How to solve this 6×6 logic puzzle

6×6 · severe · 22 steps

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This 6×6 board rates as severe (difficulty score 1248). Solving it from scratch takes 28 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 remaining candidate in this region touches F2, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
Next, every remaining candidate in this region touches A5, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
Then, every remaining candidate in this region touches D6, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
After that, marking A1 would force E2 (the last open cell in region 3), then C3 (the last open cell in row 3), and then row 4 would be left with no open cell for its marker. So A1 can't be the marker there.
Now, if B1 were the marker, it would force E2 (the last open cell in region 3), then A6 (the last open cell in region 4), then D4 (the last open cell in region 5), and row 3 would end up with no open cell for its marker, which can't happen. So it can't go there.
From there, that one can't be the marker: at C1 it would force E2 (the last open cell in region 3), then D5 (the last open cell in region 6), then F6 (the last open cell in region 5), and column A would be left with no open cell for its marker.
Following that, every remaining candidate in this region touches B3, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
First, marking D1 would immediately leave region 3 with no open cell for its marker, so it can't be the marker there.
Next, 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.
Then, marking B2 would force A6 (the last open cell in region 4), then C5 (the last open cell in column C), then E4 (the last open cell in region 5), and then row 3 would be left with no open cell for its marker. So B2 can't be the marker there.
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 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.
From there, every remaining candidate in this region touches C5, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
Following that, that one can't be the marker: at D2 it would force F1 (the last open cell in region 3), then C6 (the last open cell in region 6), then B4 (the last open cell in region 4), and row 3 would be left with no open cell for its marker.
First, place a marker at A2. Row 2 has exactly one open cell left. Placing here clears the rest of row 2, column A, and its region.
Next, 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.
Then, marking C3 would force D5 (the last open cell in region 6), and then row 4 would be left with no open cell for its marker. So C3 can't be the marker there.
After that, place a marker at C6. Column 3 has exactly one open cell left. Placing here clears the rest of row 6, column C, and its region. Placing here also clears its 1 touching neighbour.
Now, place a marker at B4. Region has exactly one open cell left. Placing here clears the rest of row 4, column B, and its region.
From there, place a marker at E5. Region has exactly one open cell left. Placing here clears the rest of row 5, column E, and its region.
Following that, place a marker at F1. Region has exactly one open cell left. Placing here clears the rest of row 1, column F, and its region.
Finally, place a marker at D3. Region has exactly one open cell left.

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