How to solve this 8×8 logic puzzle

8×8 · severe · 25 steps

🐱

5🐱

🐱

This 8×8 board rates as severe (difficulty score 1299). Solving it from scratch takes 33 logical steps, using 7 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Line confinement, Shape squeeze, Forced chain. Every step below is forced: nothing here is a guess.

First, every remaining candidate in this region touches B7, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
Next, marking A1 would force F5 (the last open cell in region 5), then H4 (the last open cell in region 4), then C7 (the last open cell in row 7), and then row 6 would be left with no open cell for its marker. So A1 can't be the marker there.
Then, that one can't be the marker: at C1 it would force B8 (the last open cell in region 6), then H7 (the last open cell in region 8), then F5 (the last open cell in region 5), and region 4 would be left with no open cell for its marker.
After that, marking D1 would force F5 (the last open cell in region 5), then H4 (the last open cell in region 4), then C7 (the last open cell in row 7), and then row 6 would be left with no open cell for its marker. So D1 can't be the marker there.
Now, if E1 were the marker, it would force F5 (the last open cell in region 5), then H4 (the last open cell in region 4), then C7 (the last open cell in row 7), and row 6 would end up with no open cell for its marker, which can't happen. So it can't go there.
From there, that one can't be the marker: place it at F1, and region 8 would be left with no open cell for its marker.
Following that, marking G1 would force F5 (the last open cell in region 5), then H4 (the last open cell in region 4), then C7 (the last open cell in row 7), and then row 6 would be left with no open cell for its marker. So G1 can't be the marker there.
First, if H1 were the marker, it would force C7 (the last open cell in region 6), then E6 (the last open cell in region 7), and region 5 would end up with no open cell for its marker, which can't happen. So it can't go there.
Next, place a marker at B1. Row 1 has exactly one open cell left. Placing here clears the rest of row 1, column B, and its region. Placing here also clears its 1 touching neighbour.
Then, every open cell in column A 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.
After that, every remaining candidate in this region touches D3, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
Now, that one can't be the marker: at D2 it would force C6 (the last open cell in column C), then F5 (the last open cell in row 5), then H4 (the last open cell in region 4), and row 3 would be left with no open cell for its marker.
From there, marking E2 would force C6 (the last open cell in column C), then D8 (the last open cell in column D), then A7 (the last open cell in region 6), and the chain continues, and then row 3 would be left with no open cell for its marker. So E2 can't be the marker there.
Following that, every open cell left in this region sits in column C, so its marker has to land there; that clears every other open cell in the column.
First, every open cell in row 2 belongs to the same region, so that region's marker has to be somewhere in this row; that clears every other open cell in the region.
Next, place a marker at C3. Row 3 has exactly one open cell left. Placing here clears the rest of row 3, column C, and its region.
Then, every open cell in row 4 belongs to the same region, so that region's marker has to be somewhere in this row; that clears every other open cell in the region.
After that, place a marker at F5. Row 5 has exactly one open cell left. Placing here clears the rest of row 5, column F, and its region. Placing here also clears its 3 touching neighbours.
Now, place a marker at H4. Region has exactly one open cell left. Placing here clears the rest of row 4, column H, and its region.
From there, place a marker at G2. Region has exactly one open cell left. Placing here clears the rest of row 2, column G, and its region.
Following that, 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.
First, every remaining candidate in this region touches D7 and E7, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
Next, place a marker at D6. Region has exactly one open cell left. Placing here clears the rest of row 6, column D, and its region.
Then, place a marker at A7. Region has exactly one open cell left.
Finally, place a marker at E8. Region has exactly one open cell left.

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