QED Logic quod erat demonstrandum
Logic Ascent

How to solve this 6×6 logic puzzle

6×6 · sharp · 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 sharp (difficulty score 936). Solving it from scratch takes 18 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, 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.
  2. Next, place a marker at C2. Region has exactly one open cell left. Placing here clears the rest of row 2, column C, and its region. Placing here also clears its 3 touching neighbours.
  3. Then, every open cell in row 6 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.
  4. After that, every remaining candidate in this region touches A4, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  5. Now, that one can't be the marker: place it at E3, and region 3 would be left with no open cell for its marker.
  6. From there, marking F3 would force E1 (the last open cell in region 2), then D4 (the last open cell in region 3), and then row 6 would be left with no open cell for its marker. So F3 can't be the marker there.
  7. Following that, place a marker at A3. Row 3 has exactly one open cell left. Placing here clears the rest of row 3, column A, and its region. Placing here also clears its 1 touching neighbour.
  8. First, place a marker at B5. Region has exactly one open cell left. Placing here clears the rest of row 5, column B, and its region.
  9. Next, place a marker at E4. Region has exactly one open cell left. Placing here clears the rest of row 4, column E, and its region.
  10. Then, 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.
  11. Finally, place a marker at D6. Region has exactly one open cell left.

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