marker has to land there), then A3, B3, A6, and 2 more cleared (every open cell in row 2 belongs to the same region, so that region's marker has to be somewhere in this row), and then row 3 would be left with no open cell for its marker. So G4 can't be the marker there.
16. Next, marking J4 would force K1 (the last open cell in region 4), then H8, H9, H10, and 1 more cleared (every open cell left in this region sits in column H, so its marker has to land there), then G9 (the last open cell in region 10), and the chain continues, and then region 7 would be left with no open cell for its marker. So J4 can't be the marker there.
17. Then, if K4 were the marker, it would force J1 (the last open cell in region 4), then I5, I10 and I11 cleared (every open cell left in this region sits in column I, so its marker has to land there), then H8, H9, H10, and 1 more cleared (every open cell left in this region sits in column H, so its marker has to land there), and the chain continues, and region 7 would end up with no open cell for its marker, which can't happen. So it can't go there.
18. After that, if D3 were the marker, it would force A4, B4, A5, and 4 more 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 H4 (the last open cell in row 4), then G9 (the last open cell in region 10), and the chain continues, and column E 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 A5 it would force H6, H7, H8, and 3 more cleared (every open cell left in this region sits in column H, so its marker has to land there), then G9 (the last open cell in region 10), then C3, E3, F3, and 2 more cleared (every open cell in row 2 belongs to the same region, so that region's marker has to be somewhere in this row), and the chain continues, and row 4 would be left with no open cell for its marker.
20. From there, marking B5 would force H6, H7, H8, and 3 more cleared (every open cell left in this region sits in column H, so its marker has to land there), then G9 (the last open cell in region 10), then C3, E3, F3, and 2 more cleared (every open cell in row 2 belongs to the same region, so that region's marker has to be somewhere in this row), and the chain continues, and then row 4 would be left with no open cell for its marker. So B5 can't be the marker there.
21. Following that, if C5 were the marker, it would force H6, H7, H8, and 3 more cleared (every open cell left in this region sits in column H, so its marker has to land there), then G9 (the last open cell in region 10), then A3, B3, A4, and 1 more cleared (every open cell in row 2 belongs to the same region, so that region's marker has to be somewhere in this row), and the chain continues, and row 4 would end up with no open cell for its marker, which can't happen. So it can't go there.
22. First, marking E5 would force H6, H7, H8, and 3 more cleared (every open cell left in this region sits in column H, so its marker has to land there), then G9 (the last open cell in region 10), then A3, B3, A4, and 4 more cleared (every open cell in row 2 belongs to the same region, so that region's marker has to be somewhere in this row), and the chain continues, and then row 4 would be left with no open cell for its marker. So E5 can't be the marker there.
23. Next, if F5 were the marker, it would force H6, H7, H8, and 3 more cleared (every open cell left in this region sits in column H, so its marker has to land there), then G9 (the last open cell in region 10), then A3, B3, A4, and 4 more cleared (every open cell in row 2 belongs to the same region, so that region's marker has to be somewhere in this row), and the chain continues, and row 4 would end up with no open cell for its marker, which can't happen. So it can't go there.
24. Then, that one can't be the marker: at G5 it would force H3 (the last open cell in region 3), and region 10 would be left with no open cell for its marker.
25. After that, if I5 were the marker, it would force J7, J9, J10, and 4 more cleared (together, two regions have open cells only in columns J and K), then G7, G10, G11, and 2 more cleared (together, two regions have open cells only in columns G and H), then F2, F3, F4, and 4 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 3 would end up with no open cell for its marker, which can't happen. So it can't go there.
26. Now, every open cell left in this region sits in column H, so its marker has to land there; that clears every other open cell in the column.
27. From there, place a marker at G9. Region has exactly one open cell left. Placing here clears the rest of row 9, column G, and its region. Placing here also clears its 2 touching neighbours.
28. Following that, every remaining candidate in this region touches J7, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
29. First, if K1 were the marker, it would force A8, B8, C8, and 2 more cleared (every open cell left in this region sits in row 8, so its marker has to land there), then J10, J11, I10, and 1 more cleared (together, two regions have open cells only in columns J and I), then F11 (the last open cell in region 11), and region 7 would end up with no open cell for its marker, which can't happen. So it can't go there.
30. Next, place a marker at J1. Region has exactly one open cell left. Placing here clears the rest of row 1, column J, and its region.
31. Then, together, two regions have open cells only in columns K and I; 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.
32. After that, place a marker at F11. Region has exactly one open cell left. Placing here clears the rest of row 11, column F, and its region. Placing here also clears its 1 touching neighbour.
33. Now, 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.
34. From there, place a marker at K7. Region has exactly one open cell left. Placing here clears the rest of row 7, column K, and its region.
35. Following that, place a marker at I6. Region has exactly one open cell left. Placing here clears the rest of row 6, column I, and its region. Placing here also clears its 1 touching neighbour.
36. First, place a marker at D5. Region has exactly one open cell left. Placing here clears the rest of row 5, column D, and its region.
37. Next, 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.
38. Then, 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.
39. After that, place a marker at H4. Region has exactly one open cell left. Placing here clears the rest of row 4, column H, and its region.
40. Now, place a marker at A2. Region has exactly one open cell left. Placing here clears the rest of row 2, column A, and its region.
41. Finally, place a marker at B10. Region has exactly one open cell left.

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