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

This 9×9 board rates as medium (difficulty score 821). 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 I, so its marker has to land there; that clears every other open cell in the column.
2. 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.
3. Then, 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.
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, every open cell left in this region sits in row 7, 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 remaining candidate in this region touches B4 and B5, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
8. First, every remaining candidate in this region touches E8 and F8, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
9. Next, place a marker at D8. Row 8 has exactly one open cell left. Placing here clears the rest of row 8, column D, and its region. Placing here also clears its 2 touching neighbours.
10. Then, place a marker at F7. Region has exactly one open cell left. Placing here clears the rest of row 7, column F, and its region.
11. After that, place a marker at G9. Region has exactly one open cell left. Placing here clears the rest of row 9, column G, and its region.
12. Now, place a marker at B3. Column 2 has exactly one open cell left. Placing here clears the rest of row 3, column B, and its region. Placing here also clears its 1 touching neighbour.
13. From there, place a marker at A5. Region has exactly one open cell left. Placing here clears the rest of row 5, column A, and its region.
14. Following that, 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.
15. First, place a marker at C1. Region has exactly one open cell left. Placing here clears the rest of row 1, column C, and its region.
16. Finally, place a marker at I2. Region has exactly one open cell left.

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