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 809). 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, every open cell left in this region sits in row 1, so its marker has to land there; that clears every other open cell in the row.
  2. Next, every open cell left in this region sits in row 2, 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 3, so its marker has to land there; that clears every other open cell in the row.
  4. After that, every remaining candidate in this region touches E1 and D3 and E3, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  5. Now, place a marker at F3. Region has exactly one open cell left. Placing here clears the rest of row 3, column F, and its region. Placing here also clears its 3 touching neighbours.
  6. From there, place a marker at D2. Region has exactly one open cell left. Placing here clears the rest of row 2, column D, and its region.
  7. Following that, place a marker at C4. Region has exactly one open cell left. Placing here clears the rest of row 4, column C, and its region. Placing here also clears its 1 touching neighbour.
  8. First, 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.
  9. Next, every open cell in column B 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.
  10. Then, place a marker at E5. Column 5 has exactly one open cell left. Placing here clears the rest of row 5, column E, and its region.
  11. After that, every remaining candidate in this region touches A6 and A7, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  12. Now, 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.
  13. From there, place a marker at B6. Region has exactly one open cell left. Placing here clears the rest of row 6, column B, and its region.
  14. Following that, 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.
  15. Finally, place a marker at G1. Region has exactly one open cell left.

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