QED Logic quod erat demonstrandum

An Expert 8×8 Puzzle Solved with Forced Chain in 19 Steps

8×8 · expert · 19 steps

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A
B
C
D
E
F
G
H
1
2
3
4
5
6
7
8
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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7×
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8×
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This 8×8 board rates as expert (difficulty score 1162). Solving it from scratch takes 19 logical steps, using 7 techniques: Single cell, Row/column exclusion, Adjacency clear, 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 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.
  2. Next, every remaining candidate in this region touches D7, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  3. Then, that one can't be the marker: at C1 it would force D8 (the last open cell in region 6), then A7 (the last open cell in region 8), then B5 (the last open cell in region 4), and the chain continues, and column E would be left with no open cell for its marker.
  4. After that, every open cell in row 1 belongs to the same region, so that region's marker has to be somewhere in this row; that clears every other open cell in the region.
  5. Now, marking D1 would force F2 (the last open cell in row 2), then C3 (the last open cell in row 3), and then region 6 would be left with no open cell for its marker. So D1 can't be the marker there.
  6. From there, if E1 were the marker, it would force C2 (the last open cell in row 2), then D8 (the last open cell in region 6), then A7 (the last open cell in region 8), and the chain continues, and row 3 would end up with no open cell for its marker, which can't happen. So it can't go there.
  7. Following that, that one can't be the marker: at F1 it would force C2 (the last open cell in row 2), then D8 (the last open cell in region 6), then A7 (the last open cell in region 8), and region 7 would be left with no open cell for its marker.
  8. First, marking G1 would force F3 (the last open cell in region 3), then C2 (the last open cell in row 2), then D8 (the last open cell in region 6), and the chain continues, and then region 8 would be left with no open cell for its marker. So G1 can't be the marker there.
  9. Next, place a marker at H1. Region has exactly one open cell left. Placing here clears the rest of row 1, column H, and its region.
  10. Then, if C2 were the marker, it would force D8 (the last open cell in region 6), then A7 (the last open cell in region 8), then B5 (the last open cell in region 4), and the chain continues, and column E would end up with no open cell for its marker, which can't happen. So it can't go there.
  11. After that, marking E2 would force G3 (the last open cell in row 3), then A4 (the last open cell in row 4), then B8 (the last open cell in region 8), and the chain continues, and then column D would be left with no open cell for its marker. So E2 can't be the marker there.
  12. Now, place a marker at F2. Row 2 has exactly one open cell left. Placing here clears the rest of row 2, column F, and its region. Placing here also clears its 1 touching neighbour.
  13. From there, every open cell in row 3 belongs to the same region, so that region's marker has to be somewhere in this row; that clears every other open cell in the region.
  14. Following that, place a marker at A4. Row 4 has exactly one open cell left. Placing here clears the rest of row 4, column A, and its region.
  15. First, place a marker at B8. Region has exactly one open cell left. Placing here clears the rest of row 8, column B, and its region. Placing here also clears its 1 touching neighbour.
  16. Next, 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.
  17. Then, place a marker at D3. Region has exactly one open cell left.
  18. After that, place a marker at G7. Region has exactly one open cell left. Placing here clears the rest of row 7, column G, and its region.
  19. Finally, place a marker at E5. Region has exactly one open cell left.

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