QED Logic quod erat demonstrandum
Logic Ascent

How to solve this 8×8 logic puzzle

8×8 · sharp · 15 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🐱
5
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6
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7
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8
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This 8×8 board rates as sharp (difficulty score 982). Solving it from scratch takes 24 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 D2. Region has exactly one open cell left. Placing here clears the rest of row 2, column D, and its region. Placing here also clears its 4 touching neighbours.
  2. Next, every open cell left in this region sits in row 1, so its marker has to land there; that clears every other open cell in the row.
  3. Then, 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.
  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, place a marker at C4. Region has exactly one open cell left. Placing here clears the rest of row 4, column C, and its region. Placing here also clears its 1 touching neighbour.
  6. 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.
  7. Following that, that one can't be the marker: at F1 it would force B6 (the last open cell in region 7), then E7 (the last open cell in region 5), and region 8 would be left with no open cell for its marker.
  8. First, together, two regions have open cells only in columns G and H; 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.
  9. Next, marking E5 would immediately leave region 5 with no open cell for its marker, so it can't be the marker there.
  10. Then, 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.
  11. After that, 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.
  12. Now, place a marker at F5. Region has exactly one open cell left. Placing here clears the rest of row 5, column F, and its region.
  13. From there, place a marker at E8. Region has exactly one open cell left. Placing here clears the rest of row 8, column E, and its region.
  14. Following that, place a marker at H7. Region has exactly one open cell left. Placing here clears the rest of row 7, column H, and its region.
  15. 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. ∎