QED Logic quod erat demonstrandum
Logic Ascent

How to solve this 8×8 logic puzzle

8×8 · gentle · 12 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 gentle (difficulty score 766). Solving it from scratch takes 20 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, 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. Placing here also clears its 2 touching neighbours.
  2. Next, 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.
  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 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.
  5. Now, place a marker at H5. Region has exactly one open cell left. Placing here clears the rest of row 5, column H, and its region.
  6. From there, 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. Placing here also clears its 2 touching neighbours.
  7. Following that, place a marker at C6. Region has exactly one open cell left. Placing here clears the rest of row 6, column C, and its region.
  8. First, 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.
  9. Next, every remaining candidate in this region touches F2, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  10. Then, 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.
  11. After that, place a marker at G2. Region has exactly one open cell left.
  12. Finally, place a marker at F7. Region has exactly one open cell left.

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