QED

How to solve this 7×7 logic puzzle

7×7 · sharp · 16 steps

This 7×7 board rates as sharp (difficulty score 1021). Solving it from scratch takes 25 logical steps, using 7 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Line confinement, Shape squeeze, Forced chain. Every step below is forced — nothing here is a guess.

  1. First, every open cell left in this region sits in row 1, so its marker has to land there — clearing every other open cell in the row.
  2. Next, every remaining candidate in this region touches row 3, column 2 — so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
  3. Then, 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.
  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, marking row 2, column 2 forces a chain of moves that breaks another row, column, or region, so it can't be the marker there.
  6. From there, 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.
  7. Following that, 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.
  8. First, every open cell in row 7 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.
  9. Next, every open cell in row 6 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.
  10. Then, place a marker at row 5, column 2. Row 5 has exactly one open cell left. Placing here clears the rest of row 5, column 2, and its region. Placing here also clears its 2 touching neighbours.
  11. After that, place a marker at row 6, column 4. Region has exactly one open cell left. Placing here clears the rest of row 6, column 4, and its region. Placing here also clears its 2 touching neighbours.
  12. Now, place a marker at row 4, column 6. Row 4 has exactly one open cell left. Placing here clears the rest of row 4, column 6, and its region. Placing here also clears its 1 touching neighbour.
  13. From there, place a marker at row 7, column 7. Region has exactly one open cell left. Placing here clears the rest of row 7, column 7, and its region.
  14. Following that, place a marker at row 1, column 5. Region has exactly one open cell left. Placing here clears the rest of row 1, column 5, and its region.
  15. 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.
  16. Finally, place a marker at row 2, 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.