A Hard 7×7 Puzzle Solved with Forced Chain in 16 Steps
Play this board yourself →A
B
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6×
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7×
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This 7×7 board rates as hard (difficulty score 1004). Solving it from scratch takes 16 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 columns B and A; 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.
- Next, every open cell left in this region sits in row 1, 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 column C, so its marker has to land there; that clears every other open cell in the column.
- After that, place a marker at D1. Region has exactly one open cell left. Placing here clears the rest of row 1, column D, and its region. Placing here also clears its 2 touching neighbours.
- Now, every open cell left in this region sits in row 7, so its marker has to land there; that clears every other open cell in the row.
- From there, every remaining candidate in this region touches F3, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- Following that, every remaining candidate in this region touches B3, 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 E6 and F6, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
- Next, if F2 were the marker, it would force A3 (the last open cell in region 3), then C4 (the last open cell in region 4), and column B would end up with no open cell for its marker, which can't happen. So it can't go there.
- Then, that one can't be the marker: at G2 it would force A3 (the last open cell in region 3), and row 6 would be left with no open cell for its marker.
- After that, place a marker at B2. Row 2 has exactly one open cell left. Placing here clears the rest of row 2, column B, and its region. Placing here also clears its 1 touching neighbour.
- Now, place a marker at C4. Region has exactly one open cell left. Placing here clears the rest of row 4, column C, and its region.
- From there, place a marker at E3. Region has exactly one open cell left. Placing here clears the rest of row 3, column E, and its region.
- Following that, place a marker at F7. Region has exactly one open cell left. Placing here clears the rest of row 7, column F, and its region. Placing here also clears its 1 touching neighbour.
- First, place a marker at G5. Region has exactly one open cell left. Placing here clears the rest of row 5, column G, 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. ∎