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 947). Solving it from scratch takes 21 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 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.
  2. Next, 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.
  3. Then, 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.
  4. After that, every open cell in column C 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.
  5. Now, every remaining candidate in this region touches A3 and C3, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  6. From there, 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.
  7. Following that, every remaining candidate in this region touches C2, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  8. First, if E1 were the marker, it would force B2 (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.
  9. Next, place a marker at C1. Row 1 has exactly one open cell left. Placing here clears the rest of row 1, column C, and its region. Placing here also clears its 2 touching neighbours.
  10. Then, 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. Placing here also clears its 1 touching neighbour.
  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 A5. Region has exactly one open cell left. Placing here clears the rest of row 5, column A, and its region.
  13. Finally, place a marker at D4. Region has exactly one open cell left.

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