QED Logic quod erat demonstrandum

An Expert 6×6 Puzzle Solved with Forced Chain in 17 Steps

6×6 · expert · 17 steps

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A
B
C
D
E
F
1
2
3
4
5
6
1×
2×
3×
×
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4×
×
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5×
6×
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This 6×6 board rates as expert (difficulty score 1119). Solving it from scratch takes 17 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 row 4, so its marker has to land there; that clears every other open cell in the row.
  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, 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.
  4. After that, every remaining candidate in this region touches E3 and F3 and E5 and F5, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  5. Now, marking A1 would force E2 (the last open cell in region 3), then F4 (the last open cell in region 5), then B3 (the last open cell in region 4), and the chain continues, and then row 6 would be left with no open cell for its marker. So A1 can't be the marker there.
  6. From there, that one can't be the marker: at C1 it would force E2 (the last open cell in region 3), then A3 (the last open cell in region 1), and row 5 would be left with no open cell for its marker.
  7. Following that, marking D1 would force B3 (the last open cell in column B), and then column A would be left with no open cell for its marker. So D1 can't be the marker there.
  8. First, together, two regions have open cells only in columns E and F; 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.
  9. Next, every remaining candidate in this region touches D5, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  10. Then, if E1 were the marker, it would force F4 (the last open cell in region 5), then B3 (the last open cell in column B), and row 2 would end up with no open cell for its marker, which can't happen. So it can't go there.
  11. After that, that one can't be the marker: at F1 it would force E4 (the last open cell in region 5), then B3 (the last open cell in column B), and column A would be left with no open cell for its marker.
  12. Now, place a marker at E2. Region has exactly one open cell left. Placing here clears the rest of row 2, column E, and its region. Placing here also clears its 1 touching neighbour.
  13. From there, place a marker at C3. Region has exactly one open cell left. Placing here clears the rest of row 3, column C, and its region.
  14. Following that, place a marker at B1. Region has exactly one open cell left.
  15. First, place a marker at F4. Region has exactly one open cell left.
  16. Next, place a marker at D6. Region has exactly one open cell left. Placing here clears the rest of row 6, column D, and its region.
  17. Finally, place a marker at A5. Region has exactly one open cell left.

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