QED Logic quod erat demonstrandum
Logic Ascent

How to solve this 8×8 logic puzzle

8×8 · steady · 14 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 steady (difficulty score 803). Solving it from scratch takes 22 logical steps, using 7 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Line confinement, Paired regions, Shape squeeze. Every step below is forced: nothing here is a guess.

  1. First, 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.
  2. Next, every open cell left in this region sits in column B, so its marker has to land there; that clears every other open cell in the column.
  3. Then, 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.
  4. After that, place a marker at D6. Region has exactly one open cell left. Placing here clears the rest of row 6, column D, and its region. Placing here also clears its 2 touching neighbours.
  5. Now, every open cell in row 4 belongs to the same region, so that region's marker has to be somewhere in this row; that clears every other open cell in the region.
  6. From there, place a marker at B5. Row 5 has exactly one open cell left. Placing here clears the rest of row 5, column B, and its region.
  7. Following that, every remaining candidate in this region touches G2, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  8. First, together, two regions have open cells only in columns E and F; 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.
  9. Next, every remaining candidate in this region touches G3 and H3, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  10. Then, 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.
  11. After that, place a marker at E3. Region has exactly one open cell left. Placing here clears the rest of row 3, column E, and its region.
  12. Now, place a marker at G4. Region has exactly one open cell left.
  13. From there, 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.
  14. Finally, place a marker at A8. Region has exactly one open cell left.

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