An Expert 11×11 Puzzle Solved with Forced Chain in 40 Steps

This 11×11 board rates as expert (difficulty score 1853). Solving it from scratch takes 40 logical steps, using 8 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Line confinement, Paired regions, Shape squeeze, Forced chain. Every step below is forced: nothing here is a guess.

1. First, every remaining candidate in this region touches A10, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
2. Next, every open cell left in this region sits in row 11, so its marker has to land there; that clears every other open cell in the row.
3. Then, every remaining candidate in this region touches B10, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
4. After that, 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.
5. Now, together, two regions have open cells only in rows 8 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.
6. From there, marking A1 would force B9 (the last open cell in region 10), then C11 (the last open cell in region 11), and then region 5 would be left with no open cell for its marker. So A1 can't be the marker there.
7. Following that, if B1 were the marker, it would force A9 (the last open cell in region 10), then C11 (the last open cell in region 11), and region 5 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 C1 it would force E2, F2 and K2 cleared (every open cell left in this region sits in row 2, so its marker has to land there), then B11 and A11 cleared (together, two regions have open cells only in columns B and A), and row 11 would be left with no open cell for its marker.
9. Next, every open cell in row 1 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.
10. Then, that one can't be the marker: at A2 it would force B9 (the last open cell in region 10), then C11 (the last open cell in region 11), and region 5 would be left with no open cell for its marker.
11. After that, marking B2 would force A9 (the last open cell in region 10), then C11 (the last open cell in region 11), and then region 5 would be left with no open cell for its marker. So B2 can't be the marker there.
12. Now, if C2 were the marker, it would force B11 and A11 cleared (together, two regions have open cells only in columns B and A), and row 11 would end up with no open cell for its marker, which can't happen. So it can't go there.
13. From there, if E1 were the marker, it would force K2 (the last open cell in row 2), then H5, I5, F6, and 6 more cleared (every open cell in column J belongs to the same region, so that region's marker has to be somewhere in this column), then H4 (the last open cell in column H), and the chain continues, and column I would end up with no open cell for its marker, which can't happen. So it can't go there.
14. Following that, that one can't be the marker: at F1 it would force K2 (the last open cell in row 2), then H5, I5, G6, and 5 more cleared (every open cell in column J belongs to the same region, so that region's marker has to be somewhere in this column), then H4 (the last open cell in column H), and the chain continues, and column I would be left with no open cell for its marker.
15. First, if A3 were the marker, it would force B9 (the last open cell in region 10), then C11 (the last open cell in region 11), and region 5 would end up with no open cell for its marker, which can't happen. So it can't go there.
16. Next, that one can't be the marker: at B3 it would force A9 (the last open cell in region 10), then C11 (the last open cell in region 11), and region 5 would be left with no open cell for its marker.
17. Then, marking C3 would force B11 and A11 cleared (together, two regions have open cells only in columns B and A), and then row 11 would be left with no open cell for its marker. So C3 can't be the marker there.
18. After that, if D3 were the marker, it would force K2 (the last open cell in row 2), then G8 (the last open cell in row 8), then A5 and C5 cleared (every open cell in row 4 belongs to the same region, so that region's marker has to be somewhere in this row), and the chain continues, and column I 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 E3 it would force K2 (the last open cell in row 2), then A5, C5, D5, and 1 more cleared (every open cell in row 4 belongs to the same region, so that region's marker has to be somewhere in this row), then H5, I5, F6, and 6 more cleared (every open cell in column J belongs to the same region, so that region's marker has to be somewhere in this column), and the chain continues, and column I would be left with no open cell for its marker.
20. From there, marking F3 would force K2 (the last open cell in row 2), then A5, C5, D5, and 1 more cleared (every open cell in row 4 belongs to the same region, so that region's marker has to be somewhere in this row), then H5, I5, G6, and 5 more cleared (every open cell in column J belongs to the same region, so that region's marker has to be somewhere in this column), and the chain continues, and then column I would be left with no open cell for its marker. So F3 can't be the marker there.
21. Following that, marking D1 would force G8 (the last open cell in row 8), then K2, J4, K4, and 1 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), then F2 (the last open cell in row 2), and the chain continues, and then row 11 would be left with no open cell for its marker. So D1 can't be the marker there.
22. First, marking A4 would force B9 (the last open cell in region 10), then C11 (the last open cell in region 11), and then region 5 would be left with no open cell for its marker. So A4 can't be the marker there.
23. Next, if B4 were the marker, it would force A9 (the last open cell in region 10), then C11 (the last open cell in region 11), and region 5 would end up with no open cell for its marker, which can't happen. So it can't go there.
24. Then, marking G1 would force D8 (the last open cell in row 8), then K2, J4, K4, and 1 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), then E2 (the last open cell in row 2), and the chain continues, and then row 11 would be left with no open cell for its marker. So G1 can't be the marker there.
25. After that, marking E2 would force J4, K4 and J5 cleared (every open cell in row 3 belongs to the same region, so that region's marker has to be somewhere in this row), then A5, C5, D5, and 1 more cleared (every open cell in row 4 belongs to the same region, so that region's marker has to be somewhere in this row), then C6, C7, C11, and 1 more cleared (together, two regions have open cells only in columns C and D), and the chain continues, and then row 11 would be left with no open cell for its marker. So E2 can't be the marker there.
26. Now, that one can't be the marker: at C4 it would force A11 and B11 cleared (together, two regions have open cells only in columns A and B), and row 11 would be left with no open cell for its marker.
27. From there, marking J1 would force F2 (the last open cell in row 2), then K4 cleared (every open cell in row 3 belongs to the same region, so that region's marker has to be somewhere in this row), then A5, C5, D5, and 1 more cleared (every open cell in row 4 belongs to the same region, so that region's marker has to be somewhere in this row), and the chain continues, and then row 11 would be left with no open cell for its marker. So J1 can't be the marker there.
28. Following that, if K1 were the marker, it would force F2 (the last open cell in row 2), then J4 and J5 cleared (every open cell in row 3 belongs to the same region, so that region's marker has to be somewhere in this row), then A5, C5, D5, and 1 more cleared (every open cell in row 4 belongs to the same region, so that region's marker has to be somewhere in this row), and the chain continues, and row 11 would end up with no open cell for its marker, which can't happen. So it can't go there.
29. First, if F2 were the marker, it would force J4, K4 and J5 cleared (every open cell in row 3 belongs to the same region, so that region's marker has to be somewhere in this row), then A5, C5, D5, and 1 more cleared (every open cell in row 4 belongs to the same region, so that region's marker has to be somewhere in this row), then D8, D10 and E10 cleared (together, two regions have open cells only in columns D and E), and the chain continues, and row 11 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 K2. Row 2 has exactly one open cell left. Placing here clears the rest of row 2, column K, and its region.
31. Then, place a marker at G3. Row 3 has exactly one open cell left. Placing here clears the rest of row 3, column G, and its region.
32. After that, place a marker at I10. Region has exactly one open cell left. Placing here clears the rest of row 10, column I, and its region.
33. Now, place a marker at H1. Region has exactly one open cell left. Placing here clears the rest of row 1, column H, and its region.
34. From there, 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. Placing here also clears its 2 touching neighbours.
35. Following that, place a marker at E4. Row 4 has exactly one open cell left. Placing here clears the rest of row 4, column E, and its region. Placing here also clears its 1 touching neighbour.
36. First, place a marker at F7. Region has exactly one open cell left. Placing here clears the rest of row 7, column F, and its region.
37. Next, 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.
38. Then, place a marker at B5. Region has exactly one open cell left. Placing here clears the rest of row 5, column B, and its region.
39. After that, 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.
40. Finally, place a marker at C11. Region has exactly one open cell left.

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