QED Logic quod erat demonstrandum
Logic Ascent

How to solve this 6×6 logic puzzle

6×6 · severe · 17 steps

A
B
C
D
E
F
1
2
3
4
5
6
1
2
3
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4
5
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6
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This 6×6 board rates as severe (difficulty score 1134). Solving it from scratch takes 24 logical steps, using 6 techniques: Single cell, Row/column exclusion, Adjacency clear, Line confinement, Shape squeeze, Forced chain. Every step below is forced: nothing here is a guess.

  1. First, every remaining candidate in this region touches B2, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  2. Next, every remaining candidate in this region touches B5, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  3. Then, marking A1 would force B6 (the last open cell in region 6), then C4 (the last open cell in region 5), then D2 (the last open cell in region 2), and then region 3 would be left with no open cell for its marker. So A1 can't be the marker there.
  4. After that, if B1 were the marker, column D 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: place it at C1, and column D would be left with no open cell for its marker.
  6. From there, every open cell in row 1 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.
  7. Following that, marking D1 would force E4 (the last open cell in region 2), then F6 (the last open cell in region 4), then C5 (the last open cell in region 5), and then region 6 would be left with no open cell for its marker. So D1 can't be the marker there.
  8. First, 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.
  9. Next, if E1 were the marker, it would force A2 (the last open cell in row 2), then B6 (the last open cell in region 6), then C4 (the last open cell in region 5), and column D would end up with no open cell for its marker, which can't happen. So it can't go there.
  10. Then, place a marker at F1. Region has exactly one open cell left. Placing here clears the rest of row 1, column F, and its region.
  11. After that, that one can't be the marker: at A2 it would force B6 (the last open cell in region 6), then C4 (the last open cell in region 5), and column D would be left with no open cell for its marker.
  12. Now, place a marker at D2. Row 2 has exactly one open cell left. Placing here clears the rest of row 2, column D, and its region. Placing here also clears its 2 touching neighbours.
  13. From there, every open cell in row 4 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.
  14. Following that, place a marker at C4. Column 3 has exactly one open cell left. Placing here clears the rest of row 4, column C, and its region. Placing here also clears its 1 touching neighbour.
  15. First, 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.
  16. 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.
  17. 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.