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

This 9×9 board rates as medium (difficulty score 798). Solving it from scratch takes 16 logical steps, using 6 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Line confinement, Shape squeeze. Every step below is forced: nothing here is a guess.

1. First, every open cell left in this region sits in column I, so its marker has to land there; that clears every other open cell in the column.
2. Next, 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.
3. 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.
4. After that, every open cell in row 1 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.
5. Now, place a marker at F2. Row 2 has exactly one open cell left. Placing here clears the rest of row 2, column F, and its region. Placing here also clears its 2 touching neighbours.
6. From there, every open cell in row 3 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.
7. Following 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.
8. First, every remaining candidate in this region touches H4, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
9. Next, place a marker at H6. Region has exactly one open cell left. Placing here clears the rest of row 6, column H, and its region. Placing here also clears its 2 touching neighbours.
10. Then, place a marker at G4. Region has exactly one open cell left.
11. After that, place a marker at D7. Region has exactly one open cell left. Placing here clears the rest of row 7, column D, and its region.
12. 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.
13. From there, 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.
14. Following that, 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.
15. First, place a marker at I8. Region has exactly one open cell left.
16. Finally, place a marker at E9. Region has exactly one open cell left.

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