QED Logic quod erat demonstrandum
Logic Ascent

How to solve this 6×6 logic puzzle

6×6 · steady · 12 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 930). Solving it from scratch takes 19 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 F2. Region has exactly one open cell left. Placing here clears the rest of row 2, column F, and its region. Placing here also clears its 2 touching neighbours.
  2. Next, 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.
  3. Then, together, two regions have open cells only in columns A and B; 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.
  4. After that, every remaining candidate in this region touches D5 and D6, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  5. Now, 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.
  6. From there, marking D1 would force B3 (the last open cell in region 1), and then row 4 would be left with no open cell for its marker. So D1 can't be the marker there.
  7. Following that, place a marker at A1. Row 1 has exactly one open cell left. Placing here clears the rest of row 1, column A, and its region.
  8. First, every remaining candidate in this region touches C3 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, place a marker at D3. Row 3 has exactly one open cell left. Placing here clears the rest of row 3, column D, and its region.
  10. Then, place a marker at B4. Row 4 has exactly one open cell left. Placing here clears the rest of row 4, column B, and its region. Placing here also clears its 1 touching neighbour.
  11. After that, 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.
  12. Finally, place a marker at E5. Region has exactly one open cell left.

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