A Hard 7×7 Puzzle Solved with Forced Chain in 16 Steps
Play this board yourself →A
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This 7×7 board rates as hard (difficulty score 1005). Solving it from scratch takes 16 logical steps, using 8 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Line confinement, Paired regions, 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 G, so its marker has to land there; that clears every other open cell in the column.
- Next, every open cell left in this region sits in column F, so its marker has to land there; that clears every other open cell in the column.
- Then, every remaining candidate in this region touches E2 and G2, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
- After that, 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. Placing here also clears its 1 touching neighbour.
- Now, 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.
- From there, together, two regions have open cells only in rows 2 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.
- Following that, every remaining candidate in this region touches D5, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- First, every remaining candidate in this region touches B6, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- Next, that one can't be the marker: at A2 it would force E4 (the last open cell in region 3), then D6 (the last open cell in region 6), and column C would be left with no open cell for its marker.
- Then, every open cell in column A 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.
- After that, marking B2 would force E4 (the last open cell in region 3), then D6 (the last open cell in region 6), and then column C would be left with no open cell for its marker. So B2 can't be the marker there.
- Now, 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 1 touching neighbour.
- From there, place a marker at C2. Region has exactly one open cell left. Placing here clears the rest of row 2, column C, and its region.
- Following that, place a marker at E6. Region has exactly one open cell left. Placing here clears the rest of row 6, column E, and its region.
- First, 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.
- Finally, place a marker at A5. Region has exactly one open cell left.
The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎