QED Logic quod erat demonstrandum
Logic Ascent

How to solve this 6×6 logic puzzle

6×6 · steady · 13 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 822). Solving it from scratch takes 19 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, every remaining candidate in this region touches E4, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  2. Next, every remaining candidate in this region touches E5, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  3. Then, every open cell left in this region sits in column F, so its marker has to land there; that clears every other open cell in the column.
  4. After that, every open cell in row 1 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 open cell in row 2 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.
  6. From there, together, two regions have open cells only in columns D and E; 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.
  7. Following that, place a marker at F3. Row 3 has exactly one open cell left. Placing here clears the rest of row 3, column F, and its region. Placing here also clears its 1 touching neighbour.
  8. First, place a marker at D2. Region has exactly one open cell left. Placing here clears the rest of row 2, column D, and its region. Placing here also clears its 1 touching neighbour.
  9. Next, place a marker at E6. Region has exactly one open cell left. Placing here clears the rest of row 6, column E, and its region.
  10. Then, every remaining candidate in this region touches B4 and B5, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  11. After that, place a marker at A5. Region has exactly one open cell left. Placing here clears the rest of row 5, column A, and its region.
  12. Now, place a marker at B1. Region has exactly one open cell left.
  13. Finally, place a marker at C4. Region has exactly one open cell left.

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