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 1200). Solving it from scratch takes 20 logical steps, using 6 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Shape squeeze, Forced chain. Every step below is forced: nothing here is a guess.
- First, 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.
- Next, 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.
- Then, marking A1 would force H2 (the last open cell in region 2), and then region 3 would be left with no open cell for its marker. So A1 can't be the marker there.
- After that, if B1 were the marker, it would force H2 (the last open cell in region 2), then F3 (the last open cell in region 4), then A4 (the last open cell in region 3), and region 7 would end up with no open cell for its marker, which can't happen. So it can't go there.
- Now, that one can't be the marker: at C1 it would force H2 (the last open cell in region 2), then F3 (the last open cell in region 4), then A4 (the last open cell in region 3), and the chain continues, and region 7 would be left with no open cell for its marker.
- From there, every remaining candidate in this region touches E2, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- Following that, marking D1 would force H2 (the last open cell in region 2), then F3 (the last open cell in region 4), then A4 (the last open cell in region 3), and the chain continues, and then region 8 would be left with no open cell for its marker. So D1 can't be the marker there.
- First, that one can't be the marker: at F1 it would force A3, C3, D3, and 1 more cleared (every open cell left in this region sits in row 3, so its marker has to land there), then D2 (the last open cell in region 1), then A4 (the last open cell in region 3), and the chain continues, and region 8 would be left with no open cell for its marker.
- Next, marking G1 would force A3, C3, D3, and 1 more cleared (every open cell left in this region sits in row 3, so its marker has to land there), then D2 (the last open cell in region 1), then A4 (the last open cell in region 3), and the chain continues, and then region 8 would be left with no open cell for its marker. So G1 can't be the marker there.
- Then, every open cell left in this region sits in column H, so its marker has to land there; that clears every other open cell in the column.
- After that, if H1 were the marker, it would force A2, B2, C2, and 2 more cleared (together, two regions have open cells only in rows 2 and 3), then A4 (the last open cell in region 3), then B8 (the last open cell in region 7), and the chain continues, and row 2 would end up with no open cell for its marker, which can't happen. So it can't go there.
- Now, place a marker at H2. Region has exactly one open cell left. Placing here clears the rest of row 2, column H, and its region. Placing here also clears its 1 touching neighbour.
- From there, place a marker at F3. Region has exactly one open cell left. Placing here clears the rest of row 3, column F, and its region. Placing here also clears its 2 touching neighbours.
- Following that, place a marker at E1. Region has exactly one open cell left. Placing here clears the rest of row 1, column E, and its region.
- First, place a marker at A4. Region has exactly one open cell left. Placing here clears the rest of row 4, column A, and its region. Placing here also clears its 1 touching neighbour.
- Next, place a marker at B8. Region has exactly one open cell left. Placing here clears the rest of row 8, column B, and its region. Placing here also clears its 1 touching neighbour.
- Then, every remaining candidate in this region touches D5 and D6, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
- After that, 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.
- Now, place a marker at C5. Region has exactly one open cell left. Placing here clears the rest of row 5, column C, and its region.
- Finally, place a marker at G6. Region has exactly one open cell left.
The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎