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 794). Solving it from scratch takes 19 logical steps, using 6 techniques: Single cell, Row/column exclusion, Adjacency clear, Line confinement, Paired regions, Shape squeeze. Every step below is forced: nothing here is a guess.

  1. First, every open cell in column F 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.
  2. Next, every open cell in column E 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.
  3. Then, 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.
  4. After that, every open cell in column C 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.
  5. Now, place a marker at F6. Row 6 has exactly one open cell left. Placing here clears the rest of row 6, column F, and its region.
  6. From there, together, two regions have open cells only in rows 4 and 5; 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.
  7. Following that, 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.
  8. First, place a marker at D3. Region has exactly one open cell left. Placing here clears the rest of row 3, column D, and its region. Placing here also clears its 2 touching neighbours.
  9. Next, 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.
  10. Then, place a marker at C5. Region has exactly one open cell left. Placing here clears the rest of row 5, column C, and its region. Placing here also clears its 1 touching neighbour.
  11. After that, 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.
  12. Finally, place a marker at B2. Region has exactly one open cell left.

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