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

This 9×9 board rates as medium (difficulty score 804). 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, 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.
2. Next, every open cell left in this region sits in row 2, so its marker has to land there; that clears every other open cell in the row.
3. Then, 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.
4. After that, place a marker at I3. Region has exactly one open cell left. Placing here clears the rest of row 3, column I, and its region. Placing here also clears its 1 touching neighbour.
5. Now, 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.
6. From there, place a marker at B2. Region has exactly one open cell left. Placing here clears the rest of row 2, column B, and its region. Placing here also clears its 1 touching neighbour.
7. Following that, 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.
8. First, every open cell left in this region sits in row 9, so its marker has to land there; that clears every other open cell in the row.
9. Next, every open cell in row 4 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, together, two regions have open cells only in columns C and E; 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.
11. After that, place a marker at C6. Row 6 has exactly one open cell left. Placing here clears the rest of row 6, column C, and its region.
12. Now, place a marker at E9. Region has exactly one open cell left. Placing here also clears its 1 touching neighbour.
13. From there, place a marker at H5. Row 5 has exactly one open cell left. Placing here clears the rest of row 5, column H, and its region. Placing here also clears its 1 touching neighbour.
14. Following that, place a marker at F4. Region has exactly one open cell left. Placing here clears the rest of row 4, column F, and its region.
15. First, place a marker at G8. Region has exactly one open cell left. Placing here clears the rest of row 8, column G, and its region.
16. Finally, place a marker at A7. Region has exactly one open cell left.

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