An Expert 8×8 Puzzle Solved with Forced Chain in 26 Steps
Play this board yourself →A
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This 8×8 board rates as expert (difficulty score 1275). Solving it from scratch takes 26 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 remaining candidate in this region touches H2, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- Next, every remaining candidate in this region touches G4, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- Then, marking A1 would force G2 (the last open cell in region 3), then H4 (the last open cell in region 2), then F5 (the last open cell in region 5), 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.
- After that, if B1 were the marker, it would force G2 (the last open cell in region 3), then H4 (the last open cell in region 2), then F5 (the last open cell in region 5), and region 6 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 G2 (the last open cell in region 3), then H4 (the last open cell in region 2), then F5 (the last open cell in region 5), and the chain continues, and column A would be left with no open cell for its marker.
- From there, marking D1 would force G2 (the last open cell in region 3), and then row 3 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 G2 (the last open cell in region 3), then H4 (the last open cell in region 2), then F5 (the last open cell in region 5), and region 8 would end up with no open cell for its marker, which can't happen. So it can't go there.
- First, that one can't be the marker: place it at F1, and region 3 would be left with no open cell for its marker.
- Next, 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.
- Then, if H1 were the marker, it would force F6, F7, F8, and 3 more cleared (together, two regions have open cells only in columns F and G), then E2, E3, E4, and 2 more cleared (every open cell left in this region sits in column E, so its marker has to land there), then D2 and D8 cleared (every open cell left in this region sits in column D, so its marker has to land there), and the chain continues, and column G 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 G1. Region has exactly one open cell left. Placing here clears the rest of row 1, column G, and its region. Placing here also clears its 1 touching neighbour.
- Now, 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.
- From there, together, two regions have open cells only in columns F and H; 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.
- Following 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.
- First, every open cell left in this region sits in column D, so its marker has to land there; that clears every other open cell in the column.
- Next, every remaining candidate in this region touches B7, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- Then, every remaining candidate in this region touches D7, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- After that, every open cell in row 7 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, place a marker at E8. Row 8 has exactly one open cell left. Placing here clears the rest of row 8, column E, and its region.
- From there, every remaining candidate in this region touches B6, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- Following that, place a marker at D6. Row 6 has exactly one open cell left. Placing here clears the rest of row 6, column D, and its region. Placing here also clears its 2 touching neighbours.
- First, place a marker at A7. Region has exactly one open cell left. Placing here clears the rest of row 7, column A, and its region.
- Next, place a marker at B5. Region has exactly one open cell left. Placing here clears the rest of row 5, column B, and its region.
- Then, place a marker at C2. Region has exactly one open cell left.
- After that, place a marker at F4. Region has exactly one open cell left. Placing here clears the rest of row 4, column F, and its region.
- Finally, place a marker at H3. Region has exactly one open cell left.
The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎