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 940). Solving it from scratch takes 21 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, 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.
  2. Next, 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.
  3. Then, every remaining candidate in this region touches E1, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  4. After that, together, two regions have open cells only in columns B and D; 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.
  5. Now, every remaining candidate in this region touches C5, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  6. From there, 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. Placing here also clears its 2 touching neighbours.
  7. Following that, 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.
  8. First, marking D1 would force F2 (the last open cell in region 2), then B4 (the last open cell in region 4), and then row 3 would be left with no open cell for its marker. So D1 can't be the marker there.
  9. Next, place a marker at D4. Column 4 has exactly one open cell left. Placing here clears the rest of row 4, column D, and its region. Placing here also clears its 2 touching neighbours.
  10. Then, place a marker at E2. Column 5 has exactly one open cell left. Placing here clears the rest of row 2, column E, and its region. Placing here also clears its 1 touching neighbour.
  11. After that, 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.
  12. Now, place a marker at A3. Region has exactly one open cell left. Placing here clears the rest of row 3, column A, and its region.
  13. Finally, place a marker at B1. Region has exactly one open cell left.

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