An Expert 8×8 Puzzle Solved with Forced Chain in 22 Steps
Play this board yourself →A
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This 8×8 board rates as expert (difficulty score 1115). Solving it from scratch takes 22 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 A7, 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 B7, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- Then, 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.
- After that, together, two regions have open cells only in rows 7 and 8; 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.
- Now, 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.
- From there, marking A1 would force B6 (the last open cell in region 6), then C8 (the last open cell in region 8), then E7 (the last open cell in region 7), and the chain continues, and then region 3 would be left with no open cell for its marker. So A1 can't be the marker there.
- Following that, if B1 were the marker, it would force A6 (the last open cell in region 6), then F2, G2 and H2 cleared (every open cell left in this region sits in row 2, so its marker has to land there), then C3, C4 and C5 cleared (every open cell left in this region sits in column C, 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.
- First, that one can't be the marker: at C1 it would force E2 (the last open cell in region 2), then B4 (the last open cell in region 3), then A6 (the last open cell in region 6), and region 8 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, 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.
- After that, every open cell left in this region sits in column C, so its marker has to land there; that clears every other open cell in the column.
- Now, every open cell left in this region sits in row 3, so its marker has to land there; that clears every other open cell in the row.
- From there, place a marker at B6. Column 2 has exactly one open cell left. Placing here clears the rest of row 6, column B, and its region. Placing here also clears its 1 touching neighbour.
- Following that, place a marker at C8. Region has exactly one open cell left. Placing here clears the rest of row 8, column C, and its region. Placing here also clears its 1 touching neighbour.
- First, place a marker at E7. Region has exactly one open cell left. Placing here clears the rest of row 7, column E, and its region.
- Next, place a marker at D3. Region has exactly one open cell left. Placing here clears the rest of row 3, column D, and its region.
- Then, 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.
- After that, every remaining candidate in this region touches G4 and G5, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
- Now, place a marker at G1. Column 7 has exactly one open cell left. Placing here clears the rest of row 1, column G, and its region. Placing here also clears its 2 touching neighbours.
- From there, place a marker at H4. Region has exactly one open cell left. Placing here clears the rest of row 4, column H, and its region.
- Following that, place a marker at A2. Region has exactly one open cell left.
- Finally, place a marker at F5. Region has exactly one open cell left.
The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎