An Expert 7×7 Puzzle Solved with Forced Chain in 17 Steps
Play this board yourself →A
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This 7×7 board rates as expert (difficulty score 1122). Solving it from scratch takes 17 logical steps, using 6 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Shape squeeze, Forced chain. Every step below is forced: nothing here is a guess.
- First, every remaining candidate in this region touches B4, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- Next, marking A1 would force B3 (the last open cell in region 3), and then region 4 would be left with no open cell for its marker. So A1 can't be the marker there.
- Then, that one can't be the marker: at C1 it would force E7, F7 and G7 cleared (every open cell left in this region sits in row 7, so its marker has to land there), then F3, G3, E4, and 2 more cleared (every open cell in row 2 belongs to the same region, so that region's marker has to be somewhere in this row), then A4 cleared (every open cell in row 3 belongs to the same region, so that region's marker has to be somewhere in this row), and the chain continues, and column G would be left with no open cell for its marker.
- After that, marking D1 would force C3 and E3 cleared (every open cell in row 2 belongs to the same region, so that region's marker has to be somewhere in this row), then A4 cleared (every open cell in row 3 belongs to the same region, so that region's marker has to be somewhere in this row), then C4 (the last open cell in row 4), and the chain continues, and then row 2 would be left with no open cell for its marker. So D1 can't be the marker there.
- Now, if E1 were the marker, it would force C3 and D3 cleared (every open cell in row 2 belongs to the same region, so that region's marker has to be somewhere in this row), then A4 cleared (every open cell in row 3 belongs to the same region, so that region's marker has to be somewhere in this row), then F6 and F7 cleared (every open cell in column G belongs to the same region, so that region's marker has to be somewhere in this column), and the chain continues, and column D 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 F1 it would force C3, D3 and E3 cleared (every open cell in row 2 belongs to the same region, so that region's marker has to be somewhere in this row), then A4 cleared (every open cell in row 3 belongs to the same region, so that region's marker has to be somewhere in this row), then E7 cleared (every open cell in column G belongs to the same region, so that region's marker has to be somewhere in this column), and the chain continues, and row 2 would be left with no open cell for its marker.
- Following that, marking G1 would force C3, D3 and E3 cleared (every open cell in row 2 belongs to the same region, so that region's marker has to be somewhere in this row), then A4 cleared (every open cell in row 3 belongs to the same region, so that region's marker has to be somewhere in this row), then B3 cleared (every remaining candidate in this region touches B3), and the chain continues, and then row 5 would be left with no open cell for its marker. So G1 can't be the marker there.
- First, place a marker at B1. Row 1 has exactly one open cell left. Placing here clears the rest of row 1, column B, and its region.
- Next, 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.
- 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 D7. Region has exactly one open cell left. Placing here clears the rest of row 7, column D, and its region. Placing here also clears its 1 touching neighbour.
- From there, 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.
- Following that, every remaining candidate in this region touches F6, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- First, 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. Placing here also clears its 1 touching neighbour.
- Next, place a marker at E5. Region has exactly one open cell left. Placing here clears the rest of row 5, column E, and its region.
- Finally, place a marker at F2. Region has exactly one open cell left.
The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎