QED Logic quod erat demonstrandum
Logic Ascent

How to solve this 8×8 logic puzzle

8×8 · steady · 16 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 832). Solving it from scratch takes 25 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 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 4 touching neighbours.
  2. Next, 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.
  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, place a marker at E2. Row 2 has exactly one open cell left. Placing here clears the rest of row 2, column E, and its region.
  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, 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.
  7. Following that, every open cell left in this region sits in row 7, so its marker has to land there; that clears every other open cell in the row.
  8. First, every remaining candidate in this region touches G6, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  9. Next, every remaining candidate in this region touches F6 and F8 and G8, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  10. Then, every open cell left in this region sits in row 5, so its marker has to land there; that clears every other open cell in the row.
  11. After that, every open cell left in this region sits in column H, so its marker has to land there; that clears every other open cell in the column.
  12. Now, every remaining candidate in this region touches G7, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  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. Following that, place a marker at G5. Region has exactly one open cell left. Placing here also clears its 1 touching neighbour.
  15. First, place a marker at H8. Region has exactly one open cell left. Placing here clears the rest of row 8, column H, and its region.
  16. Finally, place a marker at A6. Region has exactly one open cell left.

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