How to solve this 9×9 logic puzzle

9×9 · severe · 29 steps

This 9×9 board rates as severe (difficulty score 1515). Solving it from scratch takes 37 logical steps, using 6 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Line confinement, Forced chain. Every step below is forced — nothing here is a guess.

1. First, marking row 1, column 1 forces a chain of moves that breaks another row, column, or region, so it can't be the marker there.
2. Next, marking row 1, column 2 forces a chain of moves that breaks another row, column, or region, so it can't be the marker there.
3. Then, marking row 1, column 8 forces a chain of moves that breaks another row, column, or region, so it can't be the marker there.
4. After that, marking row 1, column 9 forces a chain of moves that breaks another row, column, or region, so it can't be the marker there.
5. Now, marking row 2, column 1 forces a chain of moves that breaks another row, column, or region, so it can't be the marker there.
6. From there, marking row 2, column 2 forces a chain of moves that breaks another row, column, or region, so it can't be the marker there.
7. Following that, marking row 2, column 8 forces a chain of moves that breaks another row, column, or region, so it can't be the marker there.
8. First, marking row 2, column 9 forces a chain of moves that breaks another row, column, or region, so it can't be the marker there.
9. Next, marking row 3, column 2 forces a chain of moves that breaks another row, column, or region, so it can't be the marker there.
10. Then, marking row 3, column 3 forces a chain of moves that breaks another row, column, or region, so it can't be the marker there.
11. After that, marking row 3, column 4 forces a chain of moves that breaks another row, column, or region, so it can't be the marker there.
12. Now, marking row 3, column 5 forces a chain of moves that breaks another row, column, or region, so it can't be the marker there.
13. From there, marking row 3, column 6 forces a chain of moves that breaks another row, column, or region, so it can't be the marker there.
14. Following that, marking row 3, column 7 forces a chain of moves that breaks another row, column, or region, so it can't be the marker there.
15. First, marking row 3, column 8 forces a chain of moves that breaks another row, column, or region, so it can't be the marker there.
16. Next, marking row 3, column 9 forces a chain of moves that breaks another row, column, or region, so it can't be the marker there.
17. Then, place a marker at row 3, column 1. Row 3 has exactly one open cell left. Placing here clears the rest of row 3, column 1, and its region.
18. After that, every open cell in column 2 belongs to the same region, so that region's marker has to be somewhere in this column — clearing every other open cell in the region.
19. Now, every open cell in column 3 belongs to the same region, so that region's marker has to be somewhere in this column — clearing every other open cell in the region.
20. From there, place a marker at row 6, column 4. Column 4 has exactly one open cell left. Placing here clears the rest of row 6, column 4, and its region.
21. Following that, place a marker at row 1, column 5. Column 5 has exactly one open cell left. Placing here clears the rest of row 1, column 5, and its region.
22. First, place a marker at row 2, column 3. Region has exactly one open cell left.
23. Next, every open cell left in this region sits in column 9, so its marker has to land there — clearing every other open cell in the column.
24. Then, every open cell in row 4 belongs to the same region, so that region's marker has to be somewhere in this row — clearing every other open cell in the region.
25. After that, place a marker at row 5, column 9. Row 5 has exactly one open cell left. Placing here clears the rest of row 5, column 9, and its region. Placing here also clears its 1 touching neighbour.
26. Now, place a marker at row 4, column 7. Region has exactly one open cell left. Placing here clears the rest of row 4, column 7, and its region.
27. From there, place a marker at row 7, column 8. Region has exactly one open cell left. Placing here clears the rest of row 7, column 8, and its region.
28. Following that, place a marker at row 9, column 6. Region has exactly one open cell left. Placing here clears the rest of row 9, column 6, and its region.
29. Finally, place a marker at row 8, column 2. Region has exactly one open cell left.

The key move here was Forced chain — once you can spot that, this board falls quickly. ∎