A Severe 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 severe (difficulty score 1180). Solving it from scratch takes 20 logical steps, using 6 techniques: Single cell, Row/column exclusion, Adjacency clear, Line confinement, Shape squeeze, Forced chain. Every step below is forced: nothing here is a guess.
- First, every open cell in row 8 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.
- Next, every open cell in row 7 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, 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 E5, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- Now, marking A1 would force H4, H5 and H8 cleared (every open cell left in this region sits in column H, so its marker has to land there), then G3, G4 and G8 cleared (every open cell left in this region sits in column G, so its marker has to land there), then F3 (the last open cell in region 4), and then region 5 would be left with no open cell for its marker. So A1 can't be the marker there.
- From there, if B1 were the marker, it would force A8 (the last open cell in column A), then H4 and H5 cleared (every open cell left in this region sits in column H, so its marker has to land there), then G3 and G4 cleared (every open cell left in this region sits in column G, so its marker has to land there), and the chain continues, and row 4 would end up with no open cell for its marker, which can't happen. So it can't go there.
- Following that, that one can't be the marker: at C1 it would force H4, H5 and H8 cleared (every open cell left in this region sits in column H, so its marker has to land there), then G3, G4 and G8 cleared (every open cell left in this region sits in column G, so its marker has to land there), then F3 (the last open cell in region 4), and region 5 would be left with no open cell for its marker.
- First, marking D1 would force H4, H5 and H8 cleared (every open cell left in this region sits in column H, so its marker has to land there), then G3, G4 and G8 cleared (every open cell left in this region sits in column G, so its marker has to land there), then F3 (the last open cell in region 4), and then region 5 would be left with no open cell for its marker. So D1 can't be the marker there.
- Next, if E1 were the marker, it would force H4, H5 and H8 cleared (every open cell left in this region sits in column H, so its marker has to land there), then F3, F7 and F8 cleared (every open cell left in this region sits in column F, so its marker has to land there), then G5, G6 and G8 cleared (every open cell left in this region sits in column G, so its marker has to land there), and region 6 would end up with no open cell for its marker, which can't happen. So it can't go there.
- Then, 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.
- After that, marking G1 would force H5 (the last open cell in region 6), then F3 (the last open cell in region 4), and then region 5 would be left with no open cell for its marker. So G1 can't be the marker there.
- Now, if H1 were the marker, it would force G3, G4 and G8 cleared (every open cell left in this region sits in column G, so its marker has to land there), then F3 (the last open cell in region 4), and region 5 would end up with no open cell for its marker, which can't happen. So it can't go there.
- From there, place a marker at F1. Region has exactly one open cell left. Placing here clears the rest of row 1, column F, and its region. Placing here also clears its 1 touching neighbour.
- Following that, place a marker at E4. Region has exactly one open cell left. Placing here clears the rest of row 4, column E, and its region. Placing here also clears its 2 touching neighbours.
- First, place a marker at G3. Region has exactly one open cell left. Placing here clears the rest of row 3, column G, and its region.
- Next, 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.
- Then, place a marker at A6. Row 6 has exactly one open cell left. Placing here clears the rest of row 6, column A, and its region.
- After that, place a marker at B8. Column 2 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.
- Now, 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.
- Finally, place a marker at C2. Region has exactly one open cell left.
The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎