A Medium 9×9 Puzzle Solved with Shape Squeeze in 15 Steps

This 9×9 board rates as medium (difficulty score 796). Solving it from scratch takes 15 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 B and C; 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 A, 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 D, so its marker has to land there; that clears every other open cell in the column.
4. After that, place a marker at E9. Region has exactly one open cell left. Placing here clears the rest of row 9, column E, and its region. Placing here also clears its 1 touching neighbour.
5. Now, 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 1 touching neighbour.
6. From there, place a marker at A6. Region has exactly one open cell left. Placing here clears the rest of row 6, column A, and its region.
7. Following that, 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.
8. First, every open cell in row 5 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.
9. Next, place a marker at F4. Row 4 has exactly one open cell left. Placing here clears the rest of row 4, column F, and its region. Placing here also clears its 1 touching neighbour.
10. Then, place a marker at G7. Column 7 has exactly one open cell left. Placing here clears the rest of row 7, column G, and its region.
11. After that, every remaining candidate in this region touches C2, 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 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 1 touching neighbour.
13. From there, place a marker at D1. Region has exactly one open cell left. Placing here clears the rest of row 1, column D, and its region.
14. Following that, 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.
15. Finally, place a marker at I5. Region has exactly one open cell left.

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