QED Logic quod erat demonstrandum
Logic Ascent

How to solve this 6×6 logic puzzle

6×6 · sharp · 15 steps

A
B
C
D
E
F
1
2
3
4
5
6
1
2
🐱
3
🐱
4
🐱
🐱
5
6
🐱
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This 6×6 board rates as sharp (difficulty score 1020). Solving it from scratch takes 20 logical steps, using 6 techniques: Single cell, Row/column exclusion, Adjacency clear, Paired regions, Shape squeeze, Forced chain. Every step below is forced: nothing here is a guess.

  1. First, together, two regions have open cells only in rows 1 and 2; 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.
  2. Next, 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.
  3. Then, together, two regions have open cells only in rows 5 and 6; 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.
  4. After that, 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.
  5. Now, every remaining candidate in this region touches D4, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  6. From there, marking A1 would force C2 (the last open cell in region 2), and then region 4 would be left with no open cell for its marker. So A1 can't be the marker there.
  7. Following that, if B1 were the marker, row 2 would end up with no open cell for its marker, which can't happen. So it can't go there.
  8. First, place a marker at A2. Region has exactly one open cell left. Placing here clears the rest of row 2, column A, and its region.
  9. Next, 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. Placing here also clears its 1 touching neighbour.
  10. Then, together, two regions have open cells only in columns F and E; 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.
  11. After that, every remaining candidate in this region touches E4 and F4, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  12. Now, place a marker at F3. Region has exactly one open cell left. Placing here clears the rest of row 3, column F, and its region.
  13. From there, place a marker at C4. Region has exactly one open cell left. Placing here clears the rest of row 4, column C, and its region.
  14. Following that, place a marker at D1. Region has exactly one open cell left.
  15. 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. ∎