QED Logic quod erat demonstrandum
Logic Ascent

How to solve this 6×6 logic puzzle

6×6 · gentle · 10 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 656). Solving it from scratch takes 17 logical steps, using 5 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Paired regions. Every step below is forced: nothing here is a guess.

  1. First, together, two regions have open cells only in columns E and F; 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.
  2. Next, every open cell left in this region sits in column D, so its marker has to land there; that clears every other open cell in the column.
  3. Then, 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.
  4. After that, place a marker at E5. Region has exactly one open cell left. Placing here clears the rest of row 5, column E, and its region. Placing here also clears its 1 touching neighbour.
  5. Now, place a marker at F1. Region has exactly one open cell left. Placing here clears the rest of row 1, column F, and its region.
  6. From there, 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.
  7. Following that, 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.
  8. First, place a marker at B2. Region has exactly one open cell left. Placing here clears the rest of row 2, column B, and its region.
  9. Next, 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.
  10. Finally, place a marker at C6. Region has exactly one open cell left.

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