A Medium 9×9 Puzzle Solved with Shape Squeeze in 18 Steps

This 9×9 board rates as medium (difficulty score 854). Solving it from scratch takes 18 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 D, so its marker has to land there; that clears every other open cell in the column.
2. Next, together, two regions have open cells only in rows 7 and 8; 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.
3. Then, 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.
4. After that, place a marker at G6. Region has exactly one open cell left. Placing here clears the rest of row 6, column G, and its region. Placing here also clears its 2 touching neighbours.
5. Now, 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. Placing here also clears its 2 touching neighbours.
6. From there, every open cell in column I belongs to the same region, so that region's marker has to be somewhere in this column; that clears every other open cell in the region.
7. Following that, every open cell in column H belongs to the same region, so that region's marker has to be somewhere in this column; that clears every other open cell in the region.
8. First, every remaining candidate in this region touches I1 and I2, 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 H1. Row 1 has exactly one open cell left. Placing here clears the rest of row 1, column H, and its region.
10. Then, every remaining candidate in this region touches C7 and C8, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
11. After that, together, two regions have open cells only in columns A and B; 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.
12. Now, every remaining candidate in this region touches D8, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
13. From there, 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.
14. Following that, place a marker at A8. Region has exactly one open cell left. Placing here clears the rest of row 8, column A, and its region.
15. First, place a marker at B5. Region has exactly one open cell left. Placing here clears the rest of row 5, column B, and its region.
16. Next, 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.
17. Then, place a marker at E2. Region has exactly one open cell left. Placing here clears the rest of row 2, column E, and its region.
18. Finally, place a marker at C9. Region has exactly one open cell left.

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