QED Logic quod erat demonstrandum
Logic Ascent

How to solve this 8×8 logic puzzle

8×8 · steady · 18 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 steady (difficulty score 859). Solving it from scratch takes 27 logical steps, using 6 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Line confinement, Shape squeeze. Every step below is forced: nothing here is a guess.

  1. First, 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.
  2. Next, 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.
  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 remaining candidate in this region touches D5, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  5. Now, every remaining candidate in this region touches A8 and B8, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  6. From there, place a marker at C8. Region has exactly one open cell left. Placing here clears the rest of row 8, column C, and its region. Placing here also clears its 1 touching neighbour.
  7. Following that, place a marker at A7. Region has exactly one open cell left. Placing here clears the rest of row 7, column A, and its region.
  8. First, 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.
  9. Next, every open cell in column H 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.
  10. Then, every open cell in column G 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.
  11. After that, place a marker at F1. Column 6 has exactly one open cell left. Placing here clears the rest of row 1, column F, and its region.
  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, 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 1 touching neighbour.
  14. Following that, place a marker at H2. Region has exactly one open cell left. Placing here clears the rest of row 2, column H, and its region.
  15. First, every remaining candidate in this region touches E5, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  16. 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.
  17. Then, place a marker at D3. Region has exactly one open cell left. Placing here clears the rest of row 3, column D, and its region.
  18. Finally, place a marker at E6. Region has exactly one open cell left.

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