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 1319). 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 open cell left in this region sits in column A, so its marker has to land there; that clears every other open cell in the column.
- 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 remaining candidate in this region touches D7, 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 G7, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- Now, marking D1 would force C4, C5, C6, and 1 more cleared (every open cell in column B belongs to the same region, so that region's marker has to be somewhere in this column), then C8 (the last open cell in column C), then H2, H3, H4, and 1 more cleared (every open cell left in this region sits in column H, so its marker has to land there), and the chain continues, and then row 3 would be left with no open cell for its marker. So D1 can't be the marker there.
- From there, if E1 were the marker, it would force F4 and F8 cleared (every open cell left in this region sits in column F, so its marker has to land there), then A8, B8, G8, and 1 more cleared (every open cell left in this region sits in row 8, so its marker has to land there), then H2, H3, H4, and 1 more cleared (every open cell left in this region sits in column H, so its marker has to land there), and the chain continues, and row 3 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 F1 it would force E6, E7 and E8 cleared (every open cell left in this region sits in column E, so its marker has to land there), then A8, B8, G8, and 1 more cleared (every open cell left in this region sits in row 8, so its marker has to land there), then H2, H3, H4, and 1 more cleared (every open cell left in this region sits in column H, so its marker has to land there), and the chain continues, and row 3 would be left with no open cell for its marker.
- First, marking G1 would force B3, C3 and B4 cleared (every open cell in row 2 belongs to the same region, so that region's marker has to be somewhere in this row), then H3 (the last open cell in row 3), then F8 (the last open cell in region 8), and the chain continues, and then region 5 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 A8, B8, C8, and 2 more cleared (every open cell left in this region sits in row 8, so its marker has to land there), then E2, E3, E4, and 1 more cleared (every open cell left in this region sits in column E, so its marker has to land there), then F2, F3 and F8 cleared (every open cell left in this region sits in column F, so its marker has to land there), and the chain continues, and row 3 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 E2 would force H3 (the last open cell in row 3), then G8 (the last open cell in column G), and then region 7 would be left with no open cell for its marker. So E2 can't be the marker there.
- Now, if F2 were the marker, it would force H3 (the last open cell in row 3), then G8 (the last open cell in region 8), then E6 and E7 cleared (every open cell left in this region sits in column E, so its marker has to land there), and region 7 would end up with no open cell for its marker, which can't happen. So it can't go there.
- From there, that one can't be the marker: place it at G2, and row 3 would be left with no open cell for its marker.
- Following that, that one can't be the marker: at C1 it would force H2 (the last open cell in row 2), then G8 (the last open cell in column G), then E3, E4 and E5 cleared (every open cell left in this region sits in column E, so its marker has to land there), and the chain continues, and column B would be left with no open cell for its marker.
- First, place a marker at B1. Region has exactly one open cell left. Placing here clears the rest of row 1, column B, and its region.
- Next, marking H2 would force G8 (the last open cell in column G), then E3, E4 and E5 cleared (every open cell left in this region sits in column E, so its marker has to land there), then F3 cleared (every open cell left in this region sits in column F, so its marker has to land there), and the chain continues, and then row 4 would be left with no open cell for its marker. So H2 can't be the marker there.
- Then, place a marker at D2. Row 2 has exactly one open cell left. Placing here clears the rest of row 2, column D, and its region.
- After that, place a marker at H3. Row 3 has exactly one open cell left. Placing here clears the rest of row 3, column H, and its region.
- Now, place a marker at G8. Column 7 has exactly one open cell left. Placing here clears the rest of row 8, column G, and its region. Placing here also clears its 1 touching neighbour.
- From there, every open cell left in this region sits in column E, so its marker has to land there; that clears every other open cell in the column.
- Following that, place a marker at C4. Row 4 has exactly one open cell left. Placing here clears the rest of row 4, column C, and its region.
- First, place a marker at F5. Row 5 has exactly one open cell left. Placing here clears the rest of row 5, column F, and its region. Placing here also clears its 1 touching neighbour.
- Next, 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.
- Finally, place a marker at A6. Region has exactly one open cell left.
The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎