An Expert 9×9 Puzzle Solved with Forced Chain in 22 Steps
Play this board yourself →A
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This 9×9 board rates as expert (difficulty score 1181). Solving it from scratch takes 22 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, every open cell left in this region sits in row 9, so its marker has to land there; that clears every other open cell in the row.
- Next, every remaining candidate in this region touches B8 and C8, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
- Then, marking A1 would force E5, E6, E7, and 1 more cleared (every open cell left in this region sits in column E, so its marker has to land there), then F3, F4, G4, and 10 more cleared (every open cell in column H belongs to the same region, so that region's marker has to be somewhere in this column), then F2, I2 and I3 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 then column I would be left with no open cell for its marker. So A1 can't be the marker there.
- After that, if B1 were the marker, it would force C9 (the last open cell in region 9), then D7 (the last open cell in region 7), then E5 (the last open cell in region 6), and region 2 would end up with no open cell for its marker, which can't happen. So it can't go there.
- Now, that one can't be the marker: at C1 it would force B9 (the last open cell in region 9), then E5, E6, E7, and 1 more cleared (every open cell left in this region sits in column E, so its marker has to land there), then D7 and D8 cleared (every open cell left in this region sits in column D, so its marker has to land there), and region 7 would be left with no open cell for its marker.
- From there, marking D1 would force C3, C4, C5, and 1 more cleared (every open cell left in this region sits in column C, so its marker has to land there), then B9 (the last open cell in region 9), then A5, A6 and A7 cleared (every open cell left in this region sits in column A, so its marker has to land there), and then region 5 would be left with no open cell for its marker. So D1 can't be the marker there.
- Following that, if E1 were the marker, it would force F3, F4, G4, and 10 more cleared (every open cell in column H belongs to the same region, so that region's marker has to be somewhere in this column), then F8 (the last open cell in column F), then I2 and I3 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 column I would end up with no open cell for its marker, which can't happen. So it can't go there.
- First, marking G1 would force E5, E6, E7, and 1 more cleared (every open cell left in this region sits in column E, so its marker has to land there), then F3, F4, I4, and 5 more cleared (every open cell in column H belongs to the same region, so that region's marker has to be somewhere in this column), then F8 (the last open cell in column F), and then column I would be left with no open cell for its marker. So G1 can't be the marker there.
- Next, if H1 were the marker, it would force E5, E6, E7, and 1 more cleared (every open cell left in this region sits in column E, so its marker has to land there), then F3, F4, I4, and 5 more cleared (every open cell in column G belongs to the same region, so that region's marker has to be somewhere in this column), then F8 (the last open cell in column F), and column I would end up with no open cell for its marker, which can't happen. So it can't go there.
- Then, every open cell in column H 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.
- After that, every open cell in column G 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.
- Now, place a marker at F1. Row 1 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.
- From there, place a marker at G3. Region has exactly one open cell left. Placing here clears the rest of row 3, column G, and its region. Placing here also clears its 2 touching neighbours.
- Following 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.
- First, every open cell in column E 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 B4. Row 4 has exactly one open cell left. Placing here clears the rest of row 4, column B, and its region.
- Then, place a marker at C9. Region has exactly one open cell left. Placing here clears the rest of row 9, column C, and its region. Placing here also clears its 1 touching neighbour.
- After that, 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.
- Now, place a marker at A2. Region has exactly one open cell left.
- From there, 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.
- Following that, place a marker at I8. Region has exactly one open cell left. Placing here clears the rest of row 8, column I, and its region.
- Finally, place a marker at H6. Region has exactly one open cell left.
The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎