QED Logic quod erat demonstrandum
Logic Ascent

How to solve this 8×8 logic puzzle

8×8 · severe · 20 steps

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
8🐱
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This 8×8 board rates as severe (difficulty score 1169). Solving it from scratch takes 31 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 B7, 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 E7, 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 B8 (the last open cell in region 8), then C6 (the last open cell in region 6), and then region 7 would be left with no open cell for its marker. So A1 can't be the marker there.
  4. After that, 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.
  5. Now, if B1 were the marker, region 8 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 B6 (the last open cell in region 6), then A8 (the last open cell in region 8), and region 1 would be left with no open cell for its marker.
  7. Following that, every remaining candidate in this region touches E1, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  8. First, that one can't be the marker: at F1 it would force D2 (the last open cell in region 2), then E8 (the last open cell in region 7), then A7 (the last open cell in region 8), and region 1 would be left with no open cell for its marker.
  9. Next, marking G1 would force B8 (the last open cell in region 8), then C6 (the last open cell in region 6), and then region 7 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 B8 (the last open cell in region 8), then C6 (the last open cell in region 6), and region 7 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 row 8, so its marker has to land there; that clears every other open cell in the row.
  13. From there, 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. Placing here also clears its 1 touching neighbour.
  14. Following that, place a marker at B2. Region has exactly one open cell left. Placing here clears the rest of row 2, column B, and its region. Placing here also clears its 1 touching neighbour.
  15. First, 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.
  16. Next, 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.
  17. Then, place a marker at G3. Column 7 has exactly one open cell left. Placing here clears the rest of row 3, column G, and its region. Placing here also clears its 1 touching neighbour.
  18. After 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.
  19. Now, place a marker at E4. Region has exactly one open cell left. Placing here clears the rest of row 4, column E, and its region.
  20. Finally, place a marker at F8. Region has exactly one open cell left.

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