QED Logic quod erat demonstrandum
Logic Ascent

How to solve this 7×7 logic puzzle

7×7 · sharp · 14 steps

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

This 7×7 board rates as sharp (difficulty score 974). Solving it from scratch takes 23 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, 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.
  2. Next, place a marker at E7. Region has exactly one open cell left. Placing here clears the rest of row 7, column E, and its region. Placing here also clears its 1 touching neighbour.
  3. Then, every open cell left in this region sits in column B, so its marker has to land there; that clears every other open cell in the column.
  4. After that, every remaining candidate in this region touches G2, 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 A5 and C5 and A6 and C6, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
  6. From there, place a marker at B6. Row 6 has exactly one open cell left. Placing here clears the rest of row 6, column B, and its region.
  7. Following that, place a marker at D5. Row 5 has exactly one open cell left. Placing here clears the rest of row 5, column D, and its region. Placing here also clears its 1 touching neighbour.
  8. First, marking A1 would force F2 (the last open cell in region 2), and then row 3 would be left with no open cell for its marker. So A1 can't be the marker there.
  9. Next, that one can't be the marker: place it at A2, and column C would be left with no open cell for its marker.
  10. Then, 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.
  11. After that, place a marker at F2. Row 2 has exactly one open cell left. Placing here clears the rest of row 2, column F, and its region. Placing here also clears its 1 touching neighbour.
  12. Now, place a marker at G4. Region has exactly one open cell left. Placing here clears the rest of row 4, column G, and its region.
  13. From there, place a marker at A3. Region has exactly one open cell left. Placing here clears the rest of row 3, column A, and its region.
  14. Finally, place a marker at C1. Region has exactly one open cell left.

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