QED Logic quod erat demonstrandum
Logic Ascent

How to solve this 8×8 logic puzzle

8×8 · steady · 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 steady (difficulty score 827). Solving it from scratch takes 23 logical steps, using 7 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Line confinement, Paired regions, Shape squeeze. Every step below is forced: nothing here is a guess.

  1. First, together, two regions have open cells only in rows 7 and 8; 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.
  2. Next, every open cell left in this region sits in column E, so its marker has to land there; that clears every other open cell in the column.
  3. Then, together, two regions have open cells only in rows 5 and 6; 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.
  4. After that, every open cell left in this region sits in row 4, so its marker has to land there; that clears every other open cell in the row.
  5. Now, every open cell left in this region sits in column C, so its marker has to land there; that clears every other open cell in the column.
  6. From there, 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.
  7. Following that, every remaining candidate in this region touches C2, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  8. First, 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 2 touching neighbours.
  9. Next, place a marker at D1. Region has exactly one open cell left. Placing here clears the rest of row 1, column D, and its region.
  10. Then, place a marker at A4. Region has exactly one open cell left. Placing here clears the rest of row 4, column A, and its region.
  11. After that, 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.
  12. Now, every remaining candidate in this region touches F5 and F6, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  13. From there, place a marker at G6. Region has exactly one open cell left. Placing here clears the rest of row 6, column G, and its region.
  14. Following that, place a marker at H2. Region has exactly one open cell left. Placing here clears the rest of row 2, column H, and its region.
  15. First, place a marker at E5. Region has exactly one open cell left.
  16. Finally, place a marker at F8. Region has exactly one open cell left.

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