QED Logic quod erat demonstrandum
Logic Ascent

How to solve this 6×6 logic puzzle

6×6 · steady · 16 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 steady (difficulty score 871). Solving it from scratch takes 22 logical steps, using 7 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Line confinement, Paired regions, Shape squeeze. Every step below is forced: nothing here is a guess.

  1. First, every open cell left in this region sits in row 1, so its marker has to land there; that clears every other open cell in the row.
  2. Next, every open cell left in this region sits in row 2, so its marker has to land there; that clears every other open cell in the row.
  3. Then, every open cell left in this region sits in row 3, so its marker has to land there; that clears every other open cell in the row.
  4. After that, every remaining candidate in this region touches E2, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  5. Now, every remaining candidate in this region touches E1 and E3, 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 open cell in column E 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.
  7. Following that, together, two regions have open cells only in columns D and F; with one marker each, those two markers have to fill exactly those two columns, so every other region's open cells there can be cleared.
  8. First, every remaining candidate in this region touches B4 and C4, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  9. Next, every remaining candidate in this region touches A5, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  10. Then, 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.
  11. After that, place a marker at A4. Region has exactly one open cell left. Placing here clears the rest of row 4, column A, and its region. Placing here also clears its 1 touching neighbour.
  12. Now, place a marker at C3. Region has exactly one open cell left. Placing here clears the rest of row 3, column C, and its region. Placing here also clears its 1 touching neighbour.
  13. From there, place a marker at F2. Region has exactly one open cell left. Placing here clears the rest of row 2, column F, and its region.
  14. Following that, place a marker at D1. Region has exactly one open cell left.
  15. First, place a marker at B6. Region has exactly one open cell left. Placing here clears the rest of row 6, column B, and its region.
  16. Finally, place a marker at E5. Region has exactly one open cell left.

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