QED Logic quod erat demonstrandum
Logic Ascent

How to solve this 6×6 logic puzzle

6×6 · gentle · 11 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 gentle (difficulty score 670). Solving it from scratch takes 17 logical steps, using 6 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Line confinement, Paired regions. Every step below is forced: nothing here is a guess.

  1. First, every open cell in column A 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 B 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, together, two regions have open cells only in rows 1 and 2; 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.
  4. After that, place a marker at B3. Region has exactly one open cell left. Placing here clears the rest of row 3, column B, and its region. Placing here also clears its 3 touching neighbours.
  5. Now, 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.
  6. From there, 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.
  7. Following that, place a marker at E2. Column 5 has exactly one open cell left. Placing here clears the rest of row 2, column E, and its region. Placing here also clears its 1 touching neighbour.
  8. First, 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.
  9. Next, place a marker at D6. Region has exactly one open cell left. Placing here clears the rest of row 6, column D, and its region.
  10. Then, place a marker at F4. Region has exactly one open cell left.
  11. Finally, place a marker at A5. Region has exactly one open cell left.

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