How to solve this 6×6 logic puzzle

6×6 · sharp · 13 steps

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 6 belongs to the same region, so that region's marker has to be somewhere in this column — clearing every other open cell in the region.
Next, every remaining candidate in this region touches row 2, column 3 — so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
Then, marking row 1, column 1 forces a chain of moves that breaks another row, column, or region, so it can't be the marker there.
After that, marking row 1, column 2 forces a chain of moves that breaks another row, column, or region, so it can't be the marker there.
Now, marking row 2, column 1 forces a chain of moves that breaks another row, column, or region, so it can't be the marker there.
From there, every open cell in column 1 belongs to the same region, so that region's marker has to be somewhere in this column — clearing every other open cell in the region.
Following that, marking row 1, column 6 forces a chain of moves that breaks another row, column, or region, so it can't be the marker there.
First, place a marker at row 1, column 3. Row 1 has exactly one open cell left. Placing here clears the rest of row 1, column 3, and its region. Placing here also clears its 1 touching neighbour.
Next, place a marker at row 3, column 2. Region has exactly one open cell left. Placing here clears the rest of row 3, column 2, and its region. Placing here also clears its 1 touching neighbour.
Then, place a marker at row 4, column 4. Region has exactly one open cell left. Placing here clears the rest of row 4, column 4, and its region. Placing here also clears its 1 touching neighbour.
After that, place a marker at row 6, column 5. Region has exactly one open cell left. Placing here clears the rest of row 6, column 5, and its region. Placing here also clears its 1 touching neighbour.
Now, place a marker at row 2, column 6. Region has exactly one open cell left.
Finally, place a marker at row 5, column 1. Region has exactly one open cell left.

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