An Expert 8×8 Puzzle Solved with Forced Chain in 20 Steps
Play this board yourself →A
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This 8×8 board rates as expert (difficulty score 1157). Solving it from scratch takes 20 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, 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 4 touching neighbours.
- Next, place a marker at H1. Region has exactly one open cell left. Placing here clears the rest of row 1, column H, and its region.
- Then, every open cell left in this region sits in row 8, so its marker has to land there; that clears every other open cell in the row.
- After that, every open cell in column A 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, every remaining candidate in this region touches E7, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- From there, that one can't be the marker: at A2 it would force F3 (the last open cell in region 1), then E8 (the last open cell in region 7), then B7 (the last open cell in region 6), and the chain continues, and row 5 would be left with no open cell for its marker.
- 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, marking E2 would force F8 (the last open cell in region 7), then A7 and C7 cleared (every open cell left in this region sits in row 7, so its marker has to land there), then B4 cleared (every remaining candidate in this region touches B4), and the chain continues, and then column B would be left with no open cell for its marker. So E2 can't be the marker there.
- Next, if F2 were the marker, it would force E8 (the last open cell in region 7), then B7 (the last open cell in region 6), then C4 (the last open cell in region 5), and column D would end up with no open cell for its marker, which can't happen. So it can't go there.
- Then, every remaining candidate in this region touches C3 and D3, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
- After that, that one can't be the marker: at B3 it would force D2 (the last open cell in region 1), then E5 (the last open cell in region 6), and row 4 would be left with no open cell for its marker.
- Now, every remaining candidate in this region touches C5, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- From there, that one can't be the marker: at E3 it would force C2 (the last open cell in region 1), then F8 (the last open cell in region 7), then D7 (the last open cell in column D), and the chain continues, and column B would be left with no open cell for its marker.
- Following that, place a marker at A3. Row 3 has exactly one open cell left. Placing here clears the rest of row 3, column A, and its region. Placing here also clears its 1 touching neighbour.
- First, that one can't be the marker: place it at C4, and region 4 would be left with no open cell for its marker.
- 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 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.
- After that, place a marker at C2. Region has exactly one open cell left.
- Now, place a marker at F8. Region has exactly one open cell left. Placing here clears the rest of row 8, column F, and its region.
- Finally, place a marker at E4. Region has exactly one open cell left.
The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎