QED Logic quod erat demonstrandum
Logic Ascent

How to solve this 6×6 logic puzzle

6×6 · sharp · 14 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 sharp (difficulty score 983). Solving it from scratch takes 18 logical steps, using 7 techniques: Single cell, Row/column exclusion, Adjacency clear, Line confinement, Paired regions, Shape squeeze, Forced chain. Every step below is forced: nothing here is a guess.

  1. First, place a marker at A6. Region has exactly one open cell left. Placing here clears the rest of row 6, column A, and its region. Placing here also clears its 1 touching neighbour.
  2. Next, together, two regions have open cells only in columns B and C; 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.
  3. Then, 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.
  4. After that, if B1 were the marker, it would force C5 (the last open cell in region 5), then E3 (the last open cell in region 3), and row 2 would end up with no open cell for its marker, which can't happen. So it can't go there.
  5. Now, 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.
  6. From there, 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.
  7. Following that, marking D1 would force B2 (the last open cell in region 1), then C5 (the last open cell in region 5), then E3 (the last open cell in region 3), and then row 4 would be left with no open cell for its marker. So D1 can't be the marker there.
  8. First, every open cell in column D 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.
  9. Next, 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.
  10. Then, place a marker at E1. Region has exactly one open cell left.
  11. After that, every remaining candidate in this region touches C5, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  12. Now, place a marker at B4. Region has exactly one open cell left. Placing here clears the rest of row 4, column B, and its region.
  13. From there, place a marker at C2. Region has exactly one open cell left.
  14. Finally, place a marker at D5. Region has exactly one open cell left.

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