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 1358). 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 E5, 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 F2, G2 and H2 cleared (every open cell left in this region sits in row 2, so its marker has to land there), then B6, B7 and B8 cleared (every open cell left in this region sits in column B, so its marker has to land there), then D3, D7, D8, and 4 more cleared (together, two regions have open cells only in columns D and E), and the chain continues, and then region 8 would be left with no open cell for its marker. So A1 can't be the marker there.
- Then, if B1 were the marker, it would force F2, G2 and H2 cleared (every open cell left in this region sits in row 2, so its marker has to land there), then A6, A7 and A8 cleared (every open cell left in this region sits in column A, so its marker has to land there), then D3, D7, D8, and 4 more cleared (together, two regions have open cells only in columns D and E), and the chain continues, and region 8 would end up with no open cell for its marker, which can't happen. So it can't go there.
- After that, that one can't be the marker: at C1 it would force E2 (the last open cell in region 2), then D7 and D8 cleared (every open cell left in this region sits in column D, so its marker has to land there), then A7, A8 and B8 cleared (together, two regions have open cells only in columns A and B), and region 8 would be left with no open cell for its marker.
- Now, marking D1 would immediately leave region 2 with no open cell for its marker, so it can't be the marker there.
- From there, every remaining candidate in this region touches C3, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- Following that, if H1 were the marker, it would force A2, B2 and C2 cleared (every open cell left in this region sits in row 2, so its marker has to land there), then B3 (the last open cell in region 1), then A5 (the last open cell in region 4), and the chain continues, and region 8 would end up with no open cell for its marker, which can't happen. So it can't go there.
- First, 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.
- Next, every remaining candidate in this region touches F2, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- Then, that one can't be the marker: place it at A2, and region 1 would be left with no open cell for its marker.
- After that, marking B2 would force A6, A7 and A8 cleared (every open cell left in this region sits in column A, so its marker has to land there), then D4, D5, D6, and 1 more cleared (together, two regions have open cells only in columns D and C), then E4 (the last open cell in region 6), and the chain continues, and then column D would be left with no open cell for its marker. So B2 can't be the marker there.
- Now, marking G1 would force C2 (the last open cell in row 2), then A7, A8 and B8 cleared (together, two regions have open cells only in columns A and B), then D7 (the last open cell in region 8), and the chain continues, and then row 6 would be left with no open cell for its marker. So G1 can't be the marker there.
- From there, that one can't be the marker: at G2 it would force E1 (the last open cell in region 2), then B3 (the last open cell in region 1), then A5 (the last open cell in region 4), and the chain continues, and region 8 would be left with no open cell for its marker.
- Following that, marking H2 would force B3 (the last open cell in region 1), then A5 (the last open cell in region 4), then C6 (the last open cell in region 5), and then region 8 would be left with no open cell for its marker. So H2 can't be the marker there.
- First, place a marker at C2. Row 2 has exactly one open cell left. Placing here clears the rest of row 2, column C, and its region. Placing here also clears its 1 touching neighbour.
- Next, together, two regions have open cells only in columns A and B; 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.
- Then, 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.
- After that, 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. Placing here also clears its 2 touching neighbours.
- Now, 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.
- From there, every open cell left in this region sits in row 6, so its marker has to land there; that clears every other open cell in the row.
- Following that, every open cell in row 8 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 remaining candidate in this region touches A5 and B5, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
- Next, 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.
- Then, 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.
- After that, place a marker at B6. Region has exactly one open cell left.
- Finally, place a marker at H8. Region has exactly one open cell left.
The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎