QED Logic quod erat demonstrandum
Logic Ascent

How to solve this 6×6 logic puzzle

6×6 · sharp · 16 steps

A
B
C
D
E
F
1
2
3
4
5
6
1
2
3🐱
🐱
4
5
🐱
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6
🐱
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This 6×6 board rates as sharp (difficulty score 1009). Solving it from scratch takes 22 logical steps, using 7 techniques: Single cell, Row/column exclusion, Adjacency clear, Region 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 A, 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 B, so its marker has to land there; that clears every other open cell in the column.
  4. After that, 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.
  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 D5, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  7. Following that, if C2 were the marker, it would force B4 (the last open cell in region 1), and row 5 would end up with no open cell for its marker, which can't happen. So it can't go there.
  8. First, 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.
  9. Next, every remaining candidate in this region touches E3, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  10. Then, place a marker at E6. Region has exactly one open cell left. Placing here clears the rest of row 6, column E, and its region.
  11. After that, together, two regions have open cells only in rows 4 and 5; 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.
  12. Now, that one can't be the marker: at D2 it would force B3 (the last open cell in region 1), and row 4 would be left with no open cell for its marker.
  13. From there, place a marker at D3. Region has exactly one open cell left. Placing here clears the rest of row 3, column D, and its region. Placing here also clears its 1 touching neighbour.
  14. Following that, place a marker at B2. Region has exactly one open cell left.
  15. First, 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.
  16. Finally, place a marker at A4. Region has exactly one open cell left.

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