QED Logic quod erat demonstrandum

A Sharp 8×8 Puzzle Solved with Forced Chain in 27 Steps

8×8 · sharp · 18 steps

Play this board yourself →
A
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8🐱
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This 8×8 board rates as sharp (difficulty score 1050). Solving it from scratch takes 27 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, 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 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.
  3. Then, together, two regions have open cells only in columns C and D; 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.
  4. After that, every remaining candidate in this region touches F7, 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 F8 (the last open cell in region 7), then A7 (the last open cell in region 8), then B5 (the last open cell in region 4), 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 C2 (the last open cell in row 2), then E6 (the last open cell in region 7), then G4 (the last open cell in region 5), and column H would be left with no open cell for its marker.
  7. Following that, marking E2 would force F8 (the last open cell in region 7), then A7 (the last open cell in region 8), and then column D would be left with no open cell for its marker. So E2 can't be the marker there.
  8. First, 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.
  9. Next, together, two regions have open cells only in rows 7 and 8; 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.
  10. Then, place a marker at E6. Region has exactly one open cell left. Placing here clears the rest of row 6, column E, and its region. Placing here also clears its 2 touching neighbours.
  11. After that, place a marker at D8. Region has exactly one open cell left. Placing here clears the rest of row 8, column D, and its region.
  12. Now, place a marker at A7. Region has exactly one open cell left. Placing here clears the rest of row 7, column A, and its region.
  13. From there, place a marker at B5. Region has exactly one open cell left. Placing here clears the rest of row 5, column B, and its region.
  14. Following that, 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.
  15. First, every remaining candidate in this region touches G4, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  16. Next, place a marker at F4. Region has exactly one open cell left. Placing here clears the rest of row 4, column F, and its region. Placing here also clears its 1 touching neighbour.
  17. Then, place a marker at H3. Region has exactly one open cell left. Placing here clears the rest of row 3, column H, and its region.
  18. Finally, place a marker at G1. Region has exactly one open cell left.

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