How to solve this 9×9 logic puzzle

9×9 · sharp · 20 steps

This 9×9 board rates as sharp (difficulty score 1023). Solving it from scratch takes 31 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, place a marker at row 1, column 9. Region has exactly one open cell left. Placing here clears the rest of row 1, column 9, and its region. Placing here also clears its 1 touching neighbour.
Next, every open cell left in this region sits in row 2, so its marker has to land there — clearing every other open cell in the row.
Then, every open cell left in this region sits in column 1, so its marker has to land there — clearing every other open cell in the column.
After that, every open cell left in this region sits in column 2, so its marker has to land there — clearing every other open cell in the column.
Now, place a marker at row 8, column 3. Region has exactly one open cell left. Placing here clears the rest of row 8, column 3, and its region. Placing here also clears its 3 touching neighbours.
From there, every open cell in row 9 belongs to the same region, so that region's marker has to be somewhere in this row — clearing every other open cell in the region.
Following that, every open cell in column 4 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.
First, every remaining candidate in this region touches row 3, column 5 and row 3, column 6 — so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
Next, every open cell left in this region sits in column 7, so its marker has to land there — clearing every other open cell in the column.
Then, every remaining candidate in this region touches row 3, column 8 and row 4, column 6 and row 4, column 8 — so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
After that, every remaining candidate in this region touches row 6, column 2 — so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
Now, marking row 2, column 6 forces a chain of moves that breaks another row, column, or region, so it can't be the marker there.
From there, place a marker at row 2, column 5. Region has exactly one open cell left. Placing here clears the rest of row 2, column 5, and its region. Placing here also clears its 1 touching neighbour.
Following that, marking row 3, column 7 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 4, column 7. Region has exactly one open cell left. Placing here clears the rest of row 4, column 7, and its region. Placing here also clears its 2 touching neighbours.
Next, place a marker at row 7, column 6. Region has exactly one open cell left. Placing here clears the rest of row 7, column 6, and its region.
Then, place a marker at row 6, column 1. Region has exactly one open cell left. Placing here clears the rest of row 6, column 1, and its region. Placing here also clears its 1 touching neighbour.
After that, place a marker at row 3, column 2. Region has exactly one open cell left.
Now, place a marker at row 5, column 4. Region has exactly one open cell left.
Finally, place a marker at row 9, column 8. Region has exactly one open cell left.

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