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 937). 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 B1. Region has exactly one open cell left. Placing here clears the rest of row 1, column B, and its region. Placing here also clears its 2 touching neighbours.
  2. Next, 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.
  3. Then, 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.
  4. After that, every remaining candidate in this region touches E2 and E3, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  5. Now, every open cell left in this region sits in row 4, so its marker has to land there; that clears every other open cell in the row.
  6. From there, every open cell in row 2 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.
  7. Following that, every remaining candidate in this region touches D5 and E5, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  8. First, if F2 were the marker, it would force E6 (the last open cell in region 6), then D4 (the last open cell in region 4), and column C 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 D2. Region has exactly one open cell left. Placing here clears the rest of row 2, column D, and its region. Placing here also clears its 1 touching neighbour.
  10. Then, 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. Placing here also clears its 2 touching neighbours.
  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.
  12. Now, place a marker at C5. Region has exactly one open cell left. Placing here clears the rest of row 5, column C, and its region.
  13. Finally, place a marker at A3. Region has exactly one open cell left.

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