An Expert 8×8 Puzzle Solved with Forced Chain in 18 Steps
Play this board yourself →A
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This 8×8 board rates as expert (difficulty score 1147). Solving it from scratch takes 18 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, marking A1 would force H2 (the last open cell in region 2), then G4 cleared (every open cell left in this region sits in column G, so its marker has to land there), then F5, F6, F7, and 1 more cleared (every open cell left in this region sits in column F, so its marker has to land there), and the chain continues, and then column C would be left with no open cell for its marker. So A1 can't be the marker there.
- Next, if B1 were the marker, it would force H2 (the last open cell in region 2), then G4 cleared (every open cell left in this region sits in column G, so its marker has to land there), then F5, F6, F7, and 1 more cleared (every open cell left in this region sits in column F, so its marker has to land there), and the chain continues, and column C would end up with no open cell for its marker, which can't happen. So it can't go there.
- Then, that one can't be the marker: at C1 it would force H2 (the last open cell in region 2), then G4 cleared (every open cell left in this region sits in column G, so its marker has to land there), then F5, F6, F7, and 1 more cleared (every open cell left in this region sits in column F, so its marker has to land there), and the chain continues, and row 4 would be left with no open cell for its marker.
- After that, marking D1 would force H2 (the last open cell in region 2), then G4 cleared (every open cell left in this region sits in column G, so its marker has to land there), then F5, F6, F7, and 1 more cleared (every open cell left in this region sits in column F, so its marker has to land there), and the chain continues, and then region 8 would be left with no open cell for its marker. So D1 can't be the marker there.
- Now, every open cell in row 1 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, if E1 were the marker, it would force F3, F4 and F8 cleared (every open cell left in this region sits in column F, so its marker has to land there), then D7 (the last open cell in region 8), then B6 (the last open cell in region 5), and the chain continues, and region 7 would end up with no open cell for its marker, which can't happen. So it can't go there.
- Following that, every remaining candidate in this region touches G2, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- First, marking G1 would force H3, H4 and H5 cleared (every open cell left in this region sits in column H, so its marker has to land there), then F5, F6, F7, and 1 more cleared (every open cell left in this region sits in column F, so its marker has to land there), then E6, E7 and E8 cleared (every open cell left in this region sits in column E, so its marker has to land there), and the chain continues, and then region 6 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 G3 and G4 cleared (every open cell left in this region sits in column G, so its marker has to land there), then F2, F5, F6, and 2 more cleared (every open cell left in this region sits in column F, so its marker has to land there), then E6, E7 and E8 cleared (every open cell left in this region sits in column E, so its marker has to land there), and the chain continues, and column E would end up with no open cell for its marker, which can't happen. So it can't go there.
- Then, 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.
- After that, 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.
- 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 2 touching neighbours.
- From there, 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. Placing here also clears its 2 touching neighbours.
- Following that, place a marker at A8. Region has exactly one open cell left. Placing here clears the rest of row 8, column A, and its region.
- First, place a marker at G5. Region has exactly one open cell left. Placing here clears the rest of row 5, column G, and its region. Placing here also clears its 1 touching neighbour.
- Next, place a marker at H3. Region has exactly one open cell left. Placing here clears the rest of row 3, column H, and its region.
- Then, place a marker at E4. Region has exactly one open cell left. Placing here clears the rest of row 4, column E, and its region.
- Finally, place a marker at C2. Region has exactly one open cell left.
The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎