QED Logic quod erat demonstrandum
Logic Ascent

How to solve this 6×6 logic puzzle

6×6 · sharp · 17 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 1079). Solving it from scratch takes 23 logical steps, using 7 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Line confinement, 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 remaining candidate in this region touches B5 and B6, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  3. Then, every remaining candidate in this region touches C4, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  4. After that, if B1 were the marker, it would force C5 (the last open cell in region 4), then A6 (the last open cell in region 6), and region 5 would end up with no open cell for its marker, which can't happen. So it can't go there.
  5. Now, that one can't be the marker: at C1 it would force E2 (the last open cell in region 2), and row 3 would be left with no open cell for its marker.
  6. From there, marking D1 would force B4 (the last open cell in region 4), and then column C would be left with no open cell for its marker. So D1 can't be the marker there.
  7. Following that, that one can't be the marker: at F1 it would force D2 (the last open cell in region 2), then B3 (the last open cell in region 1), and row 4 would be left with no open cell for its marker.
  8. First, place a marker at E1. Row 1 has exactly one open cell left. Placing here clears the rest of row 1, column E, and its region. Placing here also clears its 1 touching neighbour.
  9. Next, every open cell left in this region sits in column F, so its marker has to land there; that clears every other open cell in the column.
  10. Then, every open cell in row 2 belongs to the same region, so that region's marker has to be somewhere in this row; that clears every other open cell in the region.
  11. After that, place a marker at F3. Row 3 has exactly one open cell left. Placing here clears the rest of row 3, column F, and its region.
  12. Now, every open cell in column D belongs to the same region, so that region's marker has to be somewhere in this column; that clears every other open cell in the region.
  13. From there, 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.
  14. Following 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.
  15. First, place a marker at C2. Region has exactly one open cell left.
  16. Next, place a marker at A6. Region has exactly one open cell left. Placing here clears the rest of row 6, column A, and its region.
  17. Finally, place a marker at D5. Region has exactly one open cell left.

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