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 674). Solving it from scratch takes 21 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, every open cell left in this region sits in row 8, so its marker has to land there; that clears every other open cell in the row.
  2. Next, together, two regions have open cells only in columns G and H; 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, place a marker at F8. Region has exactly one open cell left. Placing here clears the rest of row 8, column F, and its region. Placing here also clears its 2 touching neighbours.
  4. After that, together, two regions have open cells only in columns D and E; 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.
  5. Now, together, two regions have open cells only in rows 6 and 7; 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.
  6. From there, place a marker at B5. Region has exactly one open cell left. Placing here clears the rest of row 5, column B, and its region. Placing here also clears its 3 touching neighbours.
  7. Following 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.
  8. First, place a marker at E6. Region has exactly one open cell left. Placing here clears the rest of row 6, column E, and its region.
  9. Next, place a marker at D1. Region has exactly one open cell left. Placing here clears the rest of row 1, column D, and its region.
  10. Then, place a marker at H4. Row 4 has exactly one open cell left. Placing here clears the rest of row 4, column H, and its region.
  11. After that, place a marker at G2. Region has exactly one open cell left. Placing here clears the rest of row 2, column G, and its region.
  12. Finally, place a marker at A3. Region has exactly one open cell left.

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