How to solve this 6×6 logic puzzle
A
B
C
D
E
F
1
2
3
4
5
6
1
2
3🐱
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4
5
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6
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This 6×6 board rates as sharp (difficulty score 941). Solving it from scratch takes 20 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, 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. Placing here also clears its 1 touching neighbour.
- Next, 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.
- Then, every open cell left in this region sits in row 2, so its marker has to land there; that clears every other open cell in the row.
- After that, together, two regions have open cells only in columns C 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.
- Now, every remaining candidate in this region touches C3 and D3, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
- From there, 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.
- Following that, every remaining candidate in this region touches D5, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- First, if C2 were the marker, it would force A3 (the last open cell in region 1), then B6 (the last open cell in region 6), then D4 (the last open cell in region 4), and row 5 would end up with no open cell for its marker, which can't happen. So it can't go there.
- Next, place a marker at D2. Region has exactly one open cell left. Placing here clears the rest of row 2, column D, and its region.
- Then, place a marker at C4. Region has exactly one open cell left. Placing here clears the rest of row 4, column C, and its region. Placing here also clears its 1 touching neighbour.
- After that, 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.
- Now, place a marker at B6. Region has exactly one open cell left. Placing here clears the rest of row 6, column B, 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. ∎