An Expert 8×8 Puzzle Solved with Forced Chain in 32 Steps

This 8×8 board rates as expert (difficulty score 1550). Solving it from scratch takes 32 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 B4, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
2. Next, every remaining candidate in this region touches B7, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
3. Then, marking A1 would force B5 (the last open cell in region 5), then C8 (the last open cell in region 7), and then region 8 would be left with no open cell for its marker. So A1 can't be the marker there.
4. After that, if B1 were the marker, it would force A6, A7 and A8 cleared (every open cell left in this region sits in column A, so its marker has to land there), then C8 (the last open cell in region 7), and region 8 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 F1 it would force G5, G6, E7, and 2 more cleared (every open cell in column H belongs to the same region, so that region's marker has to be somewhere in this column), then G3 (the last open cell in column G), then A6, A7, A8, and 2 more cleared (together, two regions have open cells only in columns A and B), and the chain continues, and region 8 would be left with no open cell for its marker.
6. From there, marking G1 would force H6, E7, H7, and 1 more cleared (every open cell in column F belongs to the same region, so that region's marker has to be somewhere in this column), and then column H 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 A6, A7, A8, and 3 more cleared (together, two regions have open cells only in columns A and B), then C8 (the last open cell in region 7), and region 8 would end up with no open cell for its marker, which can't happen. So it can't go there.
8. First, every open cell in row 1 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.
9. Next, every remaining candidate in this region touches D2, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
10. Then, if C2 were the marker, it would force E1 (the last open cell in region 1), then D7 and D8 cleared (every open cell left in this region sits in column D, so its marker has to land there), and region 8 would end up with no open cell for its marker, which can't happen. So it can't go there.
11. After that, marking E2 would force C1 (the last open cell in region 1), then D5 and D6 cleared (every open cell left in this region sits in column D, so its marker has to land there), then B3 (the last open cell in region 4), and the chain continues, and then region 7 would be left with no open cell for its marker. So E2 can't be the marker there.
12. Now, marking H2 would force G5, G6, E7, and 2 more cleared (every open cell in column F belongs to the same region, so that region's marker has to be somewhere in this column), and then column G would be left with no open cell for its marker. So H2 can't be the marker there.
13. From there, 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.
14. Following that, every remaining candidate in this region touches F3, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
15. First, if E1 were the marker, it would force G2 (the last open cell in region 3), then B3 (the last open cell in row 3), then A5 (the last open cell in region 5), and the chain continues, and column D would end up with no open cell for its marker, which can't happen. So it can't go there.
16. Next, that one can't be the marker: at B3 it would force A5 (the last open cell in region 5), then C8 (the last open cell in region 7), and region 8 would be left with no open cell for its marker.
17. Then, 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.
18. After that, that one can't be the marker: at G2 it would force E3 (the last open cell in region 2), then H6, H7 and H8 cleared (every open cell in column F belongs to the same region, so that region's marker has to be somewhere in this column), and column H would be left with no open cell for its marker.
19. Now, place a marker at F2. Region 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.
20. 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.
21. Following that, every open cell in column G 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.
22. First, that one can't be the marker: at C4 it would force D1 (the last open cell in region 1), then A5 (the last open cell in region 5), then B8 (the last open cell in region 7), and column E would be left with no open cell for its marker.
23. Next, place a marker at A4. Row 4 has exactly one open cell left. Placing here clears the rest of row 4, column A, and its region.
24. Then, every open cell in column B 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.
25. After that, every remaining candidate in this region touches C7, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
26. Now, marking D1 would force G7 (the last open cell in row 7), then C5 (the last open cell in row 5), and then row 6 would be left with no open cell for its marker. So D1 can't be the marker there.
27. From there, place a marker at C1. Region has exactly one open cell left. Placing here clears the rest of row 1, column C, and its region.
28. Following that, that one can't be the marker: at G5 it would force D7 (the last open cell in row 7), and column E would be left with no open cell for its marker.
29. First, place a marker at D5. Row 5 has exactly one open cell left. Placing here clears the rest of row 5, column D, and its region.
30. Next, place a marker at E8. Region has exactly one open cell left. Placing here clears the rest of row 8, column E, and its region.
31. Then, place a marker at B6. Region has exactly one open cell left. Placing here clears the rest of row 6, column B, and its region.
32. Finally, place a marker at G7. Region has exactly one open cell left.

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