QED Logic quod erat demonstrandum
Logic Ascent

How to solve this 8×8 logic puzzle

8×8 · severe · 22 steps

A
B
C
D
E
F
G
H
1
2
3
4
5
6
7
8
1
2
3
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4
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5🐱
6🐱
7
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8🐱

This 8×8 board rates as severe (difficulty score 1225). Solving it from scratch takes 32 logical steps, using 7 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Paired regions, Shape squeeze, Forced chain. Every step below is forced: nothing here is a guess.

  1. First, place a marker at A8. Region has exactly one open cell left. Placing here clears the rest of row 8, column A, and its region. Placing here also clears its 1 touching neighbour.
  2. Next, together, two regions have open cells only in rows 6 and 7; 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.
  3. Then, 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.
  4. After that, every remaining candidate in this region touches G2, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  5. Now, if B1 were the marker, it would force F2 (the last open cell in region 3), and row 3 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 C1 it would force F2 (the last open cell in region 3), and column G would be left with no open cell for its marker.
  7. Following that, marking D1 would force F2 (the last open cell in region 3), and then column G would be left with no open cell for its marker. So D1 can't be the marker there.
  8. First, together, two regions have open cells only in rows 3 and 4; 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.
  9. Next, if E1 were the marker, row 2 would end up with no open cell for its marker, which can't happen. So it can't go there.
  10. Then, every open cell left in this region sits in row 2, so its marker has to land there; that clears every other open cell in the row.
  11. After that, that one can't be the marker: at F1 it would force D7 (the last open cell in region 7), then B6 (the last open cell in region 6), then C2 (the last open cell in region 2), and region 1 would be left with no open cell for its marker.
  12. Now, place a marker at G1. Region has exactly one open cell left. Placing here clears the rest of row 1, column G, and its region.
  13. From there, marking B2 would force C7 (the last open cell in region 6), then D3 (the last open cell in region 1), and then column E would be left with no open cell for its marker. So B2 can't be the marker there.
  14. Following that, every remaining candidate in this region touches D3, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  15. First, together, two regions have open cells only in columns C 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.
  16. Next, 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.
  17. Then, that one can't be the marker: at D2 it would force F3 (the last open cell in row 3), and column E would be left with no open cell for its marker.
  18. After that, place a marker at E2. Region has exactly one open cell left. Placing here clears the rest of row 2, column E, and its region. Placing here also clears its 1 touching neighbour.
  19. Now, place a marker at C3. Row 3 has exactly one open cell left. Placing here clears the rest of row 3, column C, and its region. Placing here also clears its 1 touching neighbour.
  20. From there, 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.
  21. Following that, place a marker at B6. Region has exactly one open cell left.
  22. Finally, place a marker at D7. Region has exactly one open cell left.

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