QED Logic quod erat demonstrandum
Logic Ascent

How to solve this 6×6 logic puzzle

6×6 · sharp · 14 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 948). 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 B, so its marker has to land there; that clears every other open cell in the column.
  3. 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.
  4. After that, every open cell left in this region sits in column D, so its marker has to land there; that clears every other open cell in the column.
  5. Now, every remaining candidate in this region touches E1 and E2, 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 remaining candidate in this region touches A4 and C4 and C5, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  7. Following that, that one can't be the marker: at F1 it would force D2 (the last open cell in region 1), then A3 (the last open cell in region 3), then B5 (the last open cell in region 6), and column C would be left with no open cell for its marker.
  8. First, place a marker at D1. Row 1 has exactly one open cell left. Placing here clears the rest of row 1, column D, and its region.
  9. Next, together, two regions have open cells only in rows 2 and 3; 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.
  10. Then, 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 1 touching neighbour.
  11. After that, place a marker at B4. Region 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.
  12. Now, 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.
  13. From there, place a marker at E3. Region has exactly one open cell left. Placing here clears the rest of row 3, column E, and its region.
  14. Finally, place a marker at F5. Region has exactly one open cell left.

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