An Expert 11×11 Puzzle Solved with Forced Chain in 23 Steps

This 11×11 board rates as expert (difficulty score 1138). Solving it from scratch takes 23 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 open cell in column A belongs to the same region, so that region's marker has to be somewhere in this column; that clears every other open cell in the region.
2. Next, together, two regions have open cells only in rows 1 and 2; 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.
3. Then, if H1 were the marker, it would force J2 (the last open cell in region 3), then I4 (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.
4. After that, that one can't be the marker: place it at I1, and row 2 would be left with no open cell for its marker.
5. Now, marking J1 would force K5, K6, K7, and 4 more cleared (every open cell left in this region sits in column K, so its marker has to land there), then A3, C3, D3, and 10 more cleared (together, two regions have open cells only in rows 3 and 4), then H2, H5, H8, and 8 more cleared (together, two regions have open cells only in columns H and I), and the chain continues, and then region 10 would be left with no open cell for its marker. So J1 can't be the marker there.
6. From there, if K1 were the marker, it would force J3, J7, J8, and 3 more cleared (every open cell left in this region sits in column J, so its marker has to land there), then H2, H4, H5, and 9 more cleared (together, two regions have open cells only in columns H and I), then G2 (the last open cell in region 2), and the chain continues, and row 10 would end up with no open cell for its marker, which can't happen. So it can't go there.
7. Following that, place a marker at G1. Row 1 has exactly one open cell left. Placing here clears the rest of row 1, column G, and its region.
8. First, every remaining candidate in this region touches I3 and J3, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
9. Next, every remaining candidate in this region touches H4, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
10. Then, if I2 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.
11. After that, place a marker at J2. Region has exactly one open cell left. Placing here clears the rest of row 2, column J, and its region. Placing here also clears its 1 touching neighbour.
12. Now, place a marker at K4. Region has exactly one open cell left. Placing here clears the rest of row 4, column K, and its region.
13. From there, place a marker at H3. Region has exactly one open cell left. Placing here clears the rest of row 3, column H, and its region.
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, 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. Placing here also clears its 1 touching neighbour.
16. Next, place a marker at E7. Region has exactly one open cell left. Placing here clears the rest of row 7, column E, and its region. Placing here also clears its 2 touching neighbours.
17. Then, place a marker at I8. Region has exactly one open cell left. Placing here clears the rest of row 8, column I, and its region.
18. After that, place a marker at C6. Region has exactly one open cell left. Placing here clears the rest of row 6, column C, and its region.
19. Now, 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.
20. From there, 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.
21. Following that, place a marker at B9. Column 2 has exactly one open cell left. Placing here clears the rest of row 9, column B, and its region. Placing here also clears its 1 touching neighbour.
22. First, place a marker at A11. Region has exactly one open cell left. Placing here clears the rest of row 11, column A, and its region.
23. Finally, place a marker at D10. Region has exactly one open cell left.

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