QED

How to solve this 7×7 logic puzzle

7×7 · sharp · 12 steps

This 7×7 board rates as sharp (difficulty score 956). Solving it from scratch takes 21 logical steps, using 6 techniques: Single cell, Row/column exclusion, Adjacency clear, Paired regions, Shape squeeze, Forced chain. Every step below is forced — nothing here is a guess.

  1. First, place a marker at row 3, column 3. Region has exactly one open cell left. Placing here clears the rest of row 3, column 3, and its region. Placing here also clears its 4 touching neighbours.
  2. Next, together, two regions have open cells only in rows 1 and 2 — 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.
  3. Then, place a marker at row 4, column 1. Region has exactly one open cell left. Placing here clears the rest of row 4, column 1, and its region. Placing here also clears its 1 touching neighbour.
  4. After that, every remaining candidate in this region touches row 2, column 6 — so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  5. Now, every remaining candidate in this region touches row 1, column 5 — so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  6. From there, marking row 1, column 4 forces a chain of moves that breaks another row, column, or region, so it can't be the marker there.
  7. Following that, place a marker at row 2, column 5. Region has exactly one open cell left. Placing here clears the rest of row 2, column 5, and its region. Placing here also clears its 1 touching neighbour.
  8. First, place a marker at row 1, column 7. Region has exactly one open cell left. Placing here clears the rest of row 1, column 7, and its region.
  9. Next, marking row 5, column 6 immediately breaks another row, column, or region, so it can't be the marker there.
  10. Then, place a marker at row 5, column 4. Row 5 has exactly one open cell left. Placing here clears the rest of row 5, column 4, and its region.
  11. After that, place a marker at row 7, column 6. Region has exactly one open cell left. Placing here clears the rest of row 7, column 6, and its region.
  12. Finally, place a marker at row 6, column 2. Region has exactly one open cell left.

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