QED Logic quod erat demonstrandum
Logic Ascent

How to solve this 6×6 logic puzzle

6×6 · sharp · 13 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 935). Solving it from scratch takes 19 logical steps, using 7 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Line confinement, Shape squeeze, Forced chain. Every step below is forced: nothing here is a guess.

  1. First, 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. Placing here also clears its 1 touching neighbour.
  2. Next, 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.
  3. Then, 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.
  4. After that, every remaining candidate in this region touches C3 and C4 and E4, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  5. Now, place a marker at E6. Region has exactly one open cell left. Placing here clears the rest of row 6, column E, and its region.
  6. From there, 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.
  7. Following that, that one can't be the marker: place it at A2, and region 1 would be left with no open cell for its marker.
  8. First, 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.
  9. Next, every remaining candidate in this region touches B4, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  10. Then, place a marker at C5. Region has exactly one open cell left. Placing here clears the rest of row 5, column C, and its region. Placing here also clears its 1 touching neighbour.
  11. After that, place a marker at B2. Region has exactly one open cell left. Placing here also clears its 1 touching neighbour.
  12. Now, place a marker at D3. Region has exactly one open cell left.
  13. Finally, place a marker at A4. Region has exactly one open cell left.

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