A Medium 9×9 Puzzle Solved with Shape Squeeze in 20 Steps

This 9×9 board rates as medium (difficulty score 868). Solving it from scratch takes 20 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, every open cell left in this region sits in row 8, 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 4, so its marker has to land there; that clears every other open cell in the row.
4. After that, 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.
5. Now, together, two regions have open cells only in columns G and H; 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.
6. From there, together, two regions have open cells only in columns E and F; 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.
7. Following that, every remaining candidate in this region touches H1 and H2, 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 H3, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
9. Next, place a marker at G1. Region has exactly one open cell left. Placing here clears the rest of row 1, column G, and its region. Placing here also clears its 1 touching neighbour.
10. Then, place a marker at I2. Region has exactly one open cell left. Placing here clears the rest of row 2, column I, and its region.
11. After that, place a marker at H4. Region has exactly one open cell left.
12. Now, every open cell left in this region sits in row 3, so its marker has to land there; that clears every other open cell in the row.
13. From there, 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.
14. Following that, every remaining candidate in this region touches E6, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
15. First, place a marker at E7. Region has exactly one open cell left. Placing here clears the rest of row 7, column E, and its region. Placing here also clears its 3 touching neighbours.
16. Next, place a marker at F5. Region has exactly one open cell left. Placing here clears the rest of row 5, column F, and its region.
17. Then, place a marker at D9. Column 4 has exactly one open cell left. Placing here clears the rest of row 9, column D, and its region. Placing here also clears its 1 touching neighbour.
18. After that, 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.
19. Now, place a marker at A3. Region has exactly one open cell left. Placing here clears the rest of row 3, column A, and its region.
20. Finally, place a marker at C6. Region has exactly one open cell left.

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