How to solve this 8×8 logic puzzle
This 8×8 board rates as sharp (difficulty score 1142). Solving it from scratch takes 31 logical steps, using 8 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Line confinement, Paired regions, Shape squeeze, Forced chain. Every step below is forced — nothing here is a guess.
- First, every open cell left in this region sits in column 1, so its marker has to land there — clearing every other open cell in the column.
- Next, every remaining candidate in this region touches row 6, column 2 and row 7, column 2 — so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
- Then, every open cell left in this region sits in row 8, so its marker has to land there — clearing every other open cell in the row.
- After that, together, two regions have open cells only in rows 6 and 7 — 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.
- Now, every open cell in column 5 belongs to the same region, so that region's marker has to be somewhere in this column — clearing every other open cell in the region.
- From there, every remaining candidate in this region touches row 4, column 2 — so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- Following that, marking row 1, column 8 forces a chain of moves that breaks another row, column, or region, so it can't be the marker there.
- First, place a marker at row 1, column 5. Row 1 has exactly one open cell left. Placing here clears the rest of row 1, column 5, and its region. Placing here also clears its 2 touching neighbours.
- Next, every remaining candidate in this region touches row 3, column 7 — so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- Then, marking row 2, column 3 forces a chain of moves that breaks another row, column, or region, so it can't be the marker there.
- After that, marking row 2, column 7 forces a chain of moves that breaks another row, column, or region, so it can't be the marker there.
- Now, marking row 2, column 8 forces a chain of moves that breaks another row, column, or region, so it can't be the marker there.
- From there, place a marker at row 2, column 2. Row 2 has exactly one open cell left. Placing here clears the rest of row 2, column 2, and its region. Placing here also clears its 1 touching neighbour.
- Following that, place a marker at row 8, column 4. Column 4 has exactly one open cell left. Placing here clears the rest of row 8, column 4, and its region.
- First, every open cell in row 3 belongs to the same region, so that region's marker has to be somewhere in this row — clearing every other open cell in the region.
- Next, every remaining candidate in this region touches row 4, column 7 — so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- Then, place a marker at row 4, column 3. Row 4 has exactly one open cell left. Placing here clears the rest of row 4, column 3, and its region.
- After that, every remaining candidate in this region touches row 6, column 7 — so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- Now, place a marker at row 5, column 7. Column 7 has exactly one open cell left. Placing here clears the rest of row 5, column 7, and its region. Placing here also clears its 1 touching neighbour.
- From there, place a marker at row 7, column 8. Region has exactly one open cell left. Placing here clears the rest of row 7, column 8, and its region.
- Following that, place a marker at row 3, column 6. Region has exactly one open cell left.
- Finally, place a marker at row 6, column 1. Region has exactly one open cell left.
The key move here was Forced chain — once you can spot that, this board falls quickly. ∎