QED Logic quod erat demonstrandum

A Hard 6×6 Puzzle Solved with Forced Chain in 12 Steps

6×6 · hard · 12 steps

Play this board yourself →
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 hard (difficulty score 950). Solving it from scratch takes 12 logical steps, using 8 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Line confinement, 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, place a marker at B3. Region has exactly one open cell left. Placing here clears the rest of row 3, column B, and its region. Placing here also clears its 2 touching neighbours.
  3. Then, every open cell left in this region sits in row 4, so its marker has to land there; that clears every other open cell in the row.
  4. After that, every open cell in column A 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.
  5. Now, every remaining candidate in this region touches E5, 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 D1 would force F2 (the last open cell in region 3), 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, if E1 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 E6. Column 5 has exactly one open cell left. Placing here clears the rest of row 6, column E, and its region.
  9. Next, place a marker at A5. Region has exactly one open cell left.
  10. Then, place a marker at C1. Column 3 has exactly one open cell left. Placing here clears the rest of row 1, column C, and its region.
  11. After that, 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.
  12. Finally, place a marker at D4. Region has exactly one open cell left.

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