QED Logic quod erat demonstrandum
Logic Ascent

How to solve this 6×6 logic puzzle

6×6 · steady · 12 steps

A
B
C
D
E
F
1
2
3
4
5
6
1
2🐱
3
🐱
4
🐱
5
6
🐱
🐱
🐱

This 6×6 board rates as steady (difficulty score 791). Solving it from scratch takes 17 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, every open cell left in this region sits in row 1, so its marker has to land there; that clears every other open cell in the row.
  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, every open cell in row 6 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.
  5. Now, every remaining candidate in this region touches D2, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  6. From there, 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 2 touching neighbours.
  7. Following that, place a marker at C1. Region has exactly one open cell left. Placing here clears the rest of row 1, column C, and its region.
  8. First, place a marker at D6. Column 4 has exactly one open cell left. Placing here clears the rest of row 6, column D, and its region.
  9. Next, every remaining candidate in this region touches A4 and B4, 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 B5. Region has exactly one open cell left. Placing here clears the rest of row 5, column B, and its region.
  11. After that, place a marker at A3. Region has exactly one open cell left.
  12. Finally, place a marker at F4. Region has exactly one open cell left.

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