QED Logic quod erat demonstrandum
Logic Ascent

How to solve this 8×8 logic puzzle

8×8 · sharp · 17 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 1032). Solving it from scratch takes 26 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, place a marker at A8. Region has exactly one open cell left. Placing here clears the rest of row 8, column A, and its region. Placing here also clears its 1 touching neighbour.
  2. Next, place a marker at B5. Region has exactly one open cell left. Placing here clears the rest of row 5, column B, and its region. Placing here also clears its 2 touching neighbours.
  3. Then, every open cell left in this region sits in row 7, 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 6, so its marker has to land there; that clears every other open cell in the row.
  5. Now, together, two regions have open cells only in columns C and D; 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.
  6. From there, together, two regions have open cells only in columns E and F; 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.
  7. Following that, every remaining candidate in this region touches H2, 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 G3, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  9. Next, that one can't be the marker: place it at F1, and region 2 would be left with no open cell for its marker.
  10. Then, marking G1 would force F3 (the last open cell in region 1), then H4 (the last open cell in region 5), then C2 (the last open cell in region 4), and the chain continues, and then row 7 would be left with no open cell for its marker. So G1 can't be the marker there.
  11. After that, if H1 were the marker, it would force G4 (the last open cell in region 5), then F2 (the last open cell in region 1), then C3 (the last open cell in region 4), and the chain continues, and row 7 would end up with no open cell for its marker, which can't happen. So it can't go there.
  12. Now, 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. Placing here also clears its 2 touching neighbours.
  13. From there, place a marker at E1. Region has exactly one open cell left. Placing here clears the rest of row 1, column E, and its region.
  14. Following that, 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.
  15. First, place a marker at C3. Region has exactly one open cell left. Placing here clears the rest of row 3, column C, and its region.
  16. Next, place a marker at F6. Region has exactly one open cell left.
  17. Finally, place a marker at D7. Region has exactly one open cell left.

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