QED Logic quod erat demonstrandum
Logic Ascent

How to solve this 8×8 logic puzzle

8×8 · steady · 15 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 821). Solving it from scratch takes 25 logical steps, using 6 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Line confinement, Shape squeeze. Every step below is forced: nothing here is a guess.

  1. First, 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. Placing here also clears its 1 touching neighbour.
  2. Next, place a marker at H7. Region has exactly one open cell left. Placing here clears the rest of row 7, column H, and its region. Placing here also clears its 1 touching neighbour.
  3. Then, place a marker at G5. Region has exactly one open cell left. Placing here clears the rest of row 5, column G, and its region. Placing here also clears its 2 touching neighbours.
  4. After that, 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.
  5. Now, every open cell left in this region sits in column D, so its marker has to land there; that clears every other open cell in the column.
  6. From there, every open cell in row 6 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.
  7. Following that, every open cell in column F 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.
  8. First, every remaining candidate in this region touches E2, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  9. Next, place a marker at E6. Column 5 has exactly one open cell left. Placing here clears the rest of row 6, column E, and its region.
  10. Then, every remaining candidate in this region touches C2 and C3, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  11. After that, every remaining candidate in this region touches C4, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  12. Now, 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.
  13. From there, 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.
  14. Following that, place a marker at F2. Region has exactly one open cell left.
  15. Finally, place a marker at D4. Region has exactly one open cell left.

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