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 1239). Solving it from scratch takes 24 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, 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.
- 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 D2 (the last open cell in region 2), then B4 (the last open cell in region 4), then G3 (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 A1 can't be the marker there.
- After that, if B1 were the marker, it would force D2 (the last open cell in region 2), then G5, G6, G7, and 1 more cleared (every open cell left in this region sits in column G, so its marker has to land there), then A6, A7 and A8 cleared (every open cell left in this region sits in column A, so its marker has to land there), and the chain continues, and region 8 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: place it at C1, and region 2 would be left with no open cell for its marker.
- From there, marking D1 would force F5, G5, F6, and 6 more cleared (every open cell in column H belongs to the same region, so that region's marker has to be somewhere in this column), then F3 and F4 cleared (every open cell in column E belongs to the same region, so that region's marker has to be somewhere in this column), then F2 (the last open cell in column F), and then column G would be left with no open cell for its marker. So D1 can't be the marker there.
- Following that, that one can't be the marker: at F1 it would force D2 (the last open cell in region 2), then E8 cleared (every open cell left in this region sits in column E, so its marker has to land there), then H3, H4, H5, and 3 more cleared (every open cell in column G belongs to the same region, so that region's marker has to be somewhere in this column), and column H would be left with no open cell for its marker.
- First, marking G1 would force D2 (the last open cell in region 2), then F5, F6, F7, and 2 more cleared (every open cell in column H belongs to the same region, so that region's marker has to be somewhere in this column), then F3 and F4 cleared (every open cell in column E belongs to the same region, so that region's marker has to be somewhere in this column), and then column F would be left with no open cell for its marker. So G1 can't be the marker there.
- Next, if H1 were the marker, it would force D2 (the last open cell in region 2), then F5, F6, F7, and 2 more cleared (every open cell in column G belongs to the same region, so that region's marker has to be somewhere in this column), then F3 and F4 cleared (every open cell in column E belongs to the same region, so that region's marker has to be somewhere in this column), and column F would end up with no open cell for its marker, which can't happen. So it can't go there.
- Then, place a marker at E1. Row 1 has exactly one open cell left. Placing here clears the rest of row 1, column E, and its region. Placing here also clears its 1 touching neighbour.
- After that, every open cell left in this region sits in column G, so its marker has to land there; that clears every other open cell in the column.
- Now, every open cell in column H 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.
- From there, every open cell in column F 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.
- Following that, every open cell in column D 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.
- First, every remaining candidate in this region touches F3 and H3, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
- Next, place a marker at F4. Region has exactly one open cell left. Placing here clears the rest of row 4, column F, and its region. Placing here also clears its 1 touching neighbour.
- Then, 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.
- After that, place a marker at A3. Region has exactly one open cell left. Placing here clears the rest of row 3, column A, and its region.
- Now, 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.
- From there, every remaining candidate in this region touches B6 and C6, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
- Following that, place a marker at B7. Region has exactly one open cell left. Placing here clears the rest of row 7, column B, and its region.
- First, place a marker at C5. Region has exactly one open cell left. Placing here also clears its 1 touching neighbour.
- Next, place a marker at D8. Region has exactly one open cell left. Placing here clears the rest of row 8, column D, and its region.
- Finally, place a marker at H6. Region has exactly one open cell left.
The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎