An Expert 10×10 Puzzle Solved with Forced Chain in 31 Steps

This 10×10 board rates as expert (difficulty score 1434). Solving it from scratch takes 31 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 columns I and J; 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.
3. Then, 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.
4. After that, together, two regions have open cells only in columns E and F; 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.
5. Now, every remaining candidate in this region touches C10, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
6. From there, if H1 were the marker, it would force J2 (the last open cell in region 4), then I4 (the last open cell in region 5), then G5 (the last open cell in region 7), and the chain continues, and row 8 would end up with no open cell for its marker, which can't happen. So it can't go there.
7. Following 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.
8. First, every open cell left in this region sits in column J, so its marker has to land there; that clears every other open cell in the column.
9. 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.
10. Then, together, two regions have open cells only in rows 5 and 6; 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.
11. After that, every remaining candidate in this region touches C8, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
12. Now, marking J1 would force H2 (the last open cell in region 3), then I4 (the last open cell in region 5), then G5 (the last open cell in region 7), and the chain continues, and then row 8 would be left with no open cell for its marker. So J1 can't be the marker there.
13. 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. Placing here also clears its 1 touching neighbour.
14. Following that, place a marker at G1. Region has exactly one open cell left. Placing here clears the rest of row 1, column G, and its region.
15. 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.
16. Next, place a marker at H6. Region has exactly one open cell left. Placing here clears the rest of row 6, column H, and its region.
17. Then, marking F3 would force E9 (the last open cell in region 6), and then region 10 would be left with no open cell for its marker. So F3 can't be the marker there.
18. After that, place a marker at E3. Region has exactly one open cell left. Placing here clears the rest of row 3, column E, and its region.
19. Now, if C5 were the marker, it would force D9 and D10 cleared (every open cell left in this region sits in column D, so its marker has to land there), then B9 (the last open cell in region 10), and row 10 would end up with no open cell for its marker, which can't happen. So it can't go there.
20. From there, that one can't be the marker: at D5 it would force C7 (the last open cell in region 8), then F9 (the last open cell in region 6), and region 10 would be left with no open cell for its marker.
21. Following that, together, two regions have open cells only in columns A and B; 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.
22. First, marking A7 would force B5 (the last open cell in region 1), then D8 (the last open cell in region 8), and then row 10 would be left with no open cell for its marker. So A7 can't be the marker there.
23. Next, if B7 were the marker, it would force A5 (the last open cell in region 1), then D8 (the last open cell in region 8), and row 10 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 A5 it would force C9 cleared (every remaining candidate in this region touches C9), then C7 (the last open cell in column C), and row 8 would be left with no open cell for its marker.
25. After that, 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.
26. Now, marking D7 would force F9 (the last open cell in region 6), and then column C would be left with no open cell for its marker. So D7 can't be the marker there.
27. From there, that one can't be the marker: at F7 it would force D8 (the last open cell in region 8), and column C would be left with no open cell for its marker.
28. Following that, place a marker at F9. Region has exactly one open cell left. Placing here clears the rest of row 9, column F, and its region.
29. First, place a marker at D10. Region has exactly one open cell left. Placing here clears the rest of row 10, column D, and its region.
30. Next, place a marker at C7. Region has exactly one open cell left.
31. Finally, place a marker at A8. Region has exactly one open cell left.

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