QED Logic quod erat demonstrandum
Logic Ascent

How to solve this 8×8 logic puzzle

8×8 · sharp · 17 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 sharp (difficulty score 1000). Solving it from scratch takes 26 logical steps, using 7 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Line confinement, Shape squeeze, Forced chain. Every step below is forced: nothing here is a guess.

  1. First, place a marker at G8. Region has exactly one open cell left. Placing here clears the rest of row 8, column G, and its region. Placing here also clears its 2 touching neighbours.
  2. Next, 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.
  3. Then, 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.
  4. After that, place a marker at F2. Region has exactly one open cell left. Placing here clears the rest of row 2, column F, and its region. Placing here also clears its 2 touching neighbours.
  5. Now, that one can't be the marker: at C1 it would force E4 (the last open cell in region 2), and row 3 would be left with no open cell for its marker.
  6. From there, 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.
  7. Following that, every remaining candidate in this region touches D6, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  8. First, marking D1 would force B3 (the last open cell in region 1), and then row 4 would be left with no open cell for its marker. So D1 can't be the marker there.
  9. Next, place a marker at B1. Row 1 has exactly one open cell left. Placing here clears the rest of row 1, column B, and its region.
  10. Then, every open cell in column D 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.
  11. After that, every remaining candidate in this region touches D3 and D4, 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 C3. Row 3 has exactly one open cell left. Placing here clears the rest of row 3, column C, and its region.
  13. From there, place a marker at A4. Row 4 has exactly one open cell left. Placing here clears the rest of row 4, column A, and its region.
  14. Following that, every remaining candidate in this region touches E6, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  15. First, place a marker at E7. Region has exactly one open cell left. Placing here clears the rest of row 7, column E, and its region.
  16. Next, place a marker at D5. Region has exactly one open cell left. Placing here clears the rest of row 5, column D, and its region.
  17. Finally, place a marker at H6. Region has exactly one open cell left.

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