QED Logic quod erat demonstrandum
Logic Ascent

How to solve this 6×6 logic puzzle

6×6 · steady · 15 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 842). Solving it from scratch takes 22 logical steps, using 5 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Shape squeeze. Every step below is forced: nothing here is a guess.

  1. First, every open cell left in this region sits in row 5, 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 6, 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 4, 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 E6 and F6, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  5. Now, place a marker at D6. Region has exactly one open cell left. Placing here clears the rest of row 6, column D, and its region. Placing here also clears its 1 touching neighbour.
  6. From there, place a marker at F5. Region has exactly one open cell left. Placing here clears the rest of row 5, column F, and its region.
  7. Following 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.
  8. First, every remaining candidate in this region touches B2, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  9. Next, every remaining candidate in this region touches B3, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  10. Then, every open cell left in this region sits in column C, so its marker has to land there; that clears every other open cell in the column.
  11. After that, every remaining candidate in this region touches A3, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  12. Now, place a marker at C3. Row 3 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 A4. Region has exactly one open cell left. Placing here clears the rest of row 4, column A, and its region.
  14. Following that, 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.
  15. Finally, place a marker at E2. Region has exactly one open cell left.

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