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 799). Solving it from scratch takes 18 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 open cell left in this region sits in row 6, so its marker has to land there; that clears every other open cell in the row.
  2. Next, 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.
  3. Then, place a marker at A3. Region has exactly one open cell left. Placing here clears the rest of row 3, column A, and its region. Placing here also clears its 1 touching neighbour.
  4. After that, place a marker at B1. Column 2 has exactly one open cell left. Placing here clears the rest of row 1, column B, and its region.
  5. Now, 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.
  6. From there, every remaining candidate in this region touches D4, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  7. Following that, 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.
  8. First, 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.
  9. Next, place a marker at E4. Region has exactly one open cell left. Placing here clears the rest of row 4, column E, and its region.
  10. Then, place a marker at C5. Region has exactly one open cell left. Placing here also clears its 1 touching neighbour.
  11. After that, place a marker at F6. Region has exactly one open cell left. Placing here clears the rest of row 6, column F, and its region.
  12. Finally, place a marker at D2. Region has exactly one open cell left.

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