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 659). Solving it from scratch takes 18 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 left in this region sits in column C, so its marker has to land there; that clears every other open cell in the column.
  2. Next, 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.
  3. Then, 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.
  4. After that, place a marker at B3. Column 2 has exactly one open cell left. Placing here clears the rest of row 3, column B, and its region. Placing here also clears its 2 touching neighbours.
  5. Now, 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. Placing here also clears its 1 touching neighbour.
  6. From there, 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.
  7. Following that, place a marker at F2. Region has exactly one open cell left. Placing here clears the rest of row 2, column F, and its region.
  8. First, place a marker at E4. Row 4 has exactly one open cell left. Placing here clears the rest of row 4, column E, and its region. Placing here also clears its 1 touching neighbour.
  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. 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.