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 826). Solving it from scratch takes 24 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, place a marker at B8. Region has exactly one open cell left. Placing here clears the rest of row 8, column B, and its region. Placing here also clears its 2 touching neighbours.
  2. Next, place a marker at A6. Region has exactly one open cell left. Placing here clears the rest of row 6, column A, and its region.
  3. Then, 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.
  4. After that, 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.
  5. Now, every open cell left in this region sits in row 7, so its marker has to land there; that clears every other open cell in the row.
  6. From there, every open cell left in this region sits in row 5, so its marker has to land there; that clears every other open cell in the row.
  7. Following that, every open cell in row 4 belongs to the same region, so that region's marker has to be somewhere in this row; that clears every other open cell in the region.
  8. First, every remaining candidate in this region touches F1 and F2, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  9. Next, every remaining candidate in this region touches C2 and D2 and C4 and D4, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  10. Then, place a marker at G2. Row 2 has exactly one open cell left. Placing here clears the rest of row 2, column G, and its region.
  11. After that, every remaining candidate in this region touches E4 and F4, 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 H4. Region has exactly one open cell left. Placing here clears the rest of row 4, column H, and its region.
  13. From there, place a marker at D7. Region has exactly one open cell left. Placing here clears the rest of row 7, column D, and its region.
  14. Following that, 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.
  15. First, place a marker at E1. Region has exactly one open cell left. Placing here clears the rest of row 1, column E, and its region.
  16. Finally, place a marker at F5. Region has exactly one open cell left.

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