QED Logic quod erat demonstrandum
Logic Ascent

How to solve this 8×8 logic puzzle

8×8 · sharp · 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 sharp (difficulty score 948). Solving it from scratch takes 26 logical steps, using 7 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Paired regions, Shape squeeze, Forced chain. Every step below is forced: nothing here is a guess.

  1. First, place a marker at H1. Region has exactly one open cell left. Placing here clears the rest of row 1, column H, and its region. Placing here also clears its 1 touching neighbour.
  2. Next, every open cell left in this region sits in column G, 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 F, so its marker has to land there; that clears every other open cell in the column.
  4. After that, every open cell left in this region sits in row 8, so its marker has to land there; that clears every other open cell in the row.
  5. Now, together, two regions have open cells only in rows 6 and 7; 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.
  6. From there, place a marker at G4. Region has exactly one open cell left. Placing here clears the rest of row 4, column G, and its region. Placing here also clears its 2 touching neighbours.
  7. Following 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 1 touching neighbour.
  8. First, place a marker at A3. Region has exactly one open cell left. Placing here clears the rest of row 3, column A, and its region.
  9. Next, every open cell left in this region sits in row 6, so its marker has to land there; that clears every other open cell in the row.
  10. Then, every remaining candidate in this region touches B5 and C5 and B7 and C7, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  11. After that, together, two regions have open cells only in columns D and E; 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.
  12. Now, marking E5 would force D7 (the last open cell in region 7), and then column C would be left with no open cell for its marker. So E5 can't be the marker there.
  13. From there, 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. Placing here also clears its 1 touching neighbour.
  14. Following that, 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.
  15. First, place a marker at E7. Region has exactly one open cell left.
  16. Finally, place a marker at C8. Region has exactly one open cell left.

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