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 1212). Solving it from scratch takes 22 logical steps, using 7 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Paired regions, Shape squeeze, Forced chain. Every step below is forced: nothing here is a guess.
- First, marking A1 would force C2, D2, E2, and 1 more cleared (every open cell left in this region sits in row 2, so its marker has to land there), then C3 (the last open cell in region 3), then H4 (the last open cell in region 4), and the chain continues, and then region 7 would be left with no open cell for its marker. So A1 can't be the marker there.
- Next, that one can't be the marker: at C1 it would force E2 (the last open cell in region 3), and region 2 would be left with no open cell for its marker.
- Then, together, two regions have open cells only in columns B and A; 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 remaining candidate in this region touches D3, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- Now, every remaining candidate in this region touches D5, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- From there, marking D1 would force C3 (the last open cell in region 3), then E6 (the last open cell in region 6), then B5 (the last open cell in column B), and the chain continues, and then region 7 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 A5, A6, A7, and 1 more cleared (every open cell left in this region sits in column A, so its marker has to land there), then C4, C5, C6, and 2 more cleared (every open cell left in this region sits in column C, so its marker has to land there), then D7 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 row 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: at F1 it would force A5, A6, A7, and 1 more cleared (every open cell left in this region sits in column A, so its marker has to land there), then C8, D8, E8, and 2 more cleared (every open cell in row 7 belongs to the same region, so that region's marker has to be somewhere in this row), and row 8 would be left with no open cell for its marker.
- Next, marking G1 would force A5, A6, A7, and 1 more cleared (every open cell left in this region sits in column A, so its marker has to land there), then F6, C8, D8, and 3 more cleared (every open cell in row 7 belongs to the same region, so that region's marker has to be somewhere in this row), and then row 8 would be left with no open cell for its marker. So G1 can't be the marker there.
- Then, if H1 were the marker, it would force A5, A6, A7, and 1 more cleared (every open cell left in this region sits in column A, so its marker has to land there), then A3, B3 and C3 cleared (every open cell left in this region sits in row 3, so its marker has to land there), then A2 cleared (every open cell left in this region sits in row 2, so its marker has to land there), and the chain continues, and region 6 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 B1. Row 1 has exactly one open cell left. Placing here clears the rest of row 1, column B, and its region. Placing here also clears its 1 touching neighbour.
- Now, every open cell left in this region sits in row 2, so its marker has to land there; that clears every other open cell in the row.
- From there, place a marker at C3. Region has exactly one open cell left. Placing here clears the rest of row 3, column C, and its region. Placing here also clears its 1 touching neighbour.
- Following that, 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. Placing here also clears its 1 touching neighbour.
- First, 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.
- Next, every open cell left in this region sits in row 5, so its marker has to land there; that clears every other open cell in the row.
- Then, every remaining candidate in this region touches E6, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- After that, place a marker at D6. Region 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.
- Now, place a marker at F5. Region has exactly one open cell left. Placing here clears the rest of row 5, column F, and its region.
- From there, place a marker at G2. Region has exactly one open cell left. Placing here clears the rest of row 2, column G, and its region.
- Following that, place a marker at E8. Region has exactly one open cell left. Placing here clears the rest of row 8, column E, and its region.
- Finally, place a marker at A7. Region has exactly one open cell left.
The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎