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

This 9×9 board rates as medium (difficulty score 793). Solving it from scratch takes 15 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, 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 column A, so its marker has to land there; that clears every other open cell in the column.
3. Then, place a marker at B9. Region has exactly one open cell left. Placing here clears the rest of row 9, column B, and its region. Placing here also clears its 1 touching neighbour.
4. After that, place a marker at I8. Region has exactly one open cell left. Placing here clears the rest of row 8, column I, and its region. Placing here also clears its 1 touching neighbour.
5. Now, 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.
6. From there, 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.
7. Following that, every remaining candidate in this region touches G1 and G2, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
8. First, every open cell left in this region sits in column F, so its marker has to land there; that clears every other open cell in the column.
9. Next, 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. Placing here also clears its 2 touching neighbours.
10. Then, place a marker at G6. Row 6 has exactly one open cell left. Placing here clears the rest of row 6, column G, and its region.
11. After that, place a marker at C5. Row 5 has exactly one open cell left. Placing here clears the rest of row 5, column C, and its region.
12. Now, place a marker at E3. Region has exactly one open cell left. Placing here clears the rest of row 3, column E, and its region. Placing here also clears its 1 touching neighbour.
13. From there, place a marker at F1. Region has exactly one open cell left. Placing here clears the rest of row 1, column F, and its region.
14. Following that, place a marker at H2. Region has exactly one open cell left.
15. Finally, place a marker at A4. Region has exactly one open cell left.

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