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

This 9×9 board rates as medium (difficulty score 803). 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 rows 1 and 2; 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.
2. Next, every open cell left in this region sits in row 3, so its marker has to land there; that clears every other open cell in the row.
3. Then, place a marker at B4. Region has exactly one open cell left. Placing here clears the rest of row 4, column B, and its region. Placing here also clears its 2 touching neighbours.
4. After that, place a marker at D5. Region has exactly one open cell left. Placing here clears the rest of row 5, column D, and its region. Placing here also clears its 2 touching neighbours.
5. Now, 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.
6. From there, 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.
7. Following that, 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.
8. First, place a marker at E1. Region has exactly one open cell left. Placing here clears the rest of row 1, column E, and its region.
9. Next, every open cell in row 8 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.
10. Then, place a marker at C9. Row 9 has exactly one open cell left. Placing here clears the rest of row 9, column C, and its region.
11. After that, every remaining candidate in this region touches G3, 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 F3. Region has exactly one open cell left. Placing here clears the rest of row 3, column F, and its region. Placing here also clears its 1 touching neighbour.
13. From there, place a marker at H2. Region has exactly one open cell left. Placing here clears the rest of row 2, column H, and its region.
14. Following that, place a marker at I6. Region has exactly one open cell left. Placing here clears the rest of row 6, column I, and its region.
15. First, place a marker at A7. Region has exactly one open cell left.
16. Finally, place a marker at G8. Region has exactly one open cell left.

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