A Medium 9×9 Puzzle Solved with Shape Squeeze in 16 Steps

This 9×9 board rates as medium (difficulty score 820). Solving it from scratch takes 16 logical steps, using 6 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Paired regions, Shape squeeze. Every step below is forced: nothing here is a guess.

1. First, every open cell left in this region sits in column D, so its marker has to land there; that clears every other open cell in the column.
2. Next, place a marker at C3. Region has exactly one open cell left. Placing here clears the rest of row 3, column C, and its region. Placing here also clears its 2 touching neighbours.
3. Then, together, two regions have open cells only in columns A and B; with one marker each, those two markers have to fill exactly those two columns, so every other region's open cells there can be cleared.
4. After that, together, two regions have open cells only in rows 8 and 9; with one marker each, those two markers have to fill exactly those two rows, so every other region's open cells there can be cleared.
5. Now, place a marker at A7. Region has exactly one open cell left. Placing here clears the rest of row 7, column A, and its region.
6. From there, place a marker at B1. Region has exactly one open cell left. Placing here clears the rest of row 1, column B, and its region.
7. Following that, place a marker at E2. Region has exactly one open cell left. Placing here clears the rest of row 2, column E, and its region.
8. First, every open cell left in this region sits in column F, so its marker has to land there; that clears every other open cell in the column.
9. Next, every remaining candidate in this region touches H5, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
10. Then, every open cell left in this region sits in column G, so its marker has to land there; that clears every other open cell in the column.
11. After that, every remaining candidate in this region touches F5, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
12. Now, place a marker at F6. Region has exactly one open cell left. Placing here clears the rest of row 6, column F, and its region. Placing here also clears its 1 touching neighbour.
13. From there, place a marker at G4. Region has exactly one open cell left. Placing here clears the rest of row 4, column G, and its region.
14. Following that, place a marker at I5. Region has exactly one open cell left. Placing here clears the rest of row 5, column I, and its region.
15. First, place a marker at H9. Region has exactly one open cell left. Placing here clears the rest of row 9, column H, and its region.
16. Finally, place a marker at D8. Region has exactly one open cell left.

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