QED Logic quod erat demonstrandum
Logic Ascent

How to solve this 9×9 logic puzzle

9×9 · gentle · 12 steps

A
B
C
D
E
F
G
H
I
1
2
3
4
5
6
7
8
9
1
2
3
4🐱
🐱
5
6
🐱
🐱
🐱
🐱
7🐱
8
🐱
9🐱

This 9×9 board rates as gentle (difficulty score 552). Solving it from scratch takes 24 logical steps, using 5 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Line confinement. Every step below is forced: nothing here is a guess.

  1. First, place a marker at I1. Region has exactly one open cell left. Placing here clears the rest of row 1, column I, and its region. Placing here also clears its 1 touching neighbour.
  2. Next, place a marker at D9. Region has exactly one open cell left. Placing here clears the rest of row 9, column D, and its region. Placing here also clears its 2 touching neighbours.
  3. Then, every open cell left in this region sits in row 8, so its marker has to land there; that clears every other open cell in the row.
  4. After that, place a marker at C7. Region has exactly one open cell left. Placing here clears the rest of row 7, column C, and its region. Placing here also clears its 1 touching neighbour.
  5. Now, every open cell in column B belongs to the same region, so that region's marker has to be somewhere in this column; that clears every other open cell in the region.
  6. From there, place a marker at A2. Column 1 has exactly one open cell left. Placing here clears the rest of row 2, column A, and its region. Placing here also clears its 1 touching neighbour.
  7. Following that, every open cell in row 3 belongs to the same region, so that region's marker has to be somewhere in this row; that clears every other open cell in the region.
  8. First, place a marker at B4. Row 4 has exactly one open cell left. Placing here clears the rest of row 4, column B, and its region.
  9. Next, place a marker at E6. Column 5 has exactly one open cell left. Placing here clears the rest of row 6, column E, and its region.
  10. Then, place a marker at H5. Region has exactly one open cell left. Placing here clears the rest of row 5, column H, and its region.
  11. After that, place a marker at G3. Region has exactly one open cell left. Placing here clears the rest of row 3, column G, and its region.
  12. Finally, place a marker at F8. Region has exactly one open cell left.

The key move here was Line confinement. Once you can spot that, this board falls quickly. ∎