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 960). Solving it from scratch takes 19 logical steps, using 8 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Line confinement, Paired regions, Shape squeeze, Forced chain. Every step below is forced: nothing here is a guess.

  1. First, place a marker at F1. Region has exactly one open cell left. Placing here clears the rest of row 1, 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 D, so its marker has to land there; that clears every other open cell in the column.
  3. Then, together, two regions have open cells only in rows 2 and 3; with one marker each, those two markers have to fill exactly those two rows, so every other region's open cells there can be cleared.
  4. After that, every remaining candidate in this region touches C2 and C3, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  5. Now, that one can't be the marker: at A2 it would force D3 (the last open cell in region 2), then B4 (the last open cell in row 4), and region 4 would be left with no open cell for its marker.
  6. From there, 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.
  7. Following that, every open cell in column A 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.
  8. First, marking B2 would force D3 (the last open cell in region 2), then E6 (the last open cell in region 5), and then column C would be left with no open cell for its marker. So B2 can't be the marker there.
  9. Next, 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 2 touching neighbours.
  10. Then, place a marker at D2. Region has exactly one open cell left.
  11. After that, place a marker at E4. Row 4 has exactly one open cell left. Placing here clears the rest of row 4, column E, and its region.
  12. Now, 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.
  13. Finally, place a marker at A5. Region has exactly one open cell left.

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