QED Logic quod erat demonstrandum
Logic Ascent

How to solve this 8×8 logic puzzle

8×8 · steady · 17 steps

A
B
C
D
E
F
G
H
1
2
3
4
5
6
7
8
1
2🐱
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3
4
🐱
5
6
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7
🐱
8
🐱
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This 8×8 board rates as steady (difficulty score 844). Solving it from scratch takes 27 logical steps, using 7 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Line confinement, Paired regions, Shape squeeze. Every step below is forced: nothing here is a guess.

  1. First, place a marker at H1. Region has exactly one open cell left. Placing here clears the rest of row 1, column H, and its region. Placing here also clears its 1 touching neighbour.
  2. Next, every open cell left in this region sits in row 3, so its marker has to land there; that clears every other open cell in the row.
  3. Then, every open cell left in this region sits in column A, so its marker has to land there; that clears every other open cell in the column.
  4. After that, every open cell in row 8 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.
  5. Now, place a marker at A7. Row 7 has exactly one open cell left. Placing here clears the rest of row 7, column A, and its region. Placing here also clears its 2 touching neighbours.
  6. From there, together, two regions have open cells only in columns F and G; 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.
  7. Following that, 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.
  8. First, every remaining candidate in this region touches C4, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  9. Next, 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.
  10. Then, every open cell left in this region sits in row 5, so its marker has to land there; that clears every other open cell in the row.
  11. After that, every open cell left in this region sits in row 6, so its marker has to land there; that clears every other open cell in the row.
  12. Now, every remaining candidate in this region touches D5, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  13. From there, 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 1 touching neighbour.
  14. Following that, 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. Placing here also clears its 1 touching neighbour.
  15. First, place a marker at G3. Region has exactly one open cell left. Placing here clears the rest of row 3, column G, and its region.
  16. Next, place a marker at F6. Region has exactly one open cell left.
  17. Finally, place a marker at D8. Region has exactly one open cell left.

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