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 1039). 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, every open cell left in this region sits in row 1, so its marker has to land there; that clears every other open cell in the row.
  2. Next, every open cell left in this region sits in column H, so its marker has to land there; that clears every other open cell in the column.
  3. Then, place a marker at G1. Region has exactly one open cell left. Placing here clears the rest of row 1, column G, and its region. Placing here also clears its 2 touching neighbours.
  4. After that, place a marker at H3. Region has exactly one open cell left. Placing here clears the rest of row 3, column H, and its region.
  5. Now, every open cell left in this region sits in row 2, so its marker has to land there; that clears every other open cell in the row.
  6. From there, every open cell left in this region sits in column F, so its marker has to land there; that clears every other open cell in the column.
  7. Following that, every open cell in row 8 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.
  8. First, every open cell in row 7 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.
  9. Next, every remaining candidate in this region touches D8 and E8, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  10. Then, marking B2 would force F6 (the last open cell in row 6), then D7 (the last open cell in region 7), then E4 (the last open cell in region 4), and then column C would be left with no open cell for its marker. So B2 can't be the marker there.
  11. After that, place a marker at E2. Region has exactly one open cell left. Placing here clears the rest of row 2, column E, and its region.
  12. Now, place a marker at D7. Region has exactly one open cell left. Placing here clears the rest of row 7, column D, and its region. Placing here also clears its 2 touching neighbours.
  13. From there, every remaining candidate in this region touches B5, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  14. Following that, if B4 were the marker, row 5 would end up with no open cell for its marker, which can't happen. So it can't go there.
  15. First, that one can't be the marker: place it at C4, and row 5 would be left with no open cell for its marker.
  16. Next, place a marker at C5. Column 3 has exactly one open cell left. Placing here clears the rest of row 5, column C, and its region.
  17. Then, place a marker at A4. Region has exactly one open cell left. Placing here clears the rest of row 4, column A, and its region.
  18. After that, place a marker at F6. Region has exactly one open cell left.
  19. Finally, place a marker at B8. Region has exactly one open cell left.

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