QED Logic quod erat demonstrandum
Logic Ascent

How to solve this 8×8 logic puzzle

8×8 · steady · 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 steady (difficulty score 835). Solving it from scratch takes 26 logical steps, using 7 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Line confinement, Paired regions, Shape squeeze. Every step below is forced: nothing here is a guess.

  1. First, every open cell left in this region sits in column B, so its marker has to land there; that clears every other open cell in the column.
  2. 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.
  3. Then, together, two regions have open cells only in rows 6 and 7; with one marker each, those two markers have to fill exactly those two rows, so every other region's open cells there can be cleared.
  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 left in this region sits in row 8, so its marker has to land there; that clears every other open cell in the row.
  6. From there, 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.
  7. Following that, every open cell in column F 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.
  8. First, place a marker at E8. Column 5 has exactly one open cell left. Placing here clears the rest of row 8, column E, and its region. Placing here also clears its 1 touching neighbour.
  9. Next, every remaining candidate in this region touches F3 and H3 and H4, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  10. Then, place a marker at F1. Region has exactly one open cell left. Placing here clears the rest of row 1, column F, and its region.
  11. After 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. Placing here also clears its 1 touching neighbour.
  12. Now, 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.
  13. From there, every remaining candidate in this region touches C6 and C7, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  14. Following that, 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. Placing here also clears its 1 touching neighbour.
  15. First, place a marker at A5. Region has exactly one open cell left. Placing here clears the rest of row 5, column A, and its region.
  16. Next, place a marker at C3. Region has exactly one open cell left.
  17. Finally, place a marker at B7. Region has exactly one open cell left.

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