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

This 10×10 board rates as expert (difficulty score 1572). Solving it from scratch takes 31 logical steps, using 6 techniques: Single cell, Row/column exclusion, Adjacency clear, Line confinement, Shape squeeze, Forced chain. Every step below is forced: nothing here is a guess.

1. First, every remaining candidate in this region touches B9, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
2. Next, marking A1 would force B10 (the last open cell in region 9), and then region 7 would be left with no open cell for its marker. So A1 can't be the marker there.
3. Then, if B1 were the marker, it would force A3, A4, A5, and 2 more cleared (every open cell left in this region sits in column A, so its marker has to land there), then C9 (the last open cell in region 7), then D6 (the last open cell in region 4), and region 8 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: at C1 it would force I3, J3 and I4 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 B4, D4, E4, 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), then B3, B5, A3, and 3 more cleared (together, two regions have open cells only in columns B and A), and the chain continues, and region 8 would be left with no open cell for its marker.
5. Now, that one can't be the marker: at F1 it would force G3, H3, G4, 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 B4, C4, D4, 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), then J4, H5, J5, and 8 more cleared (every open cell in column I belongs to the same region, so that region's marker has to be somewhere in this column), and column J would be left with no open cell for its marker.
6. From there, marking G1 would force F3, H3 and H4 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 B4, C4, D4, and 3 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 J4, H5, J5, and 8 more cleared (every open cell in column I belongs to the same region, so that region's marker has to be somewhere in this column), and then column J would be left with no open cell for its marker. So G1 can't be the marker there.
7. Following that, if H1 were the marker, it would force F3, G3 and G4 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 B4, C4, D4, and 3 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 J4, J5, J6, and 6 more cleared (every open cell in column I belongs to the same region, so that region's marker has to be somewhere in this column), and column J would end up with no open cell for its marker, which can't happen. So it can't go there.
8. First, marking J1 would force F3, G3, H3, 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), then B4, C4, D4, and 3 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 A4 (the last open cell in row 4), and the chain continues, and then region 7 would be left with no open cell for its marker. So J1 can't be the marker there.
9. Next, that one can't be the marker: at A2 it would force B10 (the last open cell in region 9), and region 7 would be left with no open cell for its marker.
10. Then, marking B2 would force I1 (the last open cell in row 1), then A4, A5, A6, and 1 more cleared (every open cell left in this region sits in column A, so its marker has to land there), then C9 (the last open cell in region 7), and the chain continues, and then region 8 would be left with no open cell for its marker. So B2 can't be the marker there.
11. After that, if C2 were the marker, it would force I1 (the last open cell in row 1), then B4, D4, E4, 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), then H5, H9, F10, and 2 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 F would end up with no open cell for its marker, which can't happen. So it can't go there.
12. Now, that one can't be the marker: at D2 it would force I1 (the last open cell in row 1), then B4, C4, E4, 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 H5, H9, F10, and 2 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 F would be left with no open cell for its marker.
13. From there, marking E2 would force I1 (the last open cell in row 1), then B4, C4, D4, 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), then H5, H9, F10, and 2 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 F would be left with no open cell for its marker. So E2 can't be the marker there.
14. Following that, that one can't be the marker: at G2 it would force H4 cleared (every open cell in row 1 belongs to the same region, so that region's marker has to be somewhere in this row), then B4, C4, D4, and 3 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 J4, H5, J5, and 8 more cleared (every open cell in column I belongs to the same region, so that region's marker has to be somewhere in this column), and column J would be left with no open cell for its marker.
15. First, marking H2 would force F3 and G4 cleared (every open cell in row 1 belongs to the same region, so that region's marker has to be somewhere in this row), then B4, C4, D4, and 3 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 J4, J5, J6, and 6 more cleared (every open cell in column I belongs to the same region, so that region's marker has to be somewhere in this column), and then column J would be left with no open cell for its marker. So H2 can't be the marker there.
16. Next, if I2 were the marker, it would force F3, G3, G4, and 1 more cleared (every open cell in row 1 belongs to the same region, so that region's marker has to be somewhere in this row), then B4, C4, D4, and 3 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 H5, H9, F10, and 2 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 F would end up with no open cell for its marker, which can't happen. So it can't go there.
17. Then, marking D1 would force J2 (the last open cell in row 2), then B4, C4, E4, 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 A4 (the last open cell in row 4), and the chain continues, and then region 7 would be left with no open cell for its marker. So D1 can't be the marker there.
18. After that, if E1 were the marker, it would force J2 (the last open cell in row 2), then B4, C4, D4, 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), then A4 (the last open cell in row 4), 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.
19. Now, place a marker at I1. Row 1 has exactly one open cell left. Placing here clears the rest of row 1, column I, and its region.
20. From there, place a marker at F2. Row 2 has exactly one open cell left. Placing here clears the rest of row 2, column F, and its region. Placing here also clears its 1 touching neighbour.
21. Following that, every open cell in row 3 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.
22. First, every open cell in column J 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.
23. Next, every open cell in column H 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.
24. Then, place a marker at G9. Column 7 has exactly one open cell left. Placing here clears the rest of row 9, column G, and its region. Placing here also clears its 1 touching neighbour.
25. After that, place a marker at E7. Column 5 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.
26. Now, 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.
27. From there, place a marker at B8. Region has exactly one open cell left. Placing here clears the rest of row 8, column B, and its region.
28. Following that, place a marker at A10. Region has exactly one open cell left. Placing here clears the rest of row 10, column A, and its region.
29. First, place a marker at C5. Region has exactly one open cell left. Placing here clears the rest of row 5, column C, and its region.
30. Next, place a marker at D3. Region has exactly one open cell left.
31. Finally, place a marker at J4. Region has exactly one open cell left.

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