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 remaining candidate in this region touches B2, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  2. Next, if B1 were the marker, it would force F2 (the last open cell in region 3), then D3 (the last open cell in region 2), and row 4 would end up with no open cell for its marker, which can't happen. So it can't go there.
  3. Then, that one can't be the marker: at C1 it would force D3 (the last open cell in region 2), then F2 (the last open cell in region 3), and region 5 would be left with no open cell for its marker.
  4. After that, every open cell left in this region sits in column A, so its marker has to land there; that clears every other open cell in the column.
  5. Now, 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.
  6. From there, place a marker at D5. Row 5 has exactly one open cell left. Placing here clears the rest of row 5, column D, and its region. Placing here also clears its 2 touching neighbours.
  7. Following that, 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 1 touching neighbour.
  8. First, 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. Placing here also clears its 1 touching neighbour.
  9. Next, place a marker at A1. Region has exactly one open cell left. Placing here clears the rest of row 1, column A, and its region.
  10. Then, place a marker at E3. Region has exactly one open cell left.
  11. Finally, place a marker at F6. Region has exactly one open cell left.

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