QED Logic quod erat demonstrandum

An Expert 8×8 Puzzle Solved with Forced Chain in 23 Steps

8×8 · expert · 23 steps

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A
B
C
D
E
F
G
H
1
2
3
4
5
6
7
8
1×
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 1200). Solving it from scratch takes 23 logical steps, using 8 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Line 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 H, so its marker has to land there; that clears every other open cell in the column.
  2. Next, every open cell in row 8 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.
  3. Then, place a marker at C7. Row 7 has exactly one open cell left. Placing here clears the rest of row 7, column C, and its region. Placing here also clears its 2 touching neighbours.
  4. After that, together, two regions have open cells only in columns F and G; 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.
  5. Now, marking A1 would force E2 (the last open cell in region 2), and then row 8 would be left with no open cell for its marker. So A1 can't be the marker there.
  6. From there, marking D1 would force G4 and G5 cleared (every open cell left in this region sits in column G, so its marker has to land there), then H2 and H3 cleared (every remaining candidate in this region touches H2 and H3), then H4 (the last open cell in region 4), and the chain continues, and then column B would be left with no open cell for its marker. So D1 can't be the marker there.
  7. Following that, if E1 were the marker, it would force A8 (the last open cell in region 8), then F6 (the last open cell in row 6), then D5 (the last open cell in row 5), and the chain continues, and row 4 would end up with no open cell for its marker, which can't happen. So it can't go there.
  8. First, that one can't be the marker: place it at F1, and region 2 would be left with no open cell for its marker.
  9. Next, every open cell left in this region sits in column G, so its marker has to land there; that clears every other open cell in the column.
  10. Then, every remaining candidate in this region touches H2, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  11. After that, 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.
  12. Now, marking G1 would force E2 (the last open cell in region 2), then A8 (the last open cell in region 8), and then region 1 would be left with no open cell for its marker. So G1 can't be the marker there.
  13. From there, every remaining candidate in this region touches H3, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  14. Following that, if H1 were the marker, it would force E2 (the last open cell in region 2), then G3 (the last open cell in region 3), and column B would end up with no open cell for its marker, which can't happen. So it can't go there.
  15. First, place a marker at H4. Region has exactly one open cell left. Placing here clears the rest of row 4, column H, and its region. Placing here also clears its 1 touching neighbour.
  16. Next, place a marker at G2. Region has exactly one open cell left. Placing here clears the rest of row 2, column G, and its region.
  17. Then, place a marker at B1. Region has exactly one open cell left. Placing here clears the rest of row 1, column B, and its region.
  18. After that, 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.
  19. Now, every remaining candidate in this region touches E6, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  20. From there, place a marker at D5. Region has exactly one open cell left. Placing here clears the rest of row 5, column D, and its region.
  21. Following that, place a marker at A3. Region has exactly one open cell left. Placing here clears the rest of row 3, column A, and its region.
  22. First, place a marker at F6. Region has exactly one open cell left.
  23. Finally, place a marker at E8. Region has exactly one open cell left.

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