QED Logic quod erat demonstrandum
Logic Ascent

How to solve this 8×8 logic puzzle

8×8 · sharp · 19 steps

A
B
C
D
E
F
G
H
1
2
3
4
5
6
7
8
1
2
🐱
3
🐱
🐱
4
🐱
5
🐱
6🐱
7🐱
8
🐱

This 8×8 board rates as sharp (difficulty score 1081). Solving it from scratch takes 27 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.

  1. First, 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. Placing here also clears its 4 touching neighbours.
  2. Next, place a marker at D8. Region has exactly one open cell left. Placing here clears the rest of row 8, column D, and its region.
  3. Then, every open cell left in this region sits in row 6, 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 5, so its marker has to land there; that clears every other open cell in the row.
  5. Now, 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.
  6. From there, place a marker at C1. Column 3 has exactly one open cell left. Placing here clears the rest of row 1, column C, and its region.
  7. Following that, every remaining candidate in this region touches F3, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  8. First, every remaining candidate in this region touches F5 and G5, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  9. Next, if F2 were the marker, it would force G6 (the last open cell in region 6), and column H would end up with no open cell for its marker, which can't happen. So it can't go there.
  10. Then, marking H2 would force E5 (the last open cell in region 5), and then column F would be left with no open cell for its marker. So H2 can't be the marker there.
  11. After that, that one can't be the marker: at E3 it would force G4 (the last open cell in region 4), and row 5 would be left with no open cell for its marker.
  12. Now, every remaining candidate in this region touches G3, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  13. From there, 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.
  14. Following that, that one can't be the marker: at A2 it would force H3 (the last open cell in region 3), then E5 (the last open cell in region 5), and row 4 would be left with no open cell for its marker.
  15. First, 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.
  16. Next, 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.
  17. Then, 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.
  18. After that, place a marker at E4. Region has exactly one open cell left.
  19. Finally, place a marker at H5. Region has exactly one open cell left.

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