A Hard 11×11 Puzzle Solved with Forced Chain in 21 Steps

This 11×11 board rates as hard (difficulty score 1102). Solving it from scratch takes 21 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, 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.
2. Next, together, two regions have open cells only in rows 3 and 4; 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, that one can't be the marker: at C1 it would force J2 (the last open cell in region 4), then B3, B5, B6, and 1 more cleared (every open cell left in this region sits in column B, so its marker has to land there), then A5, A6, A7, and 4 more cleared (every open cell left in this region sits in column A, so its marker has to land there), and region 11 would be left with no open cell for its marker.
4. After that, if A3 were the marker, it would force B10 (the last open cell in region 11), then C5 and C6 cleared (every open cell left in this region sits in column C, so its marker has to land there), then D5 (the last open cell in region 5), and the chain continues, and region 10 would end up with no open cell for its marker, which can't happen. So it can't go there.
5. Now, that one can't be the marker: at B3 it would force C5 and C6 cleared (every open cell left in this region sits in column C, so its marker has to land there), then A5, A6 and A7 cleared (every open cell left in this region sits in column A, so its marker has to land there), then D5 (the last open cell in region 5), and the chain continues, and region 10 would be left with no open cell for its marker.
6. From there, marking C3 would force B5, B6 and B10 cleared (every open cell left in this region sits in column B, so its marker has to land there), then A5, A6 and A7 cleared (every open cell left in this region sits in column A, so its marker has to land there), then D5 (the last open cell in region 5), and the chain continues, and then region 10 would be left with no open cell for its marker. So C3 can't be the marker there.
7. Following that, every open cell left in this region sits in row 4, so its marker has to land there; that clears every other open cell in the row.
8. First, every remaining candidate in this region touches B5, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
9. Next, that one can't be the marker: at C4 it would force B6 and B10 cleared (every open cell left in this region sits in column B, so its marker has to land there), then A8, A9, A10, and 1 more cleared (every open cell left in this region sits in column A, so its marker has to land there), and region 11 would be left with no open cell for its marker.
10. Then, place a marker at A4. Region has exactly one open cell left. Placing here clears the rest of row 4, column A, and its region.
11. After that, place a marker at B10. Region has exactly one open cell left. Placing here clears the rest of row 10, column B, and its region. Placing here also clears its 2 touching neighbours.
12. Now, every open cell left in this region sits in column C, so its marker has to land there; that clears every other open cell in the column.
13. From there, 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. Placing here also clears its 1 touching neighbour.
14. 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 2 touching neighbours.
15. First, 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. 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 1 touching neighbour.
17. Then, place a marker at C8. Region has exactly one open cell left. Placing here clears the rest of row 8, column C, and its region.
18. After that, 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.
19. Now, place a marker at F1. Region has exactly one open cell left. Placing here clears the rest of row 1, column F, and its region.
20. From there, 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.
21. Finally, place a marker at K11. Region has exactly one open cell left.

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