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 1016). Solving it from scratch takes 20 logical steps, using 6 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Shape squeeze, Forced chain. Every step below is forced: nothing here is a guess.

  1. First, 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.
  2. Next, if B1 were the marker, it would force C6 (the last open cell in region 6), then D4 (the last open cell in region 4), then A5 (the last open cell in region 3), and region 5 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: place it at C1, and row 3 would be left with no open cell for its marker.
  4. After that, marking D1 would force C4 (the last open cell in region 4), then B6 (the last open cell in region 6), and then column A would be left with no open cell for its marker. So D1 can't be the marker there.
  5. Now, if E1 were the marker, it would force C2 (the last open cell in row 2), and row 3 would end up with no open cell for its marker, which can't happen. So it can't go there.
  6. From there, 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.
  7. Following that, every open cell left in this region sits in column B, so its marker has to land there; that clears every other open cell in the column.
  8. First, place a marker at C6. Region has exactly one open cell left. Placing here clears the rest of row 6, column C, and its region. Placing here also clears its 1 touching neighbour.
  9. Next, place a marker at D4. Region has exactly one open cell left. Placing here clears the rest of row 4, column D, and its region. Placing here also clears its 2 touching neighbours.
  10. Then, place a marker at F5. Region has exactly one open cell left. Placing here clears the rest of row 5, column F, and its region.
  11. After that, place a marker at E2. Region has exactly one open cell left. Placing here clears the rest of row 2, column E, and its region.
  12. Now, place a marker at B3. Region has exactly one open cell left. Placing here clears the rest of row 3, column B, and its region.
  13. Finally, place a marker at A1. Region has exactly one open cell left.

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