QED Logic quod erat demonstrandum
Logic Ascent

How to solve this 8×8 logic puzzle

8×8 · sharp · 19 steps

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

This 8×8 board rates as sharp (difficulty score 1034). Solving it from scratch takes 27 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 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, together, two regions have open cells only in columns B and A; 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.
  3. Then, 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.
  4. After that, every open cell left in this region sits in column C, so its marker has to land there; that clears every other open cell in the column.
  5. Now, every remaining candidate in this region touches D4, 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 D2 it would force C4 (the last open cell in region 3), and row 7 would be left with no open cell for its marker.
  7. Following that, every open cell left in this region sits in column E, so its marker has to land there; that clears every other open cell in the column.
  8. First, every remaining candidate in this region touches F2 and F3, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  9. Next, place a marker at E2. Row 2 has exactly one open cell left. Placing here clears the rest of row 2, column E, and its region.
  10. Then, that one can't be the marker: at F4 it would force C3 (the last open cell in region 3), then D5 (the last open cell in region 5), then G8 (the last open cell in region 7), and row 7 would be left with no open cell for its marker.
  11. After that, every open cell left in this region sits in column G, so its marker has to land there; that clears every other open cell in the column.
  12. Now, place a marker at C4. Row 4 has exactly one open cell left. Placing here clears the rest of row 4, column C, and its region. Placing here also clears its 2 touching neighbours.
  13. From there, place a marker at G3. Row 3 has exactly one open cell left. Placing here clears the rest of row 3, column G, and its region.
  14. Following that, place a marker at F5. Row 5 has exactly one open cell left. Placing here clears the rest of row 5, column F, and its region.
  15. First, 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.
  16. Next, every remaining candidate in this region touches A7 and B7, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  17. Then, 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.
  18. After that, place a marker at B6. Region has exactly one open cell left.
  19. 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. ∎