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
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This 8×8 board rates as expert (difficulty score 1238). Solving it from scratch takes 23 logical steps, using 7 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Line confinement, Shape squeeze, Forced chain. Every step below is forced: nothing here is a guess.

  1. First, every remaining candidate in this region touches E3, 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 B6, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  3. Then, marking A1 would force G5, G6, G7, and 1 more cleared (every open cell left in this region sits in column G, so its marker has to land there), then D6, E6, F6, and 6 more cleared (every open cell in column H belongs to the same region, so that region's marker has to be somewhere in this column), then E5 and F5 cleared (every open cell in column D belongs to the same region, so that region's marker has to be somewhere in this column), and the chain continues, and then column F would be left with no open cell for its marker. So A1 can't be the marker there.
  4. After that, if B1 were the marker, it would force C5, C6, C7, and 1 more cleared (every open cell left in this region sits in column C, so its marker has to land there), then A5 (the last open cell in region 7), and region 8 would end up with no open cell for its marker, which can't happen. So it can't go there.
  5. Now, every remaining candidate in this region touches B3, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  6. From there, that one can't be the marker: at C1 it would force G5, G6, G7, and 1 more cleared (every open cell left in this region sits in column G, so its marker has to land there), then D5, E5, F5, and 1 more cleared (every open cell left in this region sits in row 5, so its marker has to land there), then D6, D7 and D8 cleared (every open cell left in this region sits in column D, so its marker has to land there), and the chain continues, and column F would be left with no open cell for its marker.
  7. Following that, if E1 were the marker, it would force F5, F6, F7, and 1 more cleared (every open cell left in this region sits in column F, so its marker has to land there), then G5, G6, G7, and 1 more cleared (every open cell left in this region sits in column G, so its marker has to land there), then D6, D7 and D8 cleared (every open cell left in this region sits in column D, so its marker has to land there), and the chain continues, and region 7 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: at F1 it would force E4 (the last open cell in region 5), then G3 (the last open cell in region 3), then D2 (the last open cell in region 4), and region 1 would be left with no open cell for its marker.
  9. Next, marking G1 would force C5, C6, C7, and 1 more cleared (every open cell left in this region sits in column C, so its marker has to land there), then D5, E5, F5, and 1 more cleared (every open cell left in this region sits in row 5, so its marker has to land there), then D6, D7 and D8 cleared (every open cell left in this region sits in column D, so its marker has to land there), and the chain continues, and then column F would be left with no open cell for its marker. So G1 can't be the marker there.
  10. Then, if H1 were the marker, it would force C5, C6, C7, and 1 more cleared (every open cell left in this region sits in column C, so its marker has to land there), then D5, E5, F5, and 1 more cleared (every open cell left in this region sits in row 5, so its marker has to land there), then D6, D7 and D8 cleared (every open cell left in this region sits in column D, so its marker has to land there), and the chain continues, and column F would end up with no open cell for its marker, which can't happen. So it can't go there.
  11. After that, 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. Placing here also clears its 1 touching neighbour.
  12. Now, 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.
  13. From there, every open cell left in this region sits in row 5, so its marker has to land there; that clears every other open cell in the row.
  14. 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. Placing here also clears its 1 touching neighbour.
  15. First, every open cell in column H belongs to the same region, so that region's marker has to be somewhere in this column; that clears every other open cell in the region.
  16. Next, every remaining candidate in this region touches F3 and H3, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  17. Then, every remaining candidate in this region touches E4 and F4, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  18. After that, place a marker at F2. Region 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.
  19. Now, place a marker at G4. Region has exactly one open cell left. Placing here clears the rest of row 4, column G, and its region.
  20. From there, 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.
  21. Following that, place a marker at E5. Region has exactly one open cell left.
  22. 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.
  23. Finally, place a marker at H7. Region has exactly one open cell left.

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