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
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5
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6
7
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8
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This 8×8 board rates as sharp (difficulty score 963). Solving it from scratch takes 25 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, every remaining candidate in this region touches F2, 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 G2, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  3. Then, 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.
  4. After that, 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.
  5. Now, 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.
  6. From there, that one can't be the marker: at F1 it would force A4 (the last open cell in region 1), then C5 (the last open cell in region 5), and column B would be left with no open cell for its marker.
  7. Following that, 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. Placing here also clears its 1 touching neighbour.
  8. First, 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.
  9. Next, together, two regions have open cells only in rows 2 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.
  10. Then, place a marker at C5. Region has exactly one open cell left. Placing here clears the rest of row 5, column C, and its region. Placing here also clears its 2 touching neighbours.
  11. After that, place a marker at B2. Column 2 has exactly one open cell left. Placing here clears the rest of row 2, column B, and its region.
  12. Now, 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.
  13. From there, 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 1 touching neighbour.
  14. Following 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.
  15. Finally, place a marker at A7. Region has exactly one open cell left.

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