QED Logic quod erat demonstrandum

An Expert 6×6 Puzzle Solved with Forced Chain in 22 Steps

6×6 · expert · 22 steps

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A
B
C
D
E
F
1
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5
6
1×
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2×
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3×
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4×
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5×
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6×
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This 6×6 board rates as expert (difficulty score 1155). Solving it from scratch takes 22 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 2, 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 rows 1 and 3; 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.
  3. Then, every remaining candidate in this region touches C1 and C3, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  4. After that, 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.
  5. Now, every remaining candidate in this region touches D1, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  6. From there, 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.
  7. Following that, 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.
  8. First, marking A1 would force F3 (the last open cell in region 2), then D4 (the last open cell in region 4), and then row 5 would be left with no open cell for its marker. So A1 can't be the marker there.
  9. Next, if B1 were the marker, it would force F3 (the last open cell in region 2), then D2 (the last open cell in region 3), and region 4 would end up with no open cell for its marker, which can't happen. So it can't go there.
  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 A4 and B4, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  12. Now, if E1 were the marker, it would force C2 (the last open cell in region 3), then A3 (the last open cell in region 1), and region 5 would end up with no open cell for its marker, which can't happen. So it can't go there.
  13. From there, 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.
  14. Following that, 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.
  15. First, 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.
  16. Next, every open cell left in this region sits in row 6, so its marker has to land there; that clears every other open cell in the row.
  17. Then, every remaining candidate in this region touches B6, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  18. After that, place a marker at B3. Column 2 has exactly one open cell left. Placing here clears the rest of row 3, column B, and its region. Placing here also clears its 1 touching neighbour.
  19. Now, place a marker at D2. Region has exactly one open cell left. Placing here clears the rest of row 2, column D, and its region.
  20. From there, place a marker at E4. Region has exactly one open cell left. Placing here clears the rest of row 4, column E, and its region.
  21. Following that, place a marker at C6. Region has exactly one open cell left. Placing here clears the rest of row 6, column C, and its region.
  22. 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. ∎