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 1008). 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 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.
  2. Next, every remaining candidate in this region touches C1, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  3. Then, every remaining candidate in this region touches D4 and F4 and D5 and F5, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  4. After that, every remaining candidate in this region touches B5, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  5. Now, marking A1 would force C2 (the last open cell in region 2), and then region 3 would be left with no open cell for its marker. So A1 can't be the marker there.
  6. From there, marking D1 would force B2 (the last open cell in region 2), and then region 1 would be left with no open cell for its marker. So D1 can't be the marker there.
  7. Following that, that one can't be the marker: at F1 it would force D6 (the last open cell in region 4), then E4 (the last open cell in region 6), then A5 (the last open cell in region 5), and the chain continues, and row 2 would be left with no open cell for its marker.
  8. First, place a marker at B1. Row 1 has exactly one open cell left. Placing here clears the rest of row 1, column B, and its region. Placing here also clears its 1 touching neighbour.
  9. Next, place a marker at A3. Region has exactly one open cell left. Placing here clears the rest of row 3, column A, and its region.
  10. Then, place a marker at D2. Region has exactly one open cell left. Placing here clears the rest of row 2, column D, and its region.
  11. After that, place a marker at F6. Region has exactly one open cell left. Placing here clears the rest of row 6, column F, and its region. Placing here also clears its 1 touching neighbour.
  12. Now, 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.
  13. Finally, place a marker at C5. Region has exactly one open cell left.

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