How to solve this 6×6 logic puzzle

6×6 · severe · 20 steps

🐱

This 6×6 board rates as severe (difficulty score 1141). Solving it from scratch takes 27 logical steps, using 7 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Line confinement, Shape squeeze, Forced chain. Every step below is forced: nothing here is a guess.

First, every open cell left in this region sits in column E, so its marker has to land there; that clears every other open cell in the column.
Next, every open cell left in this region sits in column C, so its marker has to land there; that clears every other open cell in the column.
Then, 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.
After that, every remaining candidate in this region touches D2 and F2, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
Now, 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.
From there, marking A1 would force E2 (the last open cell in row 2), then B3 (the last open cell in region 2), then C5 (the last open cell in region 5), and then column D would be left with no open cell for its marker. So A1 can't be the marker there.
Following that, if B1 were the marker, it would force D3 (the last open cell in region 2), and row 2 would end up with no open cell for its marker, which can't happen. So it can't go there.
First, every open cell left in this region sits in column A, so its marker has to land there; that clears every other open cell in the column.
Next, 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.
Then, 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.
After that, every remaining candidate in this region touches D3, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
Now, if E1 were the marker, it would force B2 (the last open cell in region 2), then A4 (the last open cell in region 1), and column C would end up with no open cell for its marker, which can't happen. So it can't go there.
From there, 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.
Following that, that one can't be the marker: at F1 it would force B2 (the last open cell in region 2), then A4 (the last open cell in region 1), and column C would be left with no open cell for its marker.
First, place a marker at D1. Row 1 has exactly one open cell left. Placing here clears the rest of row 1, column D, and its region. Placing here also clears its 1 touching neighbour.
Next, place a marker at E3. Region has exactly one open cell left. Placing here clears the rest of row 3, column E, and its region. Placing here also clears its 1 touching neighbour.
Then, place a marker at C4. Region has exactly one open cell left. Placing here clears the rest of row 4, column C, and its region. Placing here also clears its 1 touching neighbour.
After that, place a marker at A2. Region has exactly one open cell left.
Now, 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.
Finally, place a marker at F5. Region has exactly one open cell left.

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