How to solve this 6×6 logic puzzle

6×6 · sharp · 13 steps

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This 6×6 board rates as sharp (difficulty score 1021). Solving it from scratch takes 21 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.

First, every open cell in column F 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.
Next, every remaining candidate in this region touches C2, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
Then, marking A1 would force F2 (the last open cell in row 2), then C3 (the last open cell in region 3), and then row 4 would be left with no open cell for its marker. So A1 can't be the marker there.
After that, if B1 were the marker, it would force C3 (the last open cell in region 3), and region 5 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 A2 it would force C3 (the last open cell in region 3), then B5 (the last open cell in region 5), and region 4 would be left with no open cell for its marker.
From there, every open cell in column A 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.
Following that, that one can't be the marker: at F1 it would force D2 (the last open cell in region 1), then B3 (the last open cell in region 3), and row 4 would be left with no open cell for its marker.
First, place a marker at C1. Row 1 has exactly one open cell left. Placing here clears the rest of row 1, column C, and its region. Placing here also clears its 1 touching neighbour.
Next, place a marker at B3. Region has exactly one open cell left. Placing here clears the rest of row 3, column B, and its region. Placing here also clears its 1 touching neighbour.
Then, place a marker at D4. Region has exactly one open cell left. Placing here clears the rest of row 4, column D, and its region. Placing here also clears its 1 touching neighbour.
After that, place a marker at E6. Region has exactly one open cell left. Placing here clears the rest of row 6, column E, and its region. Placing here also clears its 1 touching neighbour.
Now, place a marker at F2. Region has exactly one open cell left.
Finally, place a marker at A5. Region has exactly one open cell left.

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