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 663). Solving it from scratch takes 24 logical steps, using 5 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Paired regions. Every step below is forced: nothing here is a guess.

  1. First, 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.
  2. Next, place a marker at C1. Region has exactly one open cell left. Placing here clears the rest of row 1, column C, and its region. Placing here also clears its 1 touching neighbour.
  3. Then, 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.
  4. After that, 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.
  5. Now, every open cell left in this region sits in column A, so its marker has to land there; that clears every other open cell in the column.
  6. From there, 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.
  7. Following that, place a marker at E2. Region has exactly one open cell left. Placing here clears the rest of row 2, column E, and its region. Placing here also clears its 1 touching neighbour.
  8. First, 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. Placing here also clears its 1 touching neighbour.
  9. Next, 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.
  10. Then, place a marker at H6. Row 6 has exactly one open cell left. Placing here clears the rest of row 6, column H, and its region. Placing here also clears its 1 touching neighbour.
  11. After that, place a marker at G8. Region has exactly one open cell left. Placing here clears the rest of row 8, column G, and its region.
  12. Finally, place a marker at B7. Region has exactly one open cell left.

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