How to solve this 9×9 logic puzzle
A
B
C
D
E
F
G
H
I
1
2
3
4
5
6
7
8
9
1
2
3🐱
4
5
6
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7
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8
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9
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This 9×9 board rates as sharp (difficulty score 988). Solving it from scratch takes 27 logical steps, using 7 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Line confinement, Paired regions, Forced chain. Every step below is forced: nothing here is a guess.
- First, every open cell left in this region sits in column A, so its marker has to land there; that clears every other open cell in the column.
- 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.
- Then, place a marker at B3. Region has exactly one open cell left. Placing here clears the rest of row 3, column B, and its region. Placing here also clears its 1 touching neighbour.
- After that, place a marker at C5. Region has exactly one open cell left. Placing here clears the rest of row 5, column C, and its region. Placing here also clears its 2 touching neighbours.
- Now, every open cell left in this region sits in column E, so its marker has to land there; that clears every other open cell in the column.
- From there, every open cell in column D 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.
- Following that, marking G1 would immediately leave row 2 with no open cell for its marker, so it can't be the marker there.
- First, if H1 were the marker, row 2 would end up with no open cell for its marker, which can't happen. So it can't go there.
- Next, that one can't be the marker: at I1 it would force G2 (the last open cell in region 3), and region 7 would be left with no open cell for its marker.
- Then, place a marker at H2. Region has exactly one open cell left. Placing here clears the rest of row 2, column H, and its region.
- After that, place a marker at F1. Region has exactly one open cell left. Placing here clears the rest of row 1, column F, and its region.
- Now, place a marker at I4. Region has exactly one open cell left. Placing here clears the rest of row 4, column I, and its region.
- From there, place a marker at G6. Region has exactly one open cell left. Placing here clears the rest of row 6, column G, and its region.
- Following that, 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.
- First, 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.
- Finally, place a marker at A8. Region has exactly one open cell left.
The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎