QED Logic quod erat demonstrandum

A Hard 6×6 Puzzle Solved with Forced Chain in 17 Steps

6×6 · hard · 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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×
×
×
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×
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4
×
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5×
6×
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This 6×6 board rates as hard (difficulty score 1082). 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 column B, so its marker has to land there; that clears every other open cell in the column.
  2. Next, together, two regions have open cells only in rows 5 and 6; 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 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 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.
  5. Now, every remaining candidate in this region touches C5 and C6, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  6. From there, marking A1 would force C4 (the last open cell in column C), and then row 5 would be left with no open cell for its marker. So A1 can't be the marker there.
  7. Following that, that one can't be the marker: at C1 it would force D3 (the last open cell in region 2), then F2 (the last open cell in region 3), then A4 (the last open cell in region 4), and row 5 would be left with no open cell for its marker.
  8. First, marking D1 would force B5 (the last open cell in row 5), and then row 4 would be left with no open cell for its marker. So D1 can't be the marker there.
  9. Next, that one can't be the marker: at F1 it would force E6 (the last open cell in column E), then B5 (the last open cell in region 5), then D4 (the last open cell in region 4), and region 2 would be left with no open cell for its marker.
  10. Then, place a marker at E1. Row 1 has exactly one open cell left. Placing here clears the rest of row 1, column E, and its region. Placing here also clears its 1 touching neighbour.
  11. After that, place a marker at F3. Region has exactly one open cell left. Placing here clears the rest of row 3, column F, and its region.
  12. Now, every open cell left in this region sits in column D, so its marker has to land there; that clears every other open cell in the column.
  13. From there, 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.
  14. Following that, 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.
  15. First, place a marker at D5. Region has exactly one open cell left. Placing here also clears its 1 touching neighbour.
  16. Next, place a marker at A4. Region has exactly one open cell left. Placing here clears the rest of row 4, column A, and its region.
  17. Finally, place a marker at C2. Region has exactly one open cell left.

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