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

This 9×9 board rates as medium (difficulty score 802). Solving it from scratch takes 16 logical steps, using 7 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Line confinement, Paired regions, Shape squeeze. Every step below is forced: nothing here is a guess.

1. First, 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.
2. 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.
3. Then, every open cell left in this region sits in row 2, so its marker has to land there; that clears every other open cell in the row.
4. After that, every open cell left in this region sits in row 1, so its marker has to land there; that clears every other open cell in the row.
5. Now, place a marker at A3. Region has exactly one open cell left. Placing here clears the rest of row 3, column A, and its region.
6. From there, place a marker at B8. Region has exactly one open cell left. Placing here clears the rest of row 8, column B, and its region. Placing here also clears its 2 touching neighbours.
7. Following that, place a marker at C5. Region has exactly one open cell left. Placing here clears the rest of row 5, column C, and its region. Placing here also clears its 2 touching neighbours.
8. First, place a marker at E4. Region has exactly one open cell left. Placing here clears the rest of row 4, column E, and its region.
9. Next, place a marker at D2. Region has exactly one open cell left. Placing here clears the rest of row 2, column D, and its region.
10. Then, every open cell left in this region sits in column H, so its marker has to land there; that clears every other open cell in the column.
11. After that, every open cell in row 9 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.
12. Now, place a marker at I9. Column 9 has exactly one open cell left. Placing here clears the rest of row 9, column I, and its region.
13. From there, every remaining candidate in this region touches G6 and G7, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
14. Following that, 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.
15. First, place a marker at G1. Region has exactly one open cell left.
16. Finally, place a marker at H7. Region has exactly one open cell left.

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