QED Logic quod erat demonstrandum

An Expert 6×6 Puzzle Solved with Forced Chain in 18 Steps

6×6 · expert · 18 steps

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A
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This 6×6 board rates as expert (difficulty score 1193). Solving it from scratch takes 18 logical steps, using 6 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Shape squeeze, Forced chain. Every step below is forced: nothing here is a guess.

  1. First, every remaining candidate in this region touches D4, 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 D2, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  3. Then, if B1 were the marker, it would force F2 (the last open cell in region 2), then D3 (the last open cell in region 3), and row 4 would end up with no open cell for its marker, which can't happen. So it can't go there.
  4. After that, that one can't be the marker: at C1 it would force F2 (the last open cell in region 2), then D3 (the last open cell in region 3), and row 4 would be left with no open cell for its marker.
  5. Now, if E1 were the marker, it would force D3 (the last open cell in region 3), then C5 (the last open cell in region 4), and column B would end up with no open cell for its marker, which can't happen. So it can't go there.
  6. From there, that one can't be the marker: at F1 it would force A2 (the last open cell in row 2), then C3 cleared (every open cell left in this region sits in row 3, so its marker has to land there), then E3 cleared (every open cell left in this region sits in column E, so its marker has to land there), and the chain continues, and row 4 would be left with no open cell for its marker.
  7. Following that, marking B2 would immediately leave row 1 with no open cell for its marker, so it can't be the marker there.
  8. First, if C2 were the marker, it would force E3 (the last open cell in region 3), then D5 (the last open cell in region 4), then F6 (the last open cell in region 5), and region 6 would end up with no open cell for its marker, which can't happen. So it can't go there.
  9. Next, every remaining candidate in this region touches E2, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  10. Then, every open cell left in this region sits in row 3, so its marker has to land there; that clears every other open cell in the row.
  11. After that, every remaining candidate in this region touches E4, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  12. Now, marking A1 would force F2 (the last open cell in region 2), then D3 (the last open cell in region 3), and then row 4 would be left with no open cell for its marker. So A1 can't be the marker there.
  13. From there, 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.
  14. Following that, 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. Placing here also clears its 1 touching neighbour.
  15. First, place a marker at A2. Row 2 has exactly one open cell left. Placing here clears the rest of row 2, column A, and its region.
  16. Next, place a marker at C4. Row 4 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.
  17. Then, 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.
  18. 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. ∎