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 773). Solving it from scratch takes 22 logical steps, using 6 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Paired regions, Shape squeeze. Every step below is forced: nothing here is a guess.

  1. First, place a marker at H1. Region has exactly one open cell left. Placing here clears the rest of row 1, column H, and its region. Placing here also clears its 1 touching neighbour.
  2. Next, together, two regions have open cells only in columns F and G; 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.
  3. Then, every open cell left in this region sits in column E, so its marker has to land there; that clears every other open cell in the column.
  4. After that, place a marker at D2. Region has exactly one open cell left. Placing here clears the rest of row 2, column D, and its region. Placing here also clears its 1 touching neighbour.
  5. Now, place a marker at B3. Region has exactly one open cell left. Placing here clears the rest of row 3, column B, and its region. Placing here also clears its 2 touching neighbours.
  6. From there, every open cell left in this region sits in column G, so its marker has to land there; that clears every other open cell in the column.
  7. Following that, every remaining candidate in this region touches F4 and F5, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  8. First, place a marker at F6. Region has exactly one open cell left. Placing here clears the rest of row 6, column F, and its region. Placing here also clears its 2 touching neighbours.
  9. Next, place a marker at G4. Region has exactly one open cell left.
  10. Then, place a marker at E8. Region has exactly one open cell left. Placing here clears the rest of row 8, column E, and its region.
  11. After that, place a marker at C7. Region has exactly one open cell left. Placing here clears the rest of row 7, column C, and its region.
  12. Finally, place a marker at A5. Region has exactly one open cell left.

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