QED Logic quod erat demonstrandum
Logic Ascent

How to solve this 8×8 logic puzzle

8×8 · steady · 14 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 793). Solving it from scratch takes 24 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 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 row 2, so its marker has to land there; that clears every other open cell in the row.
  3. Then, together, two regions have open cells only in columns A and B; 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.
  4. After that, place a marker at C2. Region has exactly one open cell left. Placing here clears the rest of row 2, column C, and its region. Placing here also clears its 2 touching neighbours.
  5. Now, place a marker at D4. Region has exactly one open cell left. Placing here clears the rest of row 4, column D, and its region. Placing here also clears its 2 touching neighbours.
  6. From there, 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.
  7. Following that, place a marker at B8. Region has exactly one open cell left. Placing here clears the rest of row 8, column B, and its region.
  8. First, 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.
  9. Next, every open cell in column E 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 remaining candidate in this region touches E6, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  11. After that, place a marker at E7. Region has exactly one open cell left. Placing here clears the rest of row 7, column E, and its region. Placing here also clears its 1 touching neighbour.
  12. Now, place a marker at F5. Region has exactly one open cell left. Placing here clears the rest of row 5, column F, and its region.
  13. From there, place a marker at H6. Region has exactly one open cell left. Placing here clears the rest of row 6, column H, and its region.
  14. Finally, place a marker at G1. Region has exactly one open cell left.

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