How to solve this 9×9 logic puzzle

9×9 · severe · 29 steps

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This 9×9 board rates as severe (difficulty score 1515). Solving it from scratch takes 37 logical steps, using 6 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Line confinement, Forced chain. Every step below is forced: nothing here is a guess.

First, marking A1 would force C2 (the last open cell in column C), then D6 (the last open cell in column D), and then column E would be left with no open cell for its marker. So A1 can't be the marker there.
Next, if B1 were the marker, column C would end up with no open cell for its marker, which can't happen. So it can't go there.
Then, if H1 were the marker, row 9 would end up with no open cell for its marker, which can't happen. So it can't go there.
After that, that one can't be the marker: at I1 it would force H6 (the last open cell in region 6), then G8 (the last open cell in region 8), and region 9 would be left with no open cell for its marker.
Now, that one can't be the marker: at A2 it would force C1 (the last open cell in column C), then D6 (the last open cell in column D), and column E would be left with no open cell for its marker.
From there, marking B2 would immediately leave column C with no open cell for its marker, so it can't be the marker there.
Following that, marking H2 would immediately leave row 9 with no open cell for its marker, so it can't be the marker there.
First, if I2 were the marker, it would force H6 (the last open cell in region 6), then G8 (the last open cell in region 8), and region 9 would end up with no open cell for its marker, which can't happen. So it can't go there.
Next, that one can't be the marker: at B3 it would force C1 (the last open cell in column C), then D6 (the last open cell in column D), and column E would be left with no open cell for its marker.
Then, marking C3 would immediately leave column B with no open cell for its marker, so it can't be the marker there.
After that, if D3 were the marker, row 2 would end up with no open cell for its marker, which can't happen. So it can't go there.
Now, that one can't be the marker: at E3 it would force G2 (the last open cell in row 2), and row 1 would be left with no open cell for its marker.
From there, marking F3 would immediately leave row 2 with no open cell for its marker, so it can't be the marker there.
Following that, if G3 were the marker, row 2 would end up with no open cell for its marker, which can't happen. So it can't go there.
First, that one can't be the marker: place it at H3, and row 2 would be left with no open cell for its marker.
Next, marking I3 would force H6 (the last open cell in region 6), then G8 (the last open cell in region 8), and then region 9 would be left with no open cell for its marker. So I3 can't be the marker there.
Then, place a marker at A3. Row 3 has exactly one open cell left. Placing here clears the rest of row 3, column A, and its region.
After that, 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.
Now, every open cell in column C 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.
From there, place a marker at D6. Column 4 has exactly one open cell left. Placing here clears the rest of row 6, column D, and its region.
Following that, place a marker at E1. Column 5 has exactly one open cell left. Placing here clears the rest of row 1, column E, and its region.
First, place a marker at C2. Region has exactly one open cell left.
Next, every open cell left in this region sits in column I, so its marker has to land there; that clears every other open cell in the column.
Then, every open cell in row 4 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.
After that, place a marker at I5. Row 5 has exactly one open cell left. Placing here clears the rest of row 5, column I, and its region. Placing here also clears its 1 touching neighbour.
Now, place a marker at G4. Region has exactly one open cell left. Placing here clears the rest of row 4, column G, and its region.
From there, 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.
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.
Finally, place a marker at B8. Region has exactly one open cell left.

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