A Hard 7×7 Puzzle Solved with Forced Chain in 19 Steps

This 7×7 board rates as hard (difficulty score 1101). Solving it from scratch takes 19 logical steps, using 7 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Paired regions, Shape squeeze, Forced chain. Every step below is forced: nothing here is a guess.

1. First, 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.
2. Next, together, two regions have open cells only in rows 6 and 7; 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 remaining candidate in this region touches F2, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
4. After that, every remaining candidate in this region touches D3 and D5, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
5. Now, marking A1 would force B7 (the last open cell in region 6), then F6 (the last open cell in region 7), then E3 (the last open cell in region 4), and then column D would be left with no open cell for its marker. So A1 can't be the marker there.
6. From there, if B1 were the marker, it would force G2 (the last open cell in row 2), then D4 (the last open cell in column D), and column C would end up with no open cell for its marker, which can't happen. So it can't go there.
7. Following that, that one can't be the marker: at C1 it would force G2 (the last open cell in row 2), then D4 (the last open cell in column D), and column E would be left with no open cell for its marker.
8. First, if E1 were the marker, it would force D4 (the last open cell in column D), then C2 (the last open cell in column C), and region 1 would end up with no open cell for its marker, which can't happen. So it can't go there.
9. Next, together, two regions have open cells only in columns F and G; 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.
10. Then, every open cell left in this region sits in column E, so its marker has to land there; that clears every other open cell in the column.
11. After that, every remaining candidate in this region touches D4, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
12. Now, place a marker at C4. Region has exactly one open cell left. Placing here clears the rest of row 4, column C, and its region. Placing here also clears its 2 touching neighbours.
13. From there, 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.
14. Following that, place a marker at B7. Region has exactly one open cell left. Placing here clears the rest of row 7, column B, and its region.
15. First, place a marker at F6. Region has exactly one open cell left. Placing here clears the rest of row 6, column F, and its region. Placing here also clears its 1 touching neighbour.
16. Next, 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.
17. Then, 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.
18. After that, place a marker at G2. Region has exactly one open cell left.
19. Finally, place a marker at A5. Region has exactly one open cell left.

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