An Expert 8×8 Puzzle Solved with Forced Chain in 24 Steps
Play this board yourself →A
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This 8×8 board rates as expert (difficulty score 1219). Solving it from scratch takes 24 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 open cell left in this region sits in row 1, so its marker has to land there; that clears every other open cell in the row.
- Next, every remaining candidate in this region touches C2 and D2, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
- Then, every remaining candidate in this region touches E3, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- After that, every remaining candidate in this region touches B3, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- Now, that one can't be the marker: at A2 it would force F3 (the last open cell in region 3), then H6, H7 and H8 cleared (every open cell left in this region sits in column H, so its marker has to land there), then B5, D5, E5, and 1 more cleared (together, two regions have open cells only in rows 4 and 5), and the chain continues, and column G would be left with no open cell for its marker.
- From there, marking B2 would force D1 (the last open cell in region 2), then F3 (the last open cell in region 3), then C6, C7 and C8 cleared (every open cell left in this region sits in column C, so its marker has to land there), and the chain continues, and then column H would be left with no open cell for its marker. So B2 can't be the marker there.
- Following that, every open cell left in this region sits in column A, so its marker has to land there; that clears every other open cell in the column.
- First, every remaining candidate in this region touches B4, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- Next, every open cell in column B 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.
- Then, together, two regions have open cells only in columns C and D; 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.
- After that, that one can't be the marker: place it at G2, and region 3 would be left with no open cell for its marker.
- Now, marking H2 would force F3 (the last open cell in region 3), then A4 (the last open cell in region 1), then C5 (the last open cell in region 5), and then region 6 would be left with no open cell for its marker. So H2 can't be the marker there.
- From there, 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.
- Following that, marking C3 would force D1 (the last open cell in region 2), then F2 (the last open cell in region 3), then A4 (the last open cell in region 1), and the chain continues, and then region 6 would be left with no open cell for its marker. So C3 can't be the marker there.
- First, marking D1 would force F2 (the last open cell in region 3), then A4, G4, H4, and 2 more cleared (together, two regions have open cells only in rows 4 and 5), then A3 (the last open cell in region 1), and then region 4 would be left with no open cell for its marker. So D1 can't be the marker there.
- Next, place a marker at C1. Region has exactly one open cell left. Placing here clears the rest of row 1, column C, and its region.
- Then, together, two regions have open cells only in rows 3 and 4; with one marker each, those two markers have to fill exactly those two rows, so every other region's open cells there can be cleared.
- After that, place a marker at H5. Region has exactly one open cell left. Placing here clears the rest of row 5, column H, and its region. Placing here also clears its 1 touching neighbour.
- Now, place a marker at F6. Region has exactly one open cell left. Placing here clears the rest of row 6, column F, and its region. Placing here also clears its 2 touching neighbours.
- From there, place a marker at E2. Region has exactly one open cell left. Placing here clears the rest of row 2, column E, and its region. Placing here also clears its 1 touching neighbour.
- Following that, place a marker at D4. Region has exactly one open cell left. Placing here clears the rest of row 4, column D, and its region.
- First, place a marker at A3. Region has exactly one open cell left.
- Next, place a marker at G8. Region has exactly one open cell left. Placing here clears the rest of row 8, column G, and its region.
- Finally, place a marker at B7. Region has exactly one open cell left.
The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎