An Expert 8×8 Puzzle Solved with Forced Chain in 31 Steps

This 8×8 board rates as expert (difficulty score 1600). Solving it from scratch takes 31 logical steps, using 7 techniques: Single cell, Row/column exclusion, Region confinement, Line confinement, Paired regions, Shape squeeze, Forced chain. Every step below is forced: nothing here is a guess.

1. First, that one can't be the marker: at C1 it would force B5, B6 and B7 cleared (every open cell in column A belongs to the same region, so that region's marker has to be somewhere in this column), then B8 (the last open cell in column B), then A6 (the last open cell in region 5), and the chain continues, and row 3 would be left with no open cell for its marker.
2. Next, marking G1 would force A3, B3, C3, and 5 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 H3 (the last open cell in row 3), then F6 (the last open cell in region 6), and the chain continues, and then region 7 would be left with no open cell for its marker. So G1 can't be the marker there.
3. Then, if C2 were the marker, it would force B5, B6 and B7 cleared (every open cell in column A belongs to the same region, so that region's marker has to be somewhere in this column), then B8 (the last open cell in column B), then A6 (the last open cell in region 5), and the chain continues, and row 3 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 D2 it would force H1, H3 and F5 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 F1 (the last open cell in row 1), and row 3 would be left with no open cell for its marker.
5. Now, marking E2 would force G3 (the last open cell in region 2), then H1 (the last open cell in row 1), then F6 (the last open cell in region 6), and then region 8 would be left with no open cell for its marker. So E2 can't be the marker there.
6. From there, marking C3 would force H1, G2, H2, 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 F2 (the last open cell in row 2), and then row 1 would be left with no open cell for its marker. So C3 can't be the marker there.
7. Following that, if D3 were the marker, it would force H1, G2, H2, 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 F2 (the last open cell in row 2), and row 1 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 E3 it would force A5, B5, F5, and 2 more cleared (every open cell left in this region sits in row 5, so its marker has to land there), then C4, C6 and D6 cleared (every remaining candidate in this region touches C4 and C6 and D6), then F7 cleared (every remaining candidate in this region touches F7), and the chain continues, and region 7 would be left with no open cell for its marker.
9. Next, if H1 were the marker, it would force A8, B8, C8, and 1 more cleared (every open cell left in this region sits in row 8, so its marker has to land there), then F7, F8 and G8 cleared (together, two regions have open cells only in columns F and G), then E8 (the last open cell in region 8), and the chain continues, and region 4 would end up with no open cell for its marker, which can't happen. So it can't go there.
10. Then, that one can't be the marker: at A2 it would force F3 and G3 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 H3 (the last open cell in row 3), then D4 (the last open cell in row 4), and the chain continues, and column B would be left with no open cell for its marker.
11. After that, marking B2 would force F3 and G3 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 H3 (the last open cell in row 3), then D4 (the last open cell in row 4), and the chain continues, and then column C would be left with no open cell for its marker. So B2 can't be the marker there.
12. Now, marking D1 would force H3, E4, F4, and 3 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 A4, B4, C4, 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), and then row 4 would be left with no open cell for its marker. So D1 can't be the marker there.
13. From there, that one can't be the marker: at F1 it would force H2 (the last open cell in row 2), then G8 cleared (every open cell left in this region sits in column G, so its marker has to land there), then E8 (the last open cell in region 8), and the chain continues, and region 4 would be left with no open cell for its marker.
14. Following that, if F2 were the marker, it would force A3, B3, A4, and 3 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 H3 (the last open cell in row 3), then D4 (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.
15. First, every open cell in row 2 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.
16. Next, every remaining candidate in this region touches G3, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
17. Then, marking A1 would force F3 (the last open cell in region 2), then H2 (the last open cell in region 3), then D4 (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 A1 can't be the marker there.
18. After that, if B1 were the marker, it would force F3 (the last open cell in region 2), then H2 (the last open cell in region 3), then D4 (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 E1. Row 1 has exactly one open cell left. Placing here clears the rest of row 1, column E, and its region.
20. From there, 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.
21. Following that, place a marker at D4. Row 4 has exactly one open cell left. Placing here clears the rest of row 4, column D, and its region.
22. First, every remaining candidate in this region touches G7, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
23. Next, marking H2 would force A8, B8 and C8 cleared (every open cell left in this region sits in row 8, so its marker has to land there), then F7 (the last open cell in region 7), and then row 8 would be left with no open cell for its marker. So H2 can't be the marker there.
24. Then, place a marker at G2. Region has exactly one open cell left. Placing here clears the rest of row 2, column G, and its region.
25. After that, together, two regions have open cells only in columns H 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.
26. Now, every open cell left in this region sits in row 8, so its marker has to land there; that clears every other open cell in the row.
27. From there, place a marker at F6. Column 6 has exactly one open cell left. Placing here clears the rest of row 6, column F, and its region.
28. Following that, place a marker at H7. Region has exactly one open cell left. Placing here clears the rest of row 7, column H, and its region.
29. First, 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.
30. Next, place a marker at A3. Region has exactly one open cell left.
31. Finally, place a marker at C8. Region has exactly one open cell left.

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