QED Logic quod erat demonstrandum
Logic Ascent

How to solve this 8×8 logic puzzle

8×8 · steady · 14 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 804). 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 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 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, together, two regions have open cells only in columns C and D; 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.
  5. Now, place a marker at E2. Region has exactly one open cell left. Placing here clears the rest of row 2, column E, and its region. Placing here also clears its 1 touching neighbour.
  6. From there, place a marker at C3. Region has exactly one open cell left. Placing here clears the rest of row 3, column C, and its region. Placing here also clears its 1 touching neighbour.
  7. Following that, place a marker at D8. Region has exactly one open cell left. Placing here clears the rest of row 8, column D, and its region.
  8. First, 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.
  9. Next, every remaining candidate in this region touches F5 and G5, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  10. Then, every remaining candidate in this region touches B5, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  11. After that, place a marker at A5. Row 5 has exactly one open cell left. Placing here clears the rest of row 5, column A, and its region. Placing here also clears its 1 touching neighbour.
  12. Now, place a marker at B7. Region has exactly one open cell left. Placing here clears the rest of row 7, column B, and its region.
  13. From there, place a marker at F6. Region has exactly one open cell left. Placing here clears the rest of row 6, column F, and its region.
  14. Finally, place a marker at G4. Region has exactly one open cell left.

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