A Hard 8×8 Puzzle Solved with Forced Chain in 17 Steps
Play this board yourself →A
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This 8×8 board rates as hard (difficulty score 1097). Solving it from scratch takes 17 logical steps, using 6 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Paired regions, Forced chain. Every step below is forced: nothing here is a guess.
- First, together, two regions have open cells only in rows 7 and 8; with one marker each, those two markers have to fill exactly those two rows, so every other region's open cells there can be cleared.
- Next, 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.
- Then, 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.
- After that, place a marker at D4. Region has exactly one open cell left. Placing here clears the rest of row 4, column D, and its region. Placing here also clears its 2 touching neighbours.
- Now, marking A1 would force F7 (the last open cell in row 7), and then column E 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 E6 (the last open cell in region 6), then H5 (the last open cell in region 5), then G2 (the last open cell in region 3), 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 C1 it would force B8 cleared (every open cell in column A belongs to the same region, so that region's marker has to be somewhere in this column), then B6 (the last open cell in column B), then A8 (the last open cell in region 7), and column E would be left with no open cell for its marker.
- First, that one can't be the marker: at F1 it would force H5 (the last open cell in region 5), and region 3 would be left with no open cell for its marker.
- Next, marking G1 would force H3 (the last open cell in region 3), then F5 (the last open cell in region 5), then B6 (the last open cell in region 6), and then row 7 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 F5 (the last open cell in region 5), then G3 (the last open cell in region 2), then B6 (the last open cell in region 6), and row 7 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 E1. Row 1 has exactly one open cell left. Placing here clears the rest of row 1, column E, and its region.
- Now, place a marker at B6. Region has exactly one open cell left. Placing here clears the rest of row 6, column B, and its region. Placing here also clears its 1 touching neighbour.
- From there, place a marker at F7. Row 7 has exactly one open cell left. Placing here clears the rest of row 7, column F, and its region.
- Following that, 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.
- First, 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.
- Next, 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.
- Finally, place a marker at C8. Region has exactly one open cell left.
The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎