How to solve this 7×7 logic puzzle
A
B
C
D
E
F
G
1
2
3
4
5
6
7
1
2
3🐱
4🐱
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5
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6
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7
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This 7×7 board rates as severe (difficulty score 1171). Solving it from scratch takes 29 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.
- First, place a marker at G1. Region has exactly one open cell left. Placing here clears the rest of row 1, column G, and its region. Placing here also clears its 1 touching neighbour.
- Next, marking B2 would force D3 (the last open cell in region 1), then F4 (the last open cell in region 2), then E6 (the last open cell in region 5), and then region 7 would be left with no open cell for its marker. So B2 can't be the marker there.
- Then, if C2 were the marker, region 1 would end up with no open cell for its marker, which can't happen. So it can't go there.
- After that, marking E2 would force F4 (the last open cell in region 2), then D5 (the last open cell in region 5), and then region 7 would be left with no open cell for its marker. So E2 can't be the marker there.
- Now, if A3 were the marker, it would force D2 (the last open cell in region 1), then F4 (the last open cell in region 2), then E6 (the last open cell in region 5), and region 7 would end up with no open cell for its marker, which can't happen. So it can't go there.
- From there, that one can't be the marker: at B3 it would force D2 (the last open cell in region 1), then A7 (the last open cell in column A), then C6 (the last open cell in column C), and the chain continues, and row 4 would be left with no open cell for its marker.
- Following that, 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.
- First, every remaining candidate in this region touches C6, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- Next, every remaining candidate in this region touches E6, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- Then, that one can't be the marker: at D2 it would force F3 (the last open cell in row 3), then E7 (the last open cell in region 7), then C5 (the last open cell in region 6), and row 4 would be left with no open cell for its marker.
- After that, place a marker at A2. Row 2 has exactly one open cell left. Placing here clears the rest of row 2, column A, and its region.
- Now, every open cell left in this region sits in row 3, so its marker has to land there; that clears every other open cell in the row.
- From there, every open cell left in this region sits in row 4, so its marker has to land there; that clears every other open cell in the row.
- Following that, every open cell left in this region sits in row 5, so its marker has to land there; that clears every other open cell in the row.
- First, 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.
- Next, place a marker at C3. Column 3 has exactly one open cell left. Placing here clears the rest of row 3, column C, and its region.
- Then, every remaining candidate in this region touches E5, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- After that, place a marker at D5. Region 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.
- Now, place a marker at F4. Region has exactly one open cell left. Placing here clears the rest of row 4, column F, and its region.
- From there, 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.
- Finally, place a marker at B6. Region has exactly one open cell left.
The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎