A Hard 8×8 Puzzle Solved with Forced Chain in 18 Steps
Play this board yourself →A
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This 8×8 board rates as hard (difficulty score 1049). Solving it from scratch takes 18 logical steps, using 7 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Paired regions, Shape squeeze, Forced chain. Every step below is forced: nothing here is a guess.
- First, together, two regions have open cells only in rows 1 and 2; 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, together, two regions have open cells only in rows 3 and 4; 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.
- Then, together, two regions have open cells only in columns A and B; with one marker each, those two markers have to fill exactly those two columns, so every other region's open cells there can be cleared.
- After that, 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.
- Now, together, two regions have open cells only in columns G and H; with one marker each, those two markers have to fill exactly those two columns, so every other region's open cells there can be cleared.
- From there, together, two regions have open cells only in columns E and F; with one marker each, those two markers have to fill exactly those two columns, so every other region's open cells there can be cleared.
- Following that, every remaining candidate in this region touches C6 and D6, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
- First, that one can't be the marker: place it at F1, and row 2 would be left with no open cell for its marker.
- Next, marking G1 would immediately leave row 2 with no open cell for its marker, so it can't be the marker there.
- Then, if H1 were the marker, it would force F2 (the last open cell in region 2), and column E 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 G2. Region has exactly one open cell left. Placing here clears the rest of row 2, column G, and its region. Placing here also clears its 1 touching neighbour.
- Now, 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.
- From there, 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.
- Following 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.
- First, place a marker at H6. Region has exactly one open cell left.
- Next, 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. Placing here also clears its 1 touching neighbour.
- Then, 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 C5. Region has exactly one open cell left.
The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎