How to solve this 8×8 logic puzzle

8×8 · severe · 23 steps

3🐱

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This 8×8 board rates as severe (difficulty score 1321). Solving it from scratch takes 33 logical steps, using 6 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Shape squeeze, Forced chain. Every step below is forced: nothing here is a guess.

First, every remaining candidate in this region touches B2, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
Next, every remaining candidate in this region touches G8, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
Then, marking A1 would force F2 (the last open cell in region 3), then G7 (the last open cell in region 8), then H3 (the last open cell in region 4), and then region 6 would be left with no open cell for its marker. So A1 can't be the marker there.
After that, if B1 were the marker, it would force F2 (the last open cell in region 3), then G7 (the last open cell in region 8), then H3 (the last open cell in region 4), and region 1 would end up with no open cell for its marker, which can't happen. So it can't go there.
Now, that one can't be the marker: at C1 it would force F2 (the last open cell in region 3), then G7 (the last open cell in region 8), then H3 (the last open cell in region 4), and region 1 would be left with no open cell for its marker.
From there, marking D1 would force F2 (the last open cell in region 3), then G7 (the last open cell in region 8), then H3 (the last open cell in region 4), and then region 1 would be left with no open cell for its marker. So D1 can't be the marker there.
Following that, that one can't be the marker: at F1 it would force G7 (the last open cell in region 8), then E3 (the last open cell in region 4), and region 7 would be left with no open cell for its marker.
First, marking G1 would force A2 (the last open cell in region 1), then E3 (the last open cell in region 4), then D5 (the last open cell in region 2), and then region 7 would be left with no open cell for its marker. So G1 can't be the marker there.
Next, every remaining candidate in this region touches E2, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
Then, if H1 were the marker, it would force F2 (the last open cell in region 3), then G7 (the last open cell in region 8), and region 6 would end up with no open cell for its marker, which can't happen. So it can't go there.
After that, place a marker at E1. Row 1 has exactly one open cell left. Placing here clears the rest of row 1, column E, and its region. Placing here also clears its 1 touching neighbour.
Now, that one can't be the marker: at A2 it would force F6 (the last open cell in region 7), and region 8 would be left with no open cell for its marker.
From there, 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.
Following that, every remaining candidate in this region touches B4, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
First, that one can't be the marker: at G2 it would force F6 (the last open cell in region 7), and region 8 would be left with no open cell for its marker.
Next, marking H2 would force F6 (the last open cell in region 7), and then column G would be left with no open cell for its marker. So H2 can't be the marker there.
Then, place a marker at G4. Region has exactly one open cell left. Placing here clears the rest of row 4, column G, and its region. Placing here also clears its 2 touching neighbours.
After that, place a marker at C2. Row 2 has exactly one open cell left. Placing here clears the rest of row 2, column C, and its region. Placing here also clears its 1 touching neighbour.
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.
From there, place a marker at B5. Row 5 has exactly one open cell left. Placing here clears the rest of row 5, column B, and its region.
Following that, place a marker at D7. Column 4 has exactly one open cell left. Placing here clears the rest of row 7, column D, and its region.
First, place a marker at F8. Region has exactly one open cell left. Placing here clears the rest of row 8, column F, and its region.
Finally, place a marker at H6. Region has exactly one open cell left.

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