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 22 logical steps, using 6 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Line confinement, Paired regions. Every step below is forced: nothing here is a guess.

  1. First, together, two regions have open cells only in rows 1 and 2; 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.
  2. Next, every open cell left in this region sits in row 3, so its marker has to land there; that clears every other open cell in the row.
  3. Then, every open cell left in this region sits in row 4, so its marker has to land there; that clears every other open cell in the row.
  4. After that, every open cell in column A 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.
  5. Now, place a marker at B6. Column 2 has exactly one open cell left. Placing here clears the rest of row 6, column B, and its region. Placing here also clears its 2 touching neighbours.
  6. From there, place a marker at A8. Region has exactly one open cell left. Placing here clears the rest of row 8, column A, and its region.
  7. Following that, place a marker at C3. Column 3 has exactly one open cell left. Placing here clears the rest of row 3, column C, and its region. Placing here also clears its 1 touching neighbour.
  8. First, place a marker at D1. Column 4 has exactly one open cell left. Placing here clears the rest of row 1, column D, and its region.
  9. Next, 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.
  10. Then, 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. Placing here also clears its 1 touching neighbour.
  11. After that, place a marker at F7. Region has exactly one open cell left. Placing here clears the rest of row 7, column F, and its region.
  12. Finally, place a marker at E5. Region has exactly one open cell left.

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