How to solve this 6×6 logic puzzle
A
B
C
D
E
F
1
2
3
4
5
6
1
2
🐱
3
🐱
🐱
4🐱
5
6
🐱
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This 6×6 board rates as sharp (difficulty score 1019). Solving it from scratch takes 21 logical steps, using 8 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Line confinement, Paired regions, Shape squeeze, Forced chain. Every step below is forced: nothing here is a guess.
- First, every open cell left in this region sits in row 1, so its marker has to land there; that clears every other open cell in the row.
- Next, together, two regions have open cells only in columns B and C; 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.
- Then, that one can't be the marker: at A2 it would force C1 (the last open cell in region 2), then B4 (the last open cell in region 4), then D6 (the last open cell in region 6), and column E would be left with no open cell for its marker.
- After that, every open cell in row 2 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.
- Now, 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.
- From there, every remaining candidate in this region touches E3, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- Following that, together, two regions have open cells only in columns A and D; 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.
- First, marking E2 would force A3 (the last open cell in region 1), then F6 (the last open cell in region 5), and then column D would be left with no open cell for its marker. So E2 can't be the marker there.
- Next, place a marker at F2. Region has exactly one open cell left. Placing here clears the rest of row 2, column F, and its region.
- Then, if A3 were the marker, it would force D6 (the last open cell in region 6), and row 5 would end up with no open cell for its marker, which can't happen. So it can't go there.
- After that, place a marker at D3. Region has exactly one open cell left. Placing here clears the rest of row 3, column D, and its region. Placing here also clears its 2 touching neighbours.
- Now, 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. Placing here also clears its 1 touching neighbour.
- From there, place a marker at C1. Region has exactly one open cell left.
- Following that, place a marker at A6. Region has exactly one open cell left. Placing here clears the rest of row 6, column A, and its region.
- Finally, place a marker at E5. Region has exactly one open cell left.
The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎