QED Logic quod erat demonstrandum

A Severe 8×8 Puzzle Solved with Forced Chain in 24 Steps

8×8 · severe · 24 steps

Play this board yourself →
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This 8×8 board rates as severe (difficulty score 1404). Solving it from scratch takes 24 logical steps, using 6 techniques: Single cell, Row/column exclusion, Adjacency clear, 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 B2, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  2. Next, that one can't be the marker: at C1 it would force A2 (the last open cell in region 1), then B4 (the last open cell in region 4), then D6 (the last open cell in region 6), and region 8 would be left with no open cell for its marker.
  3. Then, marking D1 would force A2 (the last open cell in region 1), then B4 (the last open cell in region 4), then E5 (the last open cell in region 6), and then region 5 would be left with no open cell for its marker. So D1 can't be the marker there.
  4. After that, every remaining candidate in this region touches C3, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  5. Now, if E1 were the marker, it would force A2 (the last open cell in region 1), then B4 (the last open cell in region 4), then D3 (the last open cell in region 2), and region 6 would end up with no open cell for its marker, which can't happen. So it can't go there.
  6. From there, that one can't be the marker: at F1 it would force A2 (the last open cell in region 1), then B4 (the last open cell in region 4), then D3 (the last open cell in region 2), and the chain continues, and region 6 would be left with no open cell for its marker.
  7. Following that, marking G1 would force A2 (the last open cell in region 1), then B4 (the last open cell in region 4), then D3 (the last open cell in region 2), and the chain continues, and then region 5 would be left with no open cell for its marker. So G1 can't be the marker there.
  8. First, if H1 were the marker, it would force A2 (the last open cell in region 1), then B4 (the last open cell in region 4), then D3 (the last open cell in region 2), and the chain continues, and region 6 would end up with no open cell for its marker, which can't happen. So it can't go there.
  9. Next, 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.
  10. Then, that one can't be the marker: at D2 it would force F3 (the last open cell in region 3), then H4 (the last open cell in region 5), and region 4 would be left with no open cell for its marker.
  11. After that, marking E2 would force D6 (the last open cell in region 6), then C4 (the last open cell in region 2), and then region 8 would be left with no open cell for its marker. So E2 can't be the marker there.
  12. Now, if F2 were the marker, region 3 would end up with no open cell for its marker, which can't happen. So it can't go there.
  13. From there, that one can't be the marker: at G2 it would force E3 (the last open cell in region 3), then C4 (the last open cell in region 2), then A5 (the last open cell in region 4), and the chain continues, and region 8 would be left with no open cell for its marker.
  14. Following that, if A3 were the marker, it would force B1 (the last open cell in region 1), then H2 (the last open cell in region 3), then F5 (the last open cell in region 5), and the chain continues, and region 8 would end up with no open cell for its marker, which can't happen. So it can't go there.
  15. First, if B1 were the marker, it would force H2 (the last open cell in row 2), then D3 (the last open cell in row 3), then A4 (the last open cell in region 4), and region 5 would end up with no open cell for its marker, which can't happen. So it can't go there.
  16. Next, place a marker at A1. Region has exactly one open cell left. Placing here clears the rest of row 1, column A, and its region.
  17. Then, marking H2 would force F5 (the last open cell in region 5), then D6 (the last open cell in region 6), then C4 (the last open cell in region 2), and then row 3 would be left with no open cell for its marker. So H2 can't be the marker there.
  18. After that, place a marker at C2. Row 2 has exactly one open cell left. Placing here clears the rest of row 2, column C, and its region. Placing here also clears its 1 touching neighbour.
  19. Now, place a marker at D4. Region has exactly one open cell left. Placing here clears the rest of row 4, column D, and its region. Placing here also clears its 2 touching neighbours.
  20. From there, 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.
  21. Following that, place a marker at H5. Region has exactly one open cell left. Placing here clears the rest of row 5, column H, and its region. Placing here also clears its 1 touching neighbour.
  22. First, 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.
  23. Next, place a marker at E7. Region has exactly one open cell left. Placing here clears the rest of row 7, column E, and its region.
  24. Finally, place a marker at G8. Region has exactly one open cell left.

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